Showing papers in "Archive of Applied Mechanics in 2020"

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

Abstract: Nonlocal strain gradient continuum mechanics is a methodology widely employed in the literature to assess size effects in nano-structures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional-free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviors of structures involved in modern nano-electro-mechanical systems.

Effects of velocity second slip model and induced magnetic field on peristaltic transport of non-Newtonian fluid in the presence of double-diffusivity convection in nanofluids

Abstract: The significance of velocity second slip model of non-Newtonian fluid on peristaltic pumping in existence of double-diffusivity convection in nanofluids and induced magnetic field is deliberated. Mathematical modelling of current problem is defined in fixed frame of reference and then abridges under well- known conjecture of long wavelength and low but finite Reynolds number approximation. Precise results of coupled nonlinear partial differential equations are presented. Graphical results exhibit the performance of various supportive parameters. The phenomenon of stream functions with different wave forms is also discussed in detail. The effects of thermal energy, solute concentration, and nanoparticle fraction are also described using graphical representation.

Numerical analysis of cooling and joining speed effects on friction stir welding by smoothed particle hydrodynamics (SPH)

Abstract: This current work considers the utilization of the completely Lagrangian technique, smoothed particle hydrodynamics to improve the 3D finite element model for numerical analysis of the friction stir welding (FSW) in the air and underwater conditions. This technique was primarily applied to simulate fluid motion because of various advantages compared to conventionally grid-based methods. Newly, its usage has been developed to analyze the metal-forming analysis. The temperature history, strain and stress distributions during the FSW process in the air, as well as underwater, were considered. Besides the cooling influence, the effect of traveling speed, friction coefficient, mesh size and the mass scaling technique to find the converged model and decrease the CPU time were studied. The improved model is confirmed by comparing the numerical welding temperature with experimental outcomes. There was close compatibility between finite element analysis and experimental results. The conclusions indicated that the lower peak temperature was achieved due to higher cooling effect in underwater welding in comparison with conventional welding. Moreover, the peak temperature and strain rate decreased as traveling speed increased for both welding conditions, while stress values increased.

Free vibration of joined cylindrical–hemispherical FGM shells

Abstract: Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature method. Considering the clamped and free boundary conditions for the end of the cylindrical shell and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies of the joined shell. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick cylindrical–spherical shell system. Novel results are provided for the case of FGM joined shells to explore the influence of power-law index and geometric properties.

Rotary-impact nonlinear energy sink for shock mitigation: analytical and numerical investigations

Abstract: The nonlinear energy sink (NES) is a lightweight, strongly nonlinear dynamical attachment coupled to a (typically linear) large-scale primary structure for passive vibration mitigation. There are two nonlinear mechanisms governing the dynamics of the coupled system: irreversible targeted energy transfer (TET) from the primary structure to the NES, where energy is confined and locally dissipated, and NES-induced nonlinear energy scattering between the structural modes of the primary structure. In the literature, different NES designs have been investigated to optimize their nonlinear effects on the primary structures. One such design is the rotary NES consisting of a small mass inertially coupled to the primary structure through a rigid arm; another is the vibro-impact NES with non-smooth nonlinearities and inelastic collisions with the primary structure. These types have been found to achieve strong and rapid TET and are less sensitive to energy fluctuations. In this work, a hybrid NES design is proposed based on the synergetic synthesis of the rotary and impact-based NESs in a single rotary-impact NES (RINES). The RINES incorporates a fixed rigid barrier attached (typically) to the top floor of the primary structure to inflict impacts between its rotating mass and the top floor. An analytical study to evaluate its capacity to engage in resonance capture with a primary structure is presented first, followed by numerical investigations of cases when the RINES is attached to the top floors of small- and large-scale linear primary structures under impulsive excitation. The non-smooth nonlinearities induced through the consecutive impacts resulted in effective broadband shock mitigation at highly energetic response regimes, whereas the nonlinear inertial coupling enables similar beneficial mitigation capacity at lower-energetic response regimes. Hence, the combined effect of non-smooth and inertial nonlinearities enables effective passive mitigation capacity for a broad range of applied impulsive energies.

Modelling and analysis of a cracked rotor: a review of the literature and its implications

Abstract: Timely detection of fatigue cracks is necessary to avoid catastrophic failure of rotating machines which can lead to economical losses and accidental risk. This paper presents an exhaustive literature survey on theoretical and experimental vibration analysis of the rotating shaft in the presence of crack. Various non-destructive methods adopted by several researchers for crack detection in rotating machinery have been discussed. The vibration-based crack detection methods such as vibration-based diagnostics methods and vibration-based signal processing techniques have been broadly categorized along with their advantages and disadvantages. In general, various methodologies such as breathing mechanism, finite-element method, Hilbert–Huang transform, artificial intelligence techniques, wavelet transform and wavelet finite-element transform have been applied to investigate the presence of crack in the rotating shaft. The parameters such as natural frequencies, $$1{\times }$$, $$2{\times }$$ and $$3{\times }$$ harmonic components of dynamic response, critical speeds and whirl orbits have been significantly influenced due to the presence of crack in the rotating shaft. Several studies have been carried out to study variations in these parameters. Still, there is a need of more reliable and accurate modelling approach to detect variations in these parameters. In this paper, an attempt has been made to deliver all the modelling approaches implemented by the various researchers to detect crack within the rotating shaft. The modelling approaches are categorized based on the methodologies adopted by the various researchers to detect crack. Moreover, the critical observations made from the proposed modelling approaches are summarized and presented.

Vibration of carbon nanotube-reinforced plates via refined nth-higher-order theory

Abstract: This article presents the free vibration frequencies of composite plates reinforced with single-walled carbon nanotubes by using a refined simplified two-variable nth-higher-order theory. Four kinds of distribution of uniaxially aligned reinforcement material are presented. The most famous one is the uniform; in addition, three types of functionally graded distributions of carbon nanotubes in the through-thickness direction of the plates are investigated. The effective physical properties of composite media are given according to a refined rule of mixtures approach that contains the efficiency parameters. Exact closed-form formulation based on a refined simplified two-variable nth-higher-order plate theory that can be adapted to the vibration of such plates is investigated. Accuracy of presented approach is validated by comparing its results with those given by other investigators

Nonlinear thermo-electromechanical vibration analysis of size-dependent functionally graded flexoelectric nano-plate exposed magnetic field

Abstract: In the present study, a continuous-based thermo-electromechanic model has been developed by the Kirchhoff plate’s theory and the modified flexoelectric theory in order to study the size-dependent nonlinear free vibration of functionally graded flexoelectric nano-plate under the magnetic field. Using the Hamilton’s principle and variation method, the nonlinear governing differential equations of the nano-plate and their associated boundary conditions have been extracted and the governing equations solved by using Galerkin’s and perturbation methods. The electromechanical coupling (electromechanical stress) in the internal energy function causes nonlinearity in the governing equations. The applied magnetic field is a type of external static field along with the nano-plate thickness. The natural frequencies and related mode shapes have been determined in two modes of direct and inverse flexoelectric effects. Also, the effects of such factors as length scale parameters, geometric parameters, thermal, magnetic and electrical loadings were investigated. In the presence of flexoelectric effect, the results showed that the dependence of electromechanical behavior of the structure on size is found to be significant in nanoscales. Regarding the application of this type of nano-plate in the oscillators and considering the flexoelectric effect, the applied potential difference can play an important role in adjusting and controlling the frequency.

A review of friction damping modeling and testing

Abstract: This survey provides an insight into the modeling and testing of uniaxial friction dampers. The focus is on attenuating the linear relative movement along planar surfaces for frequencies between 10 Hz and 1 kHz. An overview of the different approaches seen in the literature concerning friction damping is provided. Examples and evaluation of such dampers excited over a wide range of frequencies are presented. The information required to develop models of friction dampers is covered. To that end, different modeling approaches are presented for dry friction. Dynamic friction models with an internal state are covered, and their advantages are described. Other modeling approaches are reported for complete systems with friction dampers. Both numerical and analytical models are covered. Experimental configurations from a selection of authors are also included. Finally, a series of suggestions for the numerical modeling and experimental testing of a friction damper are given.

Thermal and thermomechanical buckling of shear deformable FG-CNTRC cylindrical shells and toroidal shell segments with tangentially restrained edges

Abstract: This paper presents a simple and effective analytical approach to investigate buckling behavior of carbon nanotube-reinforced composite (CNTRC) cylindrical shells and toroidal shell segments surrounded by elastic media and subjected to elevated temperature, lateral pressure and thermomechanical load. The properties of constituents are assumed to be temperature-dependent, and effective properties of CNTRC are estimated according to extended rule of mixture. Carbon nanotubes (CNTs) are reinforced into matrix material such in a way that their volume fraction is varied in the thickness direction according to functional rules. Formulations are established within the framework of first-order shear deformation theory taking surrounding elastic media and tangential elasticity of edges into consideration. The solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and Galerkin method is used to derive expressions of buckling loads. In thermal buckling analysis, an iteration algorithm is employed to evaluate critical temperatures. The effects of CNT volume fraction and distribution patterns, degree of in-plane edge constraints, geometrical parameters, preexisting loads and surrounding elastic foundations on the critical loads of nanocomposite shells are analyzed through a variety of numerical examples.

Stability analysis of rigid multibody mechanical systems with holonomic and nonholonomic constraints

Abstract: In this paper, a new analytical approach suitable for the stability analysis of multibody mechanical systems is introduced in the framework of Lagrangian mechanics. The approach developed in this work is based on the direct linearization of the index-three form of the differential-algebraic dynamic equations that describe the motion of mechanical systems subjected to nonlinear constraints. One of the distinguishing features of the proposed method is that it can handle general sets of nonlinear holonomic and/or nonholonomic constraints without altering the original mathematical structure of the equations of motion. While the typical state-space dynamic description associated with multibody systems leads to the definition of a standard eigenproblem, which is impractical, if not impossible, to implement in the case of complex systems, the method developed in this paper involves a generalized state-space representation of the dynamic equations and allows for the formulation of a generalized eigenvalue problem that extends the scope of applicability of the stability analysis to complex mechanical systems. As demonstrated in this investigation employing simple numerical examples, the proposed methodology can be readily implemented in general-purpose multibody computer programs and compares favorably with several other reference computational approaches already available in the multibody literature.

Frequency- and angle-dependent scattering of a finite-sized meta-structure via the relaxed micromorphic model

Abstract: In this paper, we explore the use of micromorphic-type interface conditions for the modeling of a finite-sized metamaterial. We show how finite-domain boundary value problems can be approached in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized tractions, as well as additional conditions on the micro-distortion tensor and on the double-traction. The case of a metamaterial slab of finite width is presented, its scattering properties are studied via a semi-analytical solution of the relaxed micromorphic model and compared to a direct finite-element simulation encoding all details of the selected microstructure. The reflection and transmission coefficients obtained via the two methods are presented as a function of the frequency and of the direction of propagation of the incident wave. We find excellent agreement for a large range of frequencies going from the long-wave limit to frequencies beyond the first band-gap and for angles of incidence ranging from normal to near-parallel incidence. The present paper sets the basis for a new viewpoint on finite-size metamaterial modeling enabling the exploration of meta-structures at large scales.

Nonlinear effects of induced unbalance in the rod fastening rotor-bearing system considering nonlinear contact

Abstract: Rod fastening rotor (RFR) is characterized by discontinuity of contact interface and unbalance of multiple disks. There are few researches that focus on unbalance effect including magnitude and phase difference on the nonlinear dynamic characteristics of RFR considering contact feature. A typical RFR model is proposed to investigate the nonlinear dynamic characteristics. The nonlinear motion governing equation considering unbalance excitation, nonlinear oil-film force and nonlinear contact characteristics between disks is derived by D’Alembert principle. The contact effects are simulated by bending spring with nonlinear stiffness. The research focuses on the effects of unbalance on the onset of low-frequency instability and nonlinear response of RFR. The obtained results evidently show the distinct phenomena brought about by the variations of unbalance, which confirms that unbalance magnitude and phase difference are critical parameters for the RFR system response. To restrain large amplitude of nonsynchronous vibration and retard the occurrence of instability, the unbalance magnitude of rotor is suggested to be kept at range from U5 to U6. Meaningfully, RFR can operate relatively well with small vibration and higher instability threshold when the residual unbalance between disks is controlled at an enough-reasonable unbalance phase difference. Phase difference adjustment can accomplish active balance. The total vibration and nonsynchronous components could be reduced, and onset speed of instability could be delayed effectively by using the proposed method, which is helpful for the dynamic design, assembly, balance and vibration control of such RFR.

Exact solution for bending analysis of two-directional functionally graded Timoshenko beams

Abstract: This paper studies the bending behavior of two-dimensional functionally graded (TDFG) beam based on the Timoshenko beam theory, where the material properties of the beam vary both in the length and thickness directions. By introducing a new auxiliary function, we simplify the coupled governing equations for the deflection and rotation to a single governing equation. Moreover, all physical quantities of interest can be expressed in terms of the auxiliary function. Then, the exact analytical solutions for bending of TDFG Timoshenko beams are derived for various boundary conditions. The influence of gradient indexes on the deflection and stress distribution of TDFG Timoshenko beams is discussed subjected to different transverse loadings, including uniformly distributed loading, linearly distributed loading and concentrated external loading. The introduced approach is of benefit to exact bending analysis of TDFG beams by employing other beam theories.

Coupling multi-body dynamics and fluid dynamics to model lubricated spherical joints

Abstract: A new approach of coupling multibody dynamics and fluid dynamics is developed to model hydrodynamic lubrication of spherical clearance joints with thin fluid film and relative multidirectional motion. The model accounts for dynamics motion of articulating components as well as both squeeze- and wedge-film actions of the synovial fluid. Multibody dynamics methodology is employed to derive the motion equations and Reynolds equation governs the fluid dynamics. The finite difference method is utilized to discretize the governing equation of lubricant and the multi-grid method augments computational efficiency to acquire outcomes employing a Gauss–Seidel relaxation scheme. Fluid–structure interaction is incorporated into the methodology using a partitioned formulation embedded in a high-order Runge–Kutta time integrators for integrating the nonlinear equations of the coupled system over time of interest. A demonstrative example of total hip arthroplasty is considered and the developed model is assessed against outcomes available in the literature. The effect of initial conditions on the pressure, film thickness and dynamics of the lubricated spherical joint is analyzed and discussed. It is illustrated that maximum fluid pressure is undergone by the hip implant at the first walking cycle of movement due to an unstable state, which is strongly dependent upon the initial condition. Finally, the approach presented in this research work is a robust dynamic model to study hydrodynamic lubrication of spherical joints.

Nonlinear analysis of piezoelectric wind energy harvesters with different geometrical shapes

Abstract: Piezoelectric wind energy harvesters consisting a bluff body and a piezoelectric cantilever beam have great potential for powering small-sized wireless devices. To achieve a higher energy output, the beam is designed for large deformation. This results in the nonlinear nature of the energy harvesters. In this paper, a nonlinear model of a piezoelectric wind harvester with different geometrical parameters is developed. A comparison of the energy harvesting performance of these energy harvesters with different geometrical parameters is provided. Results show that the onset speeds of galloping for trapezoidal and exponential piezoelectric energy harvesters are significantly lower than those of rectangular beam. The average power output density of the beam with exponential shape is larger than trapezoidal and rectangular beams. Therefore, designing a beam with exponentially varying shape can obtain the largest power density and therefore can reduce the cost of piezoelectric wind energy harvester.

Inverse algorithm for real-time road roughness estimation for autonomous vehicles

Abstract: Human drivers take instant decisions about their speed, acceleration and distance from other vehicles based on different factors including their estimate of the road roughness. Having an accurate algorithm for real-time evaluation of road roughness can be critical for autonomous vehicles in order to achieve safe driving and passengers comfort. In this paper, we investigate the problem of interactive road roughness identification. We propose a novel inverse algorithm based on the knowledge of a vehicle dynamic characteristics and dynamic responses. The algorithm construct the road profile in time using one-iteration to update the wheels forces which are then used to identify the road roughness. The relation between the forces and the road profile is defined by a system of ordinary differential equations that are solved using the composite Gaussian quadrature. To reduce the error accumulation in time when noisy data is used for the vehicle response, a bidirectional filter is also implemented. We assume a simple model that is based on four degrees-of-freedom system and vibration acceleration measurements to evaluate the road roughness in real time. Although we present the results for this specific model, the algorithm can also be utilised with models of any number of degrees of freedom and can deal with models where the dynamic response is only available at some of the degrees of freedom. This is achieved by introducing a matrix reduction technique that is discussed in details. Furthermore, we evaluate the impact of uncertainty in the vehicle parameters on the algorithm estimation accuracy. The proposed algorithm is evaluated for different types of road roughness. The simulation results show that the proposed method is robust and can achieve high accuracy. The algorithm offers excellent potential for road roughness estimation not only for autonomous vehicle but also for vehicles and roads designing purposes.

Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping

Abstract: This paper presents a theoretical investigation on the response of free vibration of functionally graded material (FGM) micro-plates with thermoelastic damping (TED). Continuous through thickness variation of the mechanical and thermal properties of the FGM plate is considered. By employing the simplified one-way coupled heat conduction equation and Kirchhoff’s plate theory, governing equations for the free vibration of the FGM micro-plates with thermoelastic coupling effect are established, in which stretching-bending coupling produced by the material inhomogeneity in the thickness direction is also considered. The heat conduction equation with variable coefficients is solved effectively by a layer-wise homogenization approach. Harmonic responses of the FGM micro-plates with complex frequency are obtained from the mathematical similarity between the eigenvalue problems of the FGM micro-plate with TED and that of the homogenous one without TED. The presented analytical solutions are suitable for evaluating TED in FGM micro-plates with arbitrary through-thickness material gradient, geometry and boundary conditions. Numerical results of TED for a ceramic-metal composite FGM micro-plate with power-law material gradient profile are illustrated to quantitatively show the effects of the material gradient index, the plate thickness, and the boundary conditions on the TED. The results indicate that by adjusting the physical and geometrical parameters of the FGM micro- plate, one can get the minimum of the TED which is even smaller than that of the pure ceramic resonator.

Control of a laminated composite plate resting on Pasternak’s foundations using magnetostrictive layers

Abstract: A higher-order shear deformation theory is utilized to discuss the vibration of a laminated composite plate containing four magnetostrictive layers based on Pasternak’s foundations in the current article. Hamilton’s principle is used to derive the governing dynamic equations related to the vibration of present smart structure under velocity feedback control with constant gain distributed. Navier’s approach is utilized to give a solution of simply supported laminated composite plates. Effects of all material properties, modes, thickness ratio, aspect ratio, lamination schemes, magnitude of the feedback parameter, the elastic foundations parameters and the thickness, location and number of magnetostrictive layers, on the vibration damping characteristics of the system are investigated and extensively discussed. Findings of the damping coefficients, damped natural frequencies, damping ratio, vibration time and maximum deflection for some different laminates are computed. The influences of studied parameters on the vibration suppression of plates are illustrated graphically. The results indicate increasing of smart layers structures tends to more control of structure and elastic foundations can contribute the stability of the plate significantly.

Free vibration and buckling analyses of laminated composite plates with cutout

Abstract: This study aims to examine the effect of the diameter, number, and location of the circular cutout on the free vibration response and buckling loads of the laminated composites. Eigen-buckling and free vibrations analyses are performed for the laminated composite plates by using the finite element software ANSYS. Numerical results obtained by the finite element method are compared to the experimental ones. In the numerical analyses, the effect of the delamination around the cutout on the buckling load and the natural frequency is also examined. The critical buckling load and first natural frequency values obtained by both numerical and experimental studies are used to create a prediction model using the artificial neural networks. The Levenberg–Marquardt backpropagation algorithm is used as the training method. It is observed that both the number and location of the cutout affect the critical buckling load and first natural frequency values. Numerical and experimental results are presented together with the ANN prediction results.

The lowest vibration modes of an elastic beam composed of alternating stiff and soft components

Abstract: Harmonic vibrations of a strongly inhomogeneous elastic beam with piecewise uniform stiffnesses and densities are considered. The focus is on the lowest eigenmodes, which are often most harmful and unwanted. They are evaluated by perturbing the limiting rigid body translations and rotations of stiff beam components. The developed methodology is adapted for two particular configurations of a three-span beam. The derived approximate formulae are tested by comparison with the exact solution of a symmetric beam with two stiff outer components and free ends.

On fractional bending of beams with $$\Lambda $$Λ -fractional derivative

Abstract: Introducing the fractional $$\Lambda $$-derivative, with the corresponding $$\Lambda $$-fractional spaces, the fractional beam bending problem is presented. In fact, non-local derivatives govern the beam bending problem that accounts for the interaction of microcracks or materials non-homogeneities, such as composite materials or materials with fractal geometries. The proposed theory is implemented to the fractional bending deformation of a simply supported beam and a cantilever beam under continuously distributed loading.

A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method

Abstract: The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Karman geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced computational cost. Currently the literature describes a small number of high-order numerical forced vibration problems, the majority of which are limited to DQM. To obtain forced vibration solutions using WQEM, the authors propose two different methods to obtain frequency response curves. The obtained results indicate that the frequency response curves generated by either method closely match their DQM counterparts obtained from the literature, and this is despite the low mesh density used for the WQEM systems.

A novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamics

Abstract: A novel family of composite sub-step algorithms with controllable numerical dissipations is proposed in this paper to obtain reliable numerical responses in structural dynamics. The new scheme is a self-starting, unconditionally stable and second-order-accurate two-sub-step algorithm with the same computational cost as the Bathe algorithm. The new algorithm can control continuously numerical dissipations in the high-frequency range in an intuitive way, and the ability of numerical dissipations can range from the non-dissipative trapezoidal rule to the asymptotic annihilating Bathe algorithm. Besides, the new algorithm only involves one free parameter and always achieves the identical effective stiffness matrices inside two sub-steps, which is not always achieved in three Bathe-type algorithms, to reduce the computational cost in the analysis of linear systems. Some numerical examples are given to show the superiority of the new algorithm over the Bathe algorithm and the CH-$$\alpha $$ algorithm.

On the mechanisms of production of large irreversible strains in materials with elastic, viscous and plastic properties

Abstract: A thermodynamically and geometrically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. The viscous properties of a material are considered to provide a creep process and, therefore, the slow growth of irreversible strains during unloading and the stage preceding plastic flow. Under the fast growth of irreversible strains under the conditions of plastic flow, the viscous properties emerge as a mechanism that resists to this flow. Thus, the accumulation of irreversible strains initially occurs in the creep process, then under the plastic flow condition and finally because of material creep (during unloading). The change in the mechanism of irreversible strain growth occurs on elastoplastic boundaries moving in the deformed material. This change is only possible under the conditions of the continuity of irreversible strains and their rates. This continuity requires the coordination in the definitions of irreversible strain rates in the dependence on stresses, i.e. in laws of creep and plasticity. The change in the production mechanisms of irreversible strains means a different setting of the sources in differential equations of change (transfer equations) for these strains. Thus, irreversible strains are not divided into creep and plastic ones. The hypothesis of the independence of thermodynamic potentials (internal energy, free energy) from irreversible strains is applied with the aim of most visibility of the model relations. Under the condition of the acceptance of this hypothesis, an analogue of the Murnaghan formula is obtained, i.e. the stresses are completely determined by the level and distribution of the reversible strains as in the classical elastoplasticity theory. The main statements of the proposed model are illustrated by a boundary value problem solved in the framework of the model. This problem is about the deformation of an elastoviscoplastic material placed in the gap between two rigid cylindrical surfaces under the rotation of one of them and the material slipping in the neighbourhood of the internal surface.

Effect of rotating unbalance and engine excitations on the nonlinear dynamic response of turbocharger flexible rotor system supported on floating ring bearings

Abstract: In practical conditions, turbochargers are supported by floating ring bearings and mounted on engines. In this paper, the effect of rotating unbalance and engine excitations on turbocharger is studied. The finite element model of turbocharger system is developed considering flexible rotor, using Timoshenko beam elements. The nonlinear fluid film forces generated in floating ring bearings are derived analytically in dimensional form using short bearing approximation. A new $$\hbox {MATLAB}^{{\circledR }}$$ code has been constructed to solve the governing differential equations of motion of system using implicit Newmark-$$\upbeta $$ numerical integration scheme along with Newton–Raphson convergence method, and dynamic response of the system is computed. The orbital plots, Poincare maps, and frequency spectrum are developed to show the nonlinear behaviour of the turbocharger system. At low rotor speeds, the system exhibits chaotic behaviour and has a wide range of sub-synchronous vibrations. As the speed of turbocharger increases, the forces due to unbalance dominate over engine excitations and nonlinear bearing forces and frequency spectrum become narrow. The behaviour of compressor and turbine disc centre is governed by their respective bearing nodes.

Universal relations in nonlinear electro-magneto-elasticity

Abstract: The purpose of this article is to develop a class of universal relations for an incompressible isotropic electro-magneto-elastic (hereafter EME) material in order to generalize the continuum concept to electro-magneto-elasticity. In line with that, we adopt an electro-magneto-elasticity theory following the second law of thermodynamics-based approach. More precisely, we first extend a thermodynamically consistent deformation of a continua to a coupled EME interaction through a new amended energy function (hereafter AEF). This AEF succeeds the physical insight of the Maxwell stress tensor (hereafter MST) under large deformations. Next, we introduce a new inequality $$\mathbf{Tb} -\mathbf{bT} e 0$$ for a class of an EME material parallel to an equation $$\mathbf{Tb} -\mathbf{bT} = 0$$ for a class of an elastic material existing in the literature. At last, the formulated universal relations are applied to some homogeneous and non-homogeneous deformations to exemplify the consequences of an electromagnetic field on the mechanical deformation. Additionally, the validity of the proposed universal relations in electro-magneto-elasticity is also checked by obtaining an existing universal relation in nonlinear elasticity in the absence of an applied electromagnetic field.

A hyperelastic constitutive model for rubber-like materials

Abstract: In this contribution, a new form of the strain energy function is proposed to describe the hyperelastic behavior of rubber-like materials under various deformation. The proposed function represents an invariant-based model and contains two material parameters. The model was tested with the experimental data of vulcanized rubbers, collagen and fibrin. The material parameters are kept constant for a material subjected to different types of loading. Good agreement between model and experimental data was obtained for all materials.

A new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes—Part 1: the derivations for the wave, heat and Poisson equations in the 1-D and 2-D cases

Abstract: A new numerical approach for the time-dependent wave and heat equations as well as for the time-independent Poisson equation on irregular domains has been developed. Trivial Cartesian meshes and simple 9-point stencil equations with unknown coefficients are used for 2-D irregular domains. The calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy. The treatment of the Dirichlet and Neumann boundary conditions in the new approach is related to the development of high-order boundary conditions with the stencils that include the same or a smaller number of grid points compared to that for the regular 9-point internal stencils. At similar 9-point stencils, the accuracy of the new approach is two orders higher than that for the linear finite elements. The numerical results for irregular domains in Part 2 of the paper also show that at the same number of degrees of freedom, the new approach is even much more accurate than the quadratic and cubic finite elements with much wider stencils. Similar to our recent results on regular domains, the order of the accuracy of the new approach for the Poisson equation on irregular domains with square Cartesian meshes is higher than that with rectangular Cartesian meshes. The new approach can be directly applied to other partial differential equations.

Effect of detuning conditions on the performance of non-traditional tuned mass dampers under external excitation

Abstract: The tuned mass damper (TMD) is a widely used passive control device which is attached to a main system to suppress undesired vibration. In this paper, a non-traditional form of TMD system is investigated. Unlike the traditional TMD configuration, the considered TMD system has a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. There have been some studies on the optimization design of the non-traditional TMD (NT-TMD) for undamped main structures. Those studies have indicated that the NT-TMD provides better performance than the traditional TMD does. When there is a frequency shifting in the structural frequency or tuning frequency of TMD, to the best knowledge of the authors, there has been no study on the performance of the NT-TMD. The main idea of the study is to investigate the effect of frequency detuning on the control performance of the NT-TMD. The optimum parameters of the NT-TMD system and corresponding effectiveness are obtained for different mass ratios of the NT-TMD system. The numerical results indicate that the NT-TMD with high mass ratio provides better robustness to the changes in the target frequency ratio than the traditional TMD.