Showing papers in "Archive of Applied Mechanics in 2019"
TL;DR: In this paper, a dynamic model of a rotor-bladed system is established considering the effect of nonlinear supports at both ends of the shaft and the blades, where the shaft is modeled as a rotating beam where the gyroscopic effect is considered, while the shear deformation is ignored.
Abstract: A dynamic model of a rotor-blade system is established considering the effect of nonlinear supports at both ends. In the proposed model, the shaft is modeled as a rotating beam where the gyroscopic effect is considered, while the shear deformation is ignored. The blades are modeled as Euler–Bernoulli beams where the centrifugal stiffening effect is considered. The equations of motion of the system are derived by Hamilton principle, and then, Coleman and complex transformations are adopted to obtain the reduced-order system. The nonlinear vibration and stability of the system are studied by multiple scales method. The influences of the normal rubbing force, friction coefficient, damping and support stiffness on the response of the rotor-blade system are investigated. The results show that the original hardening type of nonlinearity may be enhanced or transformed into softening type due to the positive or negative nonlinear stiffness terms of the bearing. Compared with the system with higher support stiffness, the damping of the bearing has a more powerful effect on the system stability under lower support stiffness. With the increase in rubbing force and support stiffness, the jump-down frequency, resonant peak and the frequency range in which the system has unstable responses increase.
73 citations
TL;DR: In this article, a reduced-order model is introduced by means of a bi-dimensional elastic surface accurately describing large deformations, which is characterized by an elastic energy density that involves second space derivatives of the displacement for capturing the resistance of twisted and bent fibers in plane as well as out of plane.
Abstract: Mechanical properties are investigated for a class of microstructured materials with promising applications. Specifically, we consider a composite material with orthogonal, mutually interconnected fibers building a pantographic substructure. In order to predict the behavior of such a system in three-dimensional continuum, a reduced-order model is introduced by means of a bi-dimensional elastic surface accurately describing large deformations. The properties of this reduced-order model are characterized by an elastic energy density that involves second space derivatives of the displacement for capturing the resistance of twisted and bent fibers in plane as well as out of plane. For determining the coefficients in the elastic energy of the reduced-order model, we utilize a numerical inverse analysis and make use of ad hoc computational experiments performed by a direct numerical simulation on the microscale with detailed modeling of the pantographic substructure. This reduced-order model represents a homogenized material on macro-scale with its substructure on microscale. The homogenized model is capable of describing materials response at a significantly less computational cost than the direct numerical simulations.
60 citations
TL;DR: In this article, the authors investigated the mechanical properties of samples of MS1 Maraging Steel (untreated and heat treated), which were produced by additive technology in various orientations in the working area of the building machine.
Abstract: The objective of this paper is to investigate the mechanical properties of samples of MS1 Maraging Steel (untreated and heat treated), which were produced by additive technology in various orientations in the working area of the building machine. MS1 steel (European 1.2709 and German X3NiCoMoTi 18-9-5) is well known for its high strength, high fracture toughness, good weldability, and dimensional stability during aging. The literature review, related to the mechanical properties and fracture of MS1 steel, found that there are no available studies of the effects of both building direction and heat treatment on the mechanical properties of MS1 steel. The authors decided to address this omission and present this entirely new research in this article. The uniaxial tensile tests to fracture were completed at two of the authors’ workplaces. The results were statistically assessed using Grubbs’ test for outliers, and then the data were processed using box plots to be easily comparable from the point of view of print direction, heat treatment, and the values declared by the metal powder producer or in the tables (for conventionally produced steel). Scanning electron microscopy was used to analyze the fracture surfaces obtained after tensile testing cylindrical samples. The results showed that there was an impact on the mechanical properties depending on the sample orientation within the same heat treatment type; there was also significant influence of heat treatment, while the possibility of the natural aging effect on mechanical properties was also noted.
52 citations
TL;DR: A recent survey of mesoscopic approaches to magnetic hybrid materials can be found in this article, where an overview of recent developments of mesoscale approaches is presented, including coarse-grained but efficient dipole-spring models, explicit analytical calculations using linear elasticity theory, numerical approaches that allow to characterize nonlinear effects, or density functional theory.
Abstract: Magnetic hybrid materials in the form of magnetic gels and elastomers, that is, magnetic or magnetizable colloidal particles embedded in an elastic polymer matrix, are fascinating substances. By addressing and adjusting the magnetic interactions between the particles through external magnetic fields, their overall material properties can be tuned reversibly while in operation. A central goal is to understand how these features can be optimized and which structural properties of the materials determine their overall behavior and its tunability. Mesoscopic theories and modeling are necessary for these purposes, resolving the arrangement of the embedded particles and linking it to the macroscopic scale of the overall material behavior. Here, we overview such recent developments of mesoscopic approaches. Particularly, we address coarse-grained but efficient dipole-spring models, explicit analytical calculations using linear elasticity theory, numerical approaches that allow to characterize nonlinear effects, or density functional theory. In this way, various properties and types of behavior of these materials are revealed, for instance, their reversible tunability of static and dynamic mechanical moduli by magnetic fields, elastic interactions between the embedded particles mediated through the polymeric matrix, or a pronounced and reversibly tunable nonlinear stress–strain behavior. Links from the mesoscopic to the micro- and macroscopic level are outlined. We mention combined efforts of theoretical descriptions, modeling, numerical simulations, and experimental investigations. It becomes evident from our treatment that an integrated approach of theory, simulations, and experiments will significantly increase our further understanding of these materials in the future and will draw possible applications into sight.
52 citations
TL;DR: In this paper, free vibration of a metal foam core sandwich (MFCS) beam embedded in Winkler-Pasternak elastic foundation is studied using the Chebyshev collocation method.
Abstract: In this paper, free vibration of a metal foam core sandwich (MFCS) beam embedded in Winkler–Pasternak elastic foundation is studied using the Chebyshev collocation method (CCM). This method can achieve high precision within the range allowed by the effective number of bits of computers. Three foam distribution types along the thickness direction are considered for the core. The Timoshenko beam theory is adopted and Hamilton’s principle is utilized to derive the boundary conditions and governing equations of the model. The numerical results show that natural frequencies of the sandwich beam initially increase and then decrease with the rise in thickness of metal foam core. By arranging the foam distribution in the core, natural frequencies of the sandwich beam can be significantly changed. Moreover, natural frequencies of the uniform foam distribution beam are insensitive to the foam coefficient. For the beam with non-uniform foam distribution, however, the natural frequencies increase or decrease with the foam coefficient, depending closely on the foam type. In addition, the present method is validated by comparing with the published ones for special cases.
44 citations
TL;DR: In this article, a magneto-active elastomeric composite based on a polydimethylsiloxane matrix highly filled with a mixed magnetic powder is presented, where the powder contains a mixture of carbonyl iron and magnetically hard NdFeB alloy spherical microparticles.
Abstract: This study focusses on a magnetoactive elastomeric composite based on a polydimethylsiloxane matrix highly filled with a mixed magnetic powder The powder contains a mixture of carbonyl iron and magnetically hard NdFeB alloy spherical microparticles Magnetoactive elastomer samples with different ratios of the magnetically hard and soft filler were synthesized and characterized using dynamic axial loading Behavior of the composites was compared with the behavior of a conventional magnetorheological elastomer based solely on magnetically soft particles It was found that the passive state and active state properties of the magnetoactive composites with mixed powders can be separately tuned The passive state properties may be changed by pre-magnetization of the magnetically hard particles influencing composite’s remanence, while the active state properties can be controlled by applying external magnetic field The range of passive tuning and active control depends on the amount of magnetically hard and soft components Using external fields up to 1500 mT for a pre-magnetization and fields up to 240 mT for investigation of the active control, it was found that the passive change of samples’ storage modulus and loss factor may reach up to $$\sim $$
30–100%, while within active control these parameters can be changed up to $$\sim $$
50–200%
43 citations
TL;DR: In this article, a quasi-zero stiffness (QZS) isolator is devised to acquire the feature of high-static-low-dynamic stiffness, where two horizontal dampers are installed symmetrically, to connect in parallel with a vertical spring.
Abstract: A quasi-zero stiffness (QZS) isolator is devised to acquire the feature of high-static-low-dynamic stiffness. Cam–roller–nonlinear spring mechanisms, where two horizontal dampers are installed symmetrically, are employed as a negative stiffness provider to connect in parallel with a vertical spring. From the static analysis, the piecewise restoring force in the vertical direction of the system is inferred considering possible separation between the cam and roller. The stiffness characteristics and parameters for offering zero stiffness at the equilibrium position are then determined. The dynamic equation is established and used for the deduction of the amplitude–frequency equation by means of the Harmonic Balance Method. The definitions of force and displacement transmissibility are introduced, and their expressions are derived for subsequent investigations of the effects of horizontal spring’s nonlinearity, excitation amplitude, horizontal damping, and vertical damping on the transmissibility performance. The comparative study is implemented on the isolation performance afforded by the QZS isolator and an equivalent linear counterpart, whose static bearing stiffness is same as the QZS isolator. Results indicate that the system with softening nonlinear horizontal spring can exhibit better performance than that with opposite stiffness spring. With the increase in horizontal damping ratio, the force transmissibility is further suppressed in resonance frequency range but increased in a small segment of higher frequencies and tends to unite in high frequency range. However, the horizontal damper deteriorates the ability to isolate the displacement excitation to a certain extent. Besides, the isolation capability of the QZS system depends on the magnitude of excitation amplitude. The quasi-zero stiffness system possesses lower initial isolation frequency and better isolation ability around resonance frequency compared with the linear system. Therefore, the quasi-zero stiffness isolator has superior low-frequency ability in isolating vibration over its linear counterpart.
43 citations
TL;DR: In this paper, the first bending eigenfrequency of MSE beams depends strongly on the strength of an applied magnetic field, and the dependence of the amplification ratio on the excitation frequency is compared with the result provided by the theoretical model.
Abstract: The development of actuator and sensor systems with complex adaptive behavior and operating sensitivity is one of the actual scientific challenges. Smart materials like magneto-sensitive elastomers (MSEs) offer great potential for designing such intelligent devices, because they possess unique magnetic-field-dependent properties. The present paper deals with investigations of the free and forced vibrational behavior displayed by cantilever beams of MSEs containing magnetically soft particles in a uniform magnetic field. It is shown experimentally as well as theoretically that the first bending eigenfrequency of MSE beams depends strongly on the strength of an applied magnetic field. The proposed magneto-mechanical model is based on the vibrational dynamics of thin rods and predicts reliably the amplitude–frequency characteristics depending on the geometric configuration of the MSE and its material parameters. It is found that the vibration response of an MSE beam under kinematic excitation of its base can be modified indirectly by a magnetic field control due to the change of the vibration characteristics. As a result, the resonance can occur in different ranges of the excitation frequency. The dependencies of the amplification ratio on the excitation frequency are obtained experimentally and compared with the result provided by the theoretical model. Moreover, investigations on the potential use of the field-induced plasticity effect of MSEs in form-fit gripper applications are presented. This effect can be used to realize shape adaptable system parts. It is found that the mechanical properties of each component and its concentration within the mixture have an impact on the mechanical behavior of the whole MSE compound. Such parameters as the strength of magnetic field and geometry of the MSE sample have influence on the quality of shape adaptation. The evidence presented provides a good basis for the realization of MSE-based actuator and sensor systems with adaptable sensitivity.
41 citations
TL;DR: In this paper, the magnetostriction effect in soft magnetic elastomers is discussed, which is defined by the structure of short-range spatial order existing in the ferromagnet particle assembly.
Abstract: We discuss the magnetostriction effect in soft magnetic elastomers: stretching/shrinking of a sample under the action of uniform magnetic field in the absence of mechanical loads. Qualitative analysis shows that the field has a twofold effect on the medium; one of those mechanisms works at the macroscopic scale whereas the other one stems from the mesoscopic processes. Essentially, the latter one is defined by the “architecture” of short-range spatial order existing in the ferromagnet particle assembly. This conclusion is illustrated with the aid of numerical modeling. First, it is done on a 2D elastic array filled with linearly magnetizable particles. It is shown that it is indeed the presence of clusters that controls both the sign and magnitude of magnetostriction in the composite. In other words, two composites with the same matrix/filler content may behave very differently depending on their mesoscale structure. Further on, to get a more realistic description, the modeling is extended to a 3D array of spherical particles randomly distributed in an elastic matrix. Although the general conclusions hold, the quantitative results differ substantially.
32 citations
TL;DR: In this article, the shape and the microstructure of a lattice are optimized in order to achieve isolation of the desired frequencies, and a first attempt on the optimization of star-shaped microstructures is also presented.
Abstract: A band gap region, or simply a band gap, is a range of frequencies where vibrations of certain frequency ranges are isolated. In the present paper, such ranges are sought through the study of different cases for the shape of the unit cells of a lattice, i.e., of an assembly of classical structural elements, such as beams and plates. A lattice with a specific, special designed microstructure is considered in the present investigation. Each particular cell of the examined lattice is studied as a classical composite material consisting of a matrix and the reinforcing core (e.g., matrix-fiber composite), and it is discretized by using two-dimensional plane stress finite elements. The form of the core of the unit cells can be of several shapes, e.g., quadratic, circular, and star. Some of these shapes provide the whole lattice with auxetic behavior, with negative Poisson’s ratio at the homogenized properties. The shape and the microstructure of the lattice is optimized in order to achieve isolation of the desired frequencies. A first attempt on the optimization of star-shaped microstructures is also presented. The optimization is carried out using powerful global optimization methods, such as the genetic algorithms. Results indicate that band gaps may appear in both conventional and auxetic microstructures. Moreover, the appearance and the size of the band gaps depend on the selected microstructure.
32 citations
TL;DR: In this article, a review of various nonlocal beam and shell theories incorporating Eringen's nonlocal elasticity theory and the application of strong-and weak-form-based formulations to the current issue is presented.
Abstract: This article is intended to present an overview of various mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled (SW-, DW-, and MW-) carbon nanotubes (CNTs) with combinations of simply supported, free, and clamped edge conditions embedded or non-embedded in an elastic medium, including bending, free vibration, buckling, coupled thermo-elastic and hygro-thermo-elastic, dynamic instability, wave propagation, geometric nonlinear bending, and large amplitude vibration analyses. This review introduces the development of various nonlocal beam and shell theories incorporating Eringen’s nonlocal elasticity theory and the application of strong- and weak-form-based formulations to the current issue. Based on the principle of virtual displacements and Reissner’s mixed variational theorem, the corresponding strong- and weak-form formulations of the local Timoshenko beam theory are reformulated for the free vibration analysis of rectangular nanobeams and SW-, DW-, and MW-CNTs, and presented for illustrative purposes. A comparative study of the results obtained using assorted nonlocal beam and shell theories in combination with the analytical and numerical methods is carried out.
TL;DR: In this paper, a crack model based on nonlinear fracture mechanics was applied to investigate the development of strain softening of tensile concrete in plain concrete and slightly reinforced concrete beams.
Abstract: In this paper the analysis of failure and crack development in beams made of concrete is presented. The analysis was carried out on the basis of the performed experimental investigation and numerical simulations. A fictitious crack model based on nonlinear fracture mechanics was applied to investigate the development of strain softening of tensile concrete in plain concrete and slightly reinforced concrete beams. The role of strain softening was also discussed according to the inclined crack propagation in highly reinforced concrete beams. The analysis has brought the evidence that the mode of failure in flexural beams varies according to a longitudinal reinforcement ratio. A brittle failure due to the formation of a flexural crack takes place in plain and slightly reinforced concrete beams, and strain softening of tensile concrete is of paramount importance at failure crack initiation and propagation. A stable growth of numerous flexural cracks is possible in moderately reinforced concrete beams, and then the load carrying capacity is connected with reaching the yield stress of reinforcing steel or concrete crushing in the compression zone. In higher reinforced concrete beams without transverse reinforcement, brittle failure can take place due to shear forces and the development of diagonal cracks. However, strain softening of tensile concrete is not the only mechanism influencing the propagation of an inclined crack. Such mechanisms as aggregate interlock and dowel action of steel bars contribute more importantly to the development of failure crack.
TL;DR: The problem of the determination of an effective feedforward controller for reducing the pantograph/catenary contact force is formulated in this work as a nonlinear optimal control problem and the solution of the control optimization problem is carried out by using an adjoint-based computational procedure.
Abstract: In this paper, a closed-chain multibody model of a pantograph/catenary system is developed and used for the optimal design of a nonlinear controller based on an open-loop control architecture. The goal of the nonlinear controller is the reduction of the contact force arising from the pantograph/catenary interaction and, at the same time, the suppression of the mechanical vibrations of the pantograph mechanism. The analytical formulation employed in this paper for describing the nonlinear dynamics of the pantograph/catenary multibody system considers a Lagrangian approach and is based on a redundant set of generalized coordinates. The contact forces generated by the pantograph/catenary interaction are modeled in this work employing an elastic force element collocated between the pantograph pan-head and a moving support. The external support follows a prescribed motion law that simulates the periodic deployment of the catenary system. On the other hand, in this investigation, the algebraic constraints arising from the closed-loop topology of the pantograph multibody system are enforced employing a method based on the Udwadia–Kalaba equations recently developed in the field of analytical dynamics. Furthermore, the problem of the determination of an effective feedforward controller for reducing the pantograph/catenary contact force is formulated in this work as a nonlinear optimal control problem. For this purpose, the solution of the control optimization problem is carried out by using an adjoint-based computational procedure. Numerical simulations demonstrate the effectiveness of the nonlinear controller obtained in this investigation for the pantograph/catenary multibody system.
TL;DR: In this article, the authors focus on the different mechanisms by which ferrogels can deform in an external magnetic field and show how these mechanisms can be captured by particle-based simulations.
Abstract: Ferrogels are soft elastic materials into which magnetic particles are embedded. The resulting interplay between elastic and magnetic interactions and the materials’ response to external fields makes them promising candidates for applications such as actuation and drug delivery. In this article, after providing a very brief introduction to particle-based simulation methods, we give an overview on how they can be applied to magnetic gels. We focus on the different mechanisms by which ferrogels can deform in an external magnetic field. Based on examples from our previous work, we show how these mechanisms can be captured by particle-based simulations. Lastly, we provide some links to simulation techniques on larger length scales.
TL;DR: It is shown in this investigation that the same analytical methods can be used for effectively solving both the forward and the inverse dynamic problems relative to underactuated mechanical systems subjected to a general set of holonomic and/or nonholonomic algebraic constraint equations.
Abstract: This paper deals with the dynamics and control of underactuated nonholonomic mechanical systems. It is shown in this investigation that the same analytical methods can be used for effectively solving both the forward and the inverse dynamic problems relative to underactuated mechanical systems subjected to a general set of holonomic and/or nonholonomic algebraic constraint equations. The approach developed in this work is based on the combination of two fundamental methods of analytical dynamics, namely the Udwadia–Kalaba equations and the Underactuation Equivalence Principle. While the Udwadia–Kalaba equations represent a fundamental mathematical tool of classical mechanics, the Underactuation Equivalence Principle is a new method recently discovered in the field of analytical dynamics and is associated with nonholonomic mechanical systems. In the paper, these two important analytical methods are discussed in detail. Furthermore, numerical experiments are performed in this investigation in order to demonstrate the effectiveness of the proposed approach considering as an illustrative example of a dynamic model a mobile robot.
TL;DR: In this paper, the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing were investigated, and the motion equations of the system were formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities.
Abstract: This paper focuses on the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing. The motion equations of the system are formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the dual-rotor system. Accordingly, complex nonlinearities affected by the bearing radical clearance, the vertical constant force and the rotating speed ratio are discussed in detail. The jump phenomenon, hard resonant hysteresis characteristics are shown for a relatively large bearing clearance, and the soft resonant hysteresis characteristics can be observed for a relatively large vertical constant force. Moreover, the super-harmonic frequency components and the combined frequency components caused by the inter-shaft bearing are observed for both rotors. But the corresponding frequency components for the low-pressure rotor are more complex than that for the high-pressure rotor in same condition. These results would be helpful to recognize the nonlinear dynamic characteristics of dual-rotor bearing system.
TL;DR: In this article, damage propagation in brittle elastic beam lattices, using the quasistatic approach, is studied and compared under various criteria of the elimination of the overstressed beams.
Abstract: The paper studies damage propagation in brittle elastic beam lattices, using the quasistatic approach. The lattice is subjected to a remote tensile loading; the beams in the lattice are bent and stretched. An introduced initial flaw in a stressed lattice causes an overstress of neighboring beams. When one of the overstressed beams fails, it is eliminated from the lattice; then, the process repeats. When several beams are overstressed, one has to choose which beam to eliminate. The paper studies and compares damage propagation under various criteria of the elimination of the overstressed beams. These criteria account for the stress level, randomness of beams properties, and decay of strength due to micro-damage accumulation during the loading history. A numerical study is performed using discrete Fourier transform approach. We compare damage patterns in triangular stretch-dominated and hexagonal bending-dominated lattices. We discuss quantitative characterization of the damage pattern for different criteria. We find that the randomness in the beam stiffness increases fault tolerance, and we outline conditions restricting the most dangerous straight linear crack-like pattern.
TL;DR: In this article, a rational design of an isotropic heterogeneous beam lattice that is fault-tolerant and energy-absorbing is presented, combining triangular and hexagonal structures.
Abstract: The paper demonstrates a rational design of an isotropic heterogeneous beam lattice that is fault-tolerant and energy-absorbing. Combining triangular and hexagonal structures, we calculate elastic moduli of obtained hybrid heterogeneous structures; simulate the development of flaws in that composite lattice subjected to a uniform uniaxial deformation; investigate its damage evolution; measure various characteristics of damage that estimate fault tolerance; discuss the trade-off between stiffness and fault tolerance. A design is found that develops a cloud of small evenly spread flaws instead of a crack.
TL;DR: It can be concluded that the presented robot design can be a basis for the creation of mobile robotic systems with locomotion properties that can be controlled by the parameters of a periodic actuation force.
Abstract: Non-classical locomotion systems have the perspective for a wide application in the vast fields of bio-medical and maintenance technology. Capsule bots are small, simple, and reliable realizations with a great potential for practical application. In this paper, the motion of a capsule-type mobile robot along a straight line on a rough horizontal plane is studied applying analytical and experimental methods. The robot consists of a housing and an internal body attached to the housing by a spring. The motion of the system is generated by a force that acts between the housing and the internal body and changes periodically in a pulse-width mode. The average velocity of the motion of the robot is studied as a function of the excitation parameters. The results from the model-based and experimental investigations agree with each other. It can be concluded that the presented robot design can be a basis for the creation of mobile robotic systems with locomotion properties that can be controlled by the parameters of a periodic actuation force.
TL;DR: In this paper, a qualitative and quantitative comparison of two-and three-dimensional finite-element simulations for magneto-rheological elastomers is presented, based on a general continuum formulation of the coupled magnetomechanical boundary value problem.
Abstract: In this contribution, we present a qualitative and quantitative comparison of two- and three-dimensional finite-element simulations for magneto-rheological elastomers. Based on a general continuum formulation of the coupled magneto-mechanical boundary value problem, a microscopic modeling approach is applied. The merit of this strategy is a full resolution of the local magnetic and mechanical fields within the heterogeneous microstructure of magneto-rheological elastomers—it allows to account for systems with high particle-volume fractions and small inter-particle distances. In order to understand basic deformation mechanisms as well as local magneto-mechanical interactions of the spherical inclusions, the differences between simplified two-dimensional and realistic three-dimensional simulations are initially shown for the example of chain-like structures with varying arrangements of the particles. Afterwards, an appropriate scale transition scheme is used to connect the microscopic and macroscopic quantities: Different two- and three-dimensional, ideal and random microstructures are analyzed with regard to their effective magneto-mechanical behavior.
TL;DR: In this article, the nonlinear vibrations of asymmetric vertically supported Jeffcott rotor system were investigated and an analytical approximate solution for the considered system model in the primary resonance case was obtained.
Abstract: This article investigates the nonlinear vibrations of asymmetric vertically supported Jeffcott rotor system. Asymmetry in both linear and nonlinear stiffness coefficients of the rotating shaft is considered. The disk eccentricity and its orientation angle are included in the system model. Asymptotic analysis is sought to obtain an analytical approximate solution for the considered system model in the primary resonance case. Bifurcation diagrams for the different system parameters are obtained to explore the system steady-state lateral vibrations. The main acquired results revealed that (1) the symmetric system can oscillate by one of three stable forward whirling amplitudes at the same rotational speed depending on the initial position of the rotating disk. (2) Asymmetry in the linear stiffness coefficient does not affect the symmetry of the whirling motion, but it may change the system natural frequency. (3) Asymmetry in the nonlinear stiffness coefficient is responsible for both asymmetrical and backward whirling motions. All obtained analytical results have been verified via solving the system original equations numerically, where the analytical and numerical results are in excellent agreement.
TL;DR: In this paper, the performance of a bimorph cantilever energy harvester subjected to horizontal and vertical excitations is investigated and the results reveal that the bending deformation generated by direct excitation pushes the system out of axial deformation and overcomes the limitation of initial threshold of parametric excitation system.
Abstract: The performance of bimorph cantilever energy harvester subjected to horizontal and vertical excitations is investigated. The energy harvester is simulated as an inextensible piezoelectric beam with the Euler–Bernoulli assumptions. A horizontal base excitation along the axis of the beam is converted into the parametric excitation. The governing equations include geometric, inertia and electromechanical coupling nonlinearities. Using the Galerkin method, the electromechanical coupling Mathieu–Duffing equation is developed. Analytical solutions of the frequency response curves are presented by using the method of multiple scales. Some analytical results are obtained, which reveal the influence of different parameters such as the damping, load resistance and excitation amplitude on the output power of the energy harvester. In the case of parametric excitation, the effect of mechanical damping and load resistance on the initiation excitation threshold is studied. In the case of combination of parametric and direct excitations, the dynamic characteristics and performance of the nonlinear piezoelectric energy harvesters are studied. Our studies revealed that the bending deformation generated by direct excitation pushes the system out of axial deformation and overcomes the limitation of initial threshold of parametric excitation system. The combination of parametric and direct excitations, which compensates and complements each other, can be served as a better solution which enhances performance of energy harvesters.
TL;DR: In this paper, the authors investigated the safety level of arches by suitably reworking in semi-analytical form the graphical method of the stability area proposed by the renowned nineteenth century French scholar, Durand-Claye.
Abstract: This paper addresses the problem of characterizing the mechanical behaviour and collapse of symmetric circular and pointed masonry arches subject to their own weight. The influence on the arch’s collapse features of its shape and thickness, as well as the friction between the arch’s voussoirs, is analysed. The safety level of arches is then investigated by suitably reworking in semi-analytical form the graphical method of the stability area proposed by the renowned nineteenth century French scholar, Durand-Claye. According to Durand-Claye’s method, the arch is safe if along any given joint both the bending moment and shear force do not exceed the values determined by some given limit condition. The equilibrium conditions corresponding to all possible symmetric collapse modes are individuated. As was expected, pointed and circular arches exhibit different collapse behaviours, in terms of both collapse modes and safe domain. The limit values of arch thickness and friction coefficient are determined and the results obtained consistently compared with those published by Michon in 1857.
TL;DR: In this article, the free vibration of a flat plate with a side crack of Mode I fracture, reinforced by one stiffener parallel to the edges of the plate, is modeled separately and jointed by implementing the condition for compatibility of displacement.
Abstract: The free vibration of a flat plate with a side crack of Mode I fracture, reinforced by one stiffener parallel to the edges of the plate, is studied in this paper. Based on the classical theories of plate and beam, the plate and its stiffener are modeled separately and jointed by implementing the condition for compatibility of displacement. To describe the singularity in stress at the tip of the crack and the discontinuity in displacement across the crack, a set of functions are introduced and incorporated into the admissible functions of the displacement. The effects of location, length and orientation of side cracks on the vibration frequencies and mode shapes of the stiffened plate are demonstrated through the Ritz method with the special admissible functions. The natural frequencies of the intact and cracked stiffened plates with different stiffener locations are analyzed with two typical boundary conditions, i.e., SSSS and FSFS. The accuracy of the present solutions is verified through a convergence test. The solutions are compared with the finite element results as well.
TL;DR: In this article, the theoretical and numerical framework for the description of geomechanical and biomechanical problems including elastic, elasto-plastic and visco-elastic solid behaviour partly combined with electroactive properties is presented.
Abstract: Continuum mechanics usually considers the theoretical and computational description of standard single-phasic materials in the framework of either solid mechanics, fluid mechanics or gas dynamics. However, growing complexity in material modelling combined with the request of users leads to a growing interest in porous-media mechanics, where porous solid materials with fluid or gaseous pore content are investigated on a macroscopic scale. In this regard, the present article reviews the theoretical and numerical framework for the description of geomechanical and biomechanical problems including elastic, elasto-plastic and visco-elastic solid behaviour partly combined with electro-active properties. For this purpose, the Theory of Porous Media is applied for an elegant consideration of the coupling phenomena of porous solids with pore fluids, no matter if the fluids have to be treated as inert fluids or as fluid mixtures. In the sense of a review article, different computational examples are presented to illuminate the possibilities and challenges of porous-media mechanics.
TL;DR: In this paper, the mean stress effect in multiaxial criteria for fatigue limit estimation, with special emphasis on the mean shear stress effect, was evaluated on a large data set of 407 fatigue limits and two critical plane criteria, PCr (Papuga Criterion) and QCP (Quadratic parameter on the Critical Plane), were described, and additional local stress parameters representing the mean torsion effect were implemented.
Abstract: The paper deals with evaluating the mean stress effect in multiaxial criteria for fatigue limit estimation, with special emphasis on the mean shear stress effect. The usual practice of accepting the mean normal stress effect and neglecting the effect of static torsion is scrutinized. Two methods—two critical plane criteria, PCr (Papuga Criterion) and QCP (Quadratic parameter on the Critical Plane)—are described, and additional local stress parameters representing the mean torsion effect are implemented. The efficiency of the new implementations is evaluated on a large data set of 407 fatigue limits. Additionally, outputs of two other well-known methods—the Crossland method and the Dang Van method—are provided for comparison. The positive outcome of including the mean shear stress effect is evident not only in cases of applied mean torsion load, but also in cases with purely axial loading or with biaxial configurations.
TL;DR: In this article, the authors outline the required techniques for micro-and macroscopic investigations of magnetic hybrid materials and highlight the possibilities given by such an approach with a couple of examples.
Abstract: Magnetic hybrid materials, i.e. materials containing magnetic particles as magnetoactive component in a non-magnetic matrix, can be controlled concerning their properties by means of moderate magnetic fields. The magnetic field-driven change in their properties is a result of the complex interaction of the magnetic particles and—in case of elastomers used as non-magnetic matrix—of the interaction of the particles with the surrounding matrix. These complex interactions are the major problem to achieve an understanding of magnetic hybrid materials on a level allowing tailored material production for certain application purposes. Such an understanding requires a scale bridging description of the material behaviour and of the resulting magnetically induced effects. In this context, the term scale bridging means that it is necessary to couple changes in the internal structure of a magnetic hybrid material, i.e. effects taking place on the scale of the magnetic particles, with macroscopic changes in its properties. Such a scale bridging understanding can not only be achieved on theoretical level. The complexity of the interparticle interaction and of the interaction of the particles with matrix as well as the vice versa coupling of both kind of interactions requires experimental data as input for theoretical approaches: moreover, such data provide a benchmark for respective predictions. Coupling magnetomechanical investigations on the macroscale with microscopic characterization using X-ray microtomography as a tool for a detailed visualization of the microstructure provides the required experimental approach to a scale bridging description of such smart materials. Within this paper, we will outline the required techniques for micro-and macroscopic investigations and will highlight the possibilities given by such an approach with a couple of examples.
TL;DR: In this article, a dynamic model of the rotor-bearing system with bolted joint structure is set up based on the Lagrange's equations, which considers the bearing clearance, the gyroscopic effect and the initial deformation due to the non-uniform preload.
Abstract: A dynamic model of the rotor-bearing system with bolted joint structure is set up based on the Lagrange’s equations, which considers the bearing clearance, the gyroscopic effect and the initial deformation due to the non-uniform preload. The nonlinear dynamic responses of the system were obtained by using the Runge–Kutta–Fehlberg method, and then the influence of the radial bearing clearance on the nonlinear dynamic behaviors of the rotor system is studied by means of bifurcation diagram, frequency spectrum, shaft orbits and Poincare maps. The results indicate that the larger bearing clearance will make the system enter into chaotic motion at a lower rotating speed. In addition, with the increase in bearing clearance, the duration of the chaotic motion becomes longer. Furthermore, the influence of initial deformation on the stability of the bolted joint rotor system with bearing clearance is studied. The results show that when the bearing clearance is present, the instability speed of the rotor system will gradually rise with the increase in initial deformation. Meanwhile, as the bearing clearance continuously increases, the regions of the chaotic motion become less and smaller, and the motion state should be completely changed under certain initial deformation. The related results can provide guidance for the optimization and design of the bolted joint rotor-bearing system.
TL;DR: In this paper, the electromechanical equation of motion for a galloping-based energy harvesting system is derived and experimentally validated, which consists of a bluff body that elastically mounted in fluid flow and a piezoelectric energy harvesting device, which is placed inside it.
Abstract: In this study, the electromechanical equation of motion for a galloping-based energy harvesting system is derived and experimentally validated. This system consists of a bluff body that elastically mounted in fluid flow and a piezoelectric energy harvesting device, which is placed inside it. To confirm dynamic behavior of the system in fluid flow, periodic response of the variables is analytically obtained by employing the harmonic balance method. The validated equations are used to study effect of changing the system parameters on electromechanical behavior of the energy harvester. Then, application of the system is investigated in a realistic condition. Employing several user-oriented charts, the energy harvesting system is optimized and it is shown that this system can optimally be used in normal wind speed.
TL;DR: In this paper, the authors proposed a new constitutive model for shape memory polymers and polymeric composites under the use of level-set functions as additional variables of state, which can describe the interface separating the two distinct phases in an implicit manner.
Abstract: This work proposes a new constitutive model for shape memory polymers and shape memory polymeric composites under the use of level-set functions as additional variables of state. The model regards shape memory polymers as inhomogeneous bodies consisting of two different phases, an active (rubbery elastic) phase and a frozen (glassy elastic) phase. Introducing the level-set function provides the potential to describe the interface separating the two distinct phases in an implicit manner. Under proper thermodynamical arguments, an appropriate evolution equation is derived that provides the tool to describe phase transformations in shape memory polymers. Furthermore, an extended model version is developed that applies in shape memory polymeric composites by introducing two (or more) level-set functions so as to represent implicitly three (or more) material phases capturing the behavior of multi-shape memory polymers. The level-set constitutive equations are formulated in three dimensions, although the one-dimensional case is adopted and analyzed thoroughly. The reproduction of the shape memory thermomechanical cycles of polymers and polymeric composites provides validity and credibility to the current model.