Showing papers in "Meccanica in 2017"

Growth and remodeling of load-bearing biological soft tissues

Abstract: The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.

On the notion of fractional derivative and applications to the hysteresis phenomena

Abstract: In the first part of the paper, we discuss on the general properties of a fractional derivative. In particular we found that the definition presented in Caputo and Fabrizio (Prog Fract Differ Appl 1(2):73–85, 2015) satisfies these general conditions, including the non-locality. So by means of numerical simulations we have shown different behaviors of this new operator with respect to Caputo’s derivative. In particular we have shown that the memory effects are less evident when we consider the new derivative. Finally, in the second part, a model for the study of the magnetic hysteresis phenomena is presented. The thermodynamic compatibility is proven, and a checking of the model is tested with some numerical simulations.

Thermoelastic analysis of functionally graded graphene reinforced rectangular plates based on 3D elasticity

Abstract: Thermoelastic bending behaviour of novel functionally graded polymer nanocomposite rectangular plate reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction is investigated. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of nanocomposite rectangular plate with two opposite edges simply supported and under a uniformly distributed transverse load and a temperature change. Three GPL distribution patterns are considered. Comparison between the present analytical solutions and those available in literature is carried out to verify the accuracy of our analytical solutions. A parametric study is conducted to examine the effects of GPL’s weight fraction, distribution pattern, geometry and size as well as the temperature change and plate boundary conditions on the stress and deformation fields of the nanocomposite plates. Numerical results show that the addition of GPLs at a very low content can have a significant reinforcing effect on the thermo-mechanical response of the plate.

Numerical and experimental investigations of a rotating nonlinear energy sink

Abstract: In this work, passive nonlinear targeted energy transfer (TET) is addressed by numerically and experimentally investigating a lightweight rotating nonlinear energy sink (NES) which is coupled to a primary two-degree-of-freedom linear oscillator through an essentially nonlinear (i.e., non-linearizable) inertial nonlinearity. It is found that the rotating NES passively absorbs and rapidly dissipates a considerable portion of impulse energy initially induced in the primary oscillator. The parameters of the rotating NES are optimized numerically for optimal performance under intermediate and strong loads. The fundamental mechanism for effective TET to the NES is the excitation of its rotational nonlinear mode, since its oscillatory mode dissipates far less energy. This involves a highly energetic and intense resonance capture of the transient nonlinear dynamics at the lowest modal frequency of the primary system; this is studied in detail by constructing an appropriate frequency–energy plot. A series of experimental tests is then performed to validate the theoretical predictions. Based on the obtained numerical and experimental results, the performance of the rotating NES is found to be comparable to other current translational NES designs; however, the proposed rotating device is less complicated and more compact than current types of NESs.

Design, manufacturing, and flight testing of a fixed wing micro air vehicle with Zimmerman planform

Abstract: An optimized and comprehensive method is used to design and manufacture a fixed wing micro air vehicle (MAV) with Zimmerman planform. The design process includes four stages which are the specification of the flight mission, determination of the best aspect ratio, identification of the optimum wing loading and thrust loading values, and estimation of the weight of the structural components of the MAV. To do this, various statistical and analytical methods are utilized. Based on an aerodynamic analysis, the results show that an optimum aspect ratio that maximizes the performance of the Zimmerman MAV for a well-defined cruise speed is determined. Considering six possible flights, a constraint analysis is performed and an optimum wing loading value is determined. It is shown that the computational method is beneficial to determine the exact masses for the structural components including the wing, fuselage, and vertical tail. Using the 3D panel method, the determination of the shape of the reflexed airfoil for the MAV is successfully done by minimizing the drag force and the angle of attack to use less powerful motor and avoid any stall effect, respectively. A stability analysis is then performed to check the safe flight of the designed vehicle. During test flight, the results show that the designed Zimmerman MAV satisfies the pre-defined specification. The final characteristics of the manufactured MAV are: wingspan of 44 cm, weight of 450 g, aspect ratio of 1.51, cruise speed of 20 m/s, and flight endurance of 20 min.

Free vibration of carbon nanotube reinforced composite plate on point Supports using Lagrangian multipliers

Abstract: Chebyshev polynomial functions are used in the Lagrangian multipliers method to study the free vibration characteristics of rectangular moderately thick composite plates reinforced with carbon nanotubes (CNTs). Plate is resting on point supports. Distribution of CNTs across the plate thickness is considered to be either uniform or functionally graded. Properties of the plate are obtained using a refined rule of mixtures approach which includes the efficiency parameters to capture the size dependent characteristics of the composite plate. Using a Ritz solution method, an eigenvalue problem is established which results in natural frequencies and mode shapes of the plate. Based on the developed solution method, number and position of point supports are arbitrary and also various boundary conditions may be assumed for the four edges of the plate. After performing comparison studies for isotropic homogeneous plates on point supports, parametric studies are provided to explore the vibration characteristics of the carbon nanotube reinforced composite plates on point supports. It is shown that, frequencies of the plate increase as the volume fraction of CNTs increases.

Active and passive controls of nanoparticles in Maxwell stagnation point flow over a slipped stretched surface

Abstract: A steady stagnation-point flow of an incompressible Maxwell fluid towards a linearly stretching sheet with active and passive controls of nanoparticles is studied numerically. The momentum equation of the Maxwell nanofluid is inserted with an external velocity term as a result of the flow approaches the stagnation point. Conventional energy equation is modified by incorporation of nanofluid Brownian and thermophoresis effects. The condition of zero normal flux of nanoparticles at the stretching surface is defined to impulse the particles away from the surface in combination with nonzero normal flux condition. A hydrodynamic slip velocity is also added to the initial condition as a component of the entrenched stretching velocity. The governing partial differential equations are then reduced into a system of ordinary differential equations by using similarity transformation. A classical shooting method is applied to solve the nonlinear coupled differential equations. The velocity, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, Nusselt number and Sherwood number are graphically presented to visualize the effects of particular parameters. Temperature distributions in passive control model are consistently lower than in the active control model. The magnitude of the reduced skin friction coefficient, Nusselt number and Sherwood number decrease as the hydrodynamic slip parameter increases while the Brownian parameter has negligible effect on the reduced heat transfer rate when nanoparticles are passively controlled at the surface. It is also found that the stagnation parameter contributes better heat transfer performance of the nanofluid under both active and passive controls of normal mass flux.

Numerical investigation of rising bubbles bursting at a free surface through a multiphase SPH model

Abstract: As a Lagrangian meshless method, smoothed particle hydrodynamics (SPH) method is robust in modelling multi-fluid flows with interface fragmentations. However, the application for the simulation of a rising bubble bursting at a fluid surface is rarely documented. In this paper, the multiphase SPH model is extended and applied to simulate this challenging phenomenon. Different numerical techniques developed in different SPH models are combined in the present SPH model. The adoption of a background pressure determined based on the surface tension can help to avoid tensile instability and interface penetrations. An accurate surface tension model is employed. This model is suitable for bubble rising problems of small scales and high density ratios. An interface sharpness force is adopted to achieve a smoother bubble surface. A suitable formula of viscous force, which is proven to be able to accurately capture the bubble splitting and small bubble detachment, is employed. Moreover, a modified prediction-correction time-stepping scheme for a better numerical stability and allows a relatively larger CFL factor is adopted. It is also worthwhile to mention that the particle shifting technique, which helps to make the particle distribute in an arrangement of lower disorder, can significantly improve the numerical accuracy. Regarding the treatment of the fluid surface, particles of lighter phase are arranged above the free surface of the denser phase to avoid the kernel truncation in the density approximation. Furthermore, this technique also allows an accurate calculation of the surface tension on the fluid surface. A number of cases of bubbly flows are presented, which confirms the capability of the present multiphase SPH model in modelling complex bubble-surface interactions with the density ratio and viscosity ratio up to 1000 and 100 respectively.

On the behavior of a three-dimensional fractional viscoelastic constitutive model

Abstract: In this paper a three-dimensional isotropic fractional viscoelastic model is examined. It is shown that if different time scales for the volumetric and deviatoric components are assumed, the Poisson ratio is time varying function; in particular viscoelastic Poisson ratio may be obtained both increasing and decreasing with time. Moreover, it is shown that, from a theoretical point of view, one-dimensional fractional constitutive laws for normal stress and strain components are not correct to fit uniaxial experimental test, unless the time scale of deviatoric and volumetric are equal. Finally, the model is proved to satisfy correspondence principles also for the viscoelastic Poisson’s ratio and some issues about thermodynamic consistency of the model are addressed.

On the time differential dual-phase-lag thermoelastic model

Abstract: This paper studies the time differential dual-phase-lag model of a thermoelastic material, where the elastic deformation is accompanied by thermal effects governed by a time differential equation for the heat flux with dual phase lags. This coupling gives rise to a complex differential system requiring a special treatment. Uniqueness and continuous dependence results are established for the solutions of the mixed initial boundary value problems associated with the model of the linear theory of thermoelasticity with dual-phase-lag for an anisotropic and inhomogeneous material. Two methods are developed in this paper, both being based on an identity of Lagrange type and of a conservation law applied to appropriate initial boundary value problems associated with the model in concern. The uniqueness results are established under mild constitutive hypotheses (right like those in the classical linear thermoelasticity), without any restrictions upon the delay times (excepting the class of thermoelastic materials for which the delay time of phase lag of the conductive temperature gradient is vanishing and the delay time in the phase lag of heat flux vector is strictly positive, when an ill-posed model should be expected). The continuous dependence results are established by using a conservation law and a Gronwall inequality, under certain constitutive restrictions upon the thermoelastic coefficients and the delay times.

A class of linear viscoelastic models based on Bessel functions

Abstract: In this paper we investigate a general class of linear viscoelastic models whose creep and relaxation memory functions are expressed in Laplace domain by suitable ratios of modified Bessel functions of contiguous order. In time domain these functions are shown to be expressed by Dirichlet series (that is infinite Prony series). It follows that the corresponding creep compliance and relaxation modulus turn out to be characterized by infinite discrete spectra of retardation and relaxation time respectively. As a matter of fact, we get a class of viscoelastic models depending on a real parameter $$ u > -1$$ . Such models exhibit rheological properties akin to those of a fractional Maxwell model (of order 1/2) for short times and of a standard Maxwell model for long times.

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

Abstract: In this study, nonlocal elasticity theory in conjunction with Gurtin–Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a visco-Pasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton’s principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

Time-varying mesh characteristics of a spur gear pair considering the tip-fillet and friction

Abstract: Considering the effects of the tip-fillet and friction between teeth surfaces, an improved analytical model for time-varying mesh stiffness (TVMS) calculation is further developed based on our previous works (Ma et al. in Mech Mach Theory, 98:64–80, 2016) in which the effects of extended tooth contact, revised fillet-foundation stiffness and nonlinear contact stiffness are taken into account. The proposed model is also verified by comparing the TVMS with that obtained from finite element method. Combined effects of the tip-fillet and friction on the TVMS, loaded transmission error and loaded sharing factor are discussed. The results show that TVMS between double- and single-tooth engagements becomes smooth under the small radii of the tip-fillet, however, an abrupt change of the TVMS from double-tooth contact to single-tooth contact can be observed under the large radii of the tip-fillet. The range of the double-tooth engagement decreases and the single-tooth engagement increases with the increase of the radius of the tip-fillet. In addition, the tooth-surface friction mainly affects the mesh stiffness in single-tooth engagement region due to the change of friction force direction near pitch point, and the extent of variation increases with the increase of friction coefficient. The friction has a larger effect on the TVMS than the tip-fillet for the selected parameters of tip-fillet and friction. This study can provide a basis for the structural design of the spur gears.

Bending, buckling and free vibration analyses of functionally graded curved beams with variable curvatures using isogeometric approach

Abstract: A study on the bending, buckling and free vibration of functionally graded curved beams with variable curvatures using isogeometric analysis is presented here. Non-uniform rational B-splines, known from computer aided geometric design, are employed to describe the exact geometry and approximate the unknown fields of a curved beam element based on Timoshenko model. Material properties of the beam are assumed to vary continuously through the thickness direction according to the power law form. The numerical examples investigated in this paper deal with circular, elliptic, parabolic and cycloid curved beams. Results have been verified with the previously published works in both cases of straight functionally graded beam and isotropic curved beam. The effects of material distribution, aspect ratio and slenderness ratio on the response of the beam with different boundary conditions are numerically studied. Furthermore, an interesting phenomenon of changing mode shapes for both buckling and free vibration characteristics corresponding to the variation in the parameters mentioned above is also examined.

Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments

Abstract: Investigation of transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of isotropic solids and orthotropic composites by an extended meshfree method is described. We adopt the recently developed extended meshfree radial point interpolation method (X-RPIM), which combines either the standard branch functions or the new linear ramp function associated with Heaviside functions to capture crack-tip behaviors. It is the first time the linear ramp function integrating into meshfree X-RPIM has been presented in a dynamical fracture context. We are particularly interested in exploring insight into the behaviors of DSIFs under dynamic impact loadings (e.g., step, blast and sine loading types) using our meshfree method. For some of these problems numerical examples have been performed using the new ramp functions, and the obtained results of DSIFs have also been compared with those using the standard enrichment functions under which the two schemes have the same setting. In each case it is found that the numerical solutions delivered using the X-RPIM associated with the ramp enrichments are in good agreement with those with the standard functions. The paper first describes formulations and then provides verification of our developed approach through a series of numerical examples in transient dynamic fracture for both solids and orthotropic composites. Illustration of scattered elastic stress waves propagating in the cracked body is depicted to take an insight look at the behavior of dynamic response.

Benchmark solution for free vibration of thick open cylindrical shells on Pasternak foundation with general boundary conditions

Abstract: In the present article, a new three-dimensional exact solution for free vibration of thick open cylindrical shells on Pasternak foundation with general boundary conditions is presented. The three-dimensional elasticity theory is employed to formulate the theoretical model. The admissible functions of the thick shells are described as a combination of a three-dimensional (3-D) Fourier cosine series and auxiliary functions. Compared with the traditional Fourier series, the improved Fourier series can eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions. The excellent accuracy and reliability of the current solutions are demonstrated by numerical examples and comparison of the present results with those available in the literature and obtained by using ABAQUS which is based on the finite element method. Numerous new results for thick open cylindrical shells on Pasternak foundation with elastic boundary conditions are presented. In addition, comprehensive studies on the effects of the elastic restraint parameters, geometric parameters and elastic foundation coefficients are also reported.

Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory

Abstract: This paper aims to analyze the axial and transverse dynamic response of a functionally graded nanobeam under a moving constant load. The governing equations are obtained using the Hamilton principle and nonlocal Euler–Bernoulli beam theory. The mechanical properties vary in the thickness direction. The simply supported boundary condition is assumed and using the Laplace transform, the exact solution for the transverse and axial dynamic response is presented. Some examples were used to analyze nonlocal parameters such as power law index of FG materials, aspect ratio and the velocity of a moving constant load and also their influence on axial and transverse dynamic and maximum deflections. By obtaining a good agreement between the presented natural frequencies in this study and previous works, the results of this study are validated.

Equilibrium formulation of masonry helical stairs

Abstract: In this paper the lower bound theorem of limit analysis for No-Tension materials is applied to study the equilibrium of spiral vaults, modeled as continuous unilateral membranes. The most efficient approach to the equilibrium of a thin shell is the covariant representation proposed by Pucher and adopted in the present study. Statically admissible singular stresses in the form of line or surface Dirac deltas and lying inside the masonry, are taken into account. The unilateral restrictions require that the Airy stress function representing the stress, be concave. The case study is a helical stair with a central pillar in Sanfelice Palace in Naples, whose structure is a tuff masonry spiral vault. The maps of the stress corresponding to two different stress functions and the safety factors in the two cases are provided.

Kinematic synthesis and testing of a new portable hand exoskeleton

Abstract: In this research activity, a new methodology for the synthesis of hand exoskeleton mechanisms has been developed and validated through real prototypes. The innovative methodology is based on a new parallel mechanism and has been tested by building a robotic assistive device for hand opening disabilities applied to real cases. The studied robotic orthosis is designed to be a low-cost, adaptable and portable hand exoskeletons to assist people with hand opening disabilities in their activities of daily livings. As regards the methodology for the synthesis of hand exoskeleton mechanism, the authors propose to use a motion capture system to acquire the real hand phalanx trajectories and the geometrical characteristics of the patient’s hand, and to use optimization algorithms to properly defines the novel kinematic mechanism that better fits the finger trajectories. The preliminary testing phase of the prototype on a single patient is concluded; currently, through the collaboration with an Italian rehabilitation center, a group of patients are testing the proposed HES methodology.

Control of nonlinear vibrations using the adjoint method

Abstract: In this paper, a new methodology is proposed to address the problems of suppressing structural vibrations and attenuating contact forces in nonlinear mechanical systems. The computational algorithms developed in this work are based on the mathematical framework of the calculus of variation and take advantage of the numerical implementation of the adjoint method. To this end, the principal aspects of the optimal control theory are reviewed and employed to derive the adjoint equations which form a nonlinear differential-algebraic two-point boundary value problem that defines the mathematical solution of the optimal control problem. The adjoint equations are obtained and solved numerically for the optimal design of control strategies considering a twofold control structure: a feedforward (open-loop) control architecture and a feedback (closed-loop) control scheme. While the feedforward control strategy can be implemented using only the active control paradigm, the feedback control method can be realized employing both the active and the passive control approaches. For this purpose, two dual numerical procedures are developed to numerically compute a set of optimal control policies, namely the adjoint-based control optimization method for feedforward control actions and the adjoint-based parameter optimization method for feedback control actions. The computational methods developed in this work are suitable for controlling nonlinear nonautonomous dynamical systems and feature a broad scope of application. In particular, it is shown in this paper that by setting an appropriate mathematical form of the cost functional, the proposed methods allow for simultaneously solving the problems of suppressing vibrations and attenuating interaction forces for a general class of nonlinear mechanical systems. The numerical example described in the paper illustrates the key features of the adjoint method and demonstrates the feasibility and the effectiveness of the proposed adjoint-based computational procedures.

Methodologies for weight estimation of fixed and flapping wing micro air vehicles

Abstract: One of the important steps in the sizing process of fixed and flapping wing micro air vehicles (MAVs) is weight estimation of the electrical and structural components In order to enhance the flight performance and endurance of MAVs, it is required to carefully estimate their weight with a minimum error In this study, methodologies to estimate the weight of fixed and flapping wing MAVs are proposed After dividing the total weight of the MAV into weights of structural and electrical components, these two weights are separately identified The weight of the MAV electrical components is estimated by using engineering design techniques and the weight of the structure is identified by using statistical and computational methods The proposed methodology for structural weight estimation is based on calculating the percentage of the used material in the construction of different parts of MAVs and then presenting the weight of each part in terms of the wing surface The proposed computational method gives the exact estimation for the weight of each structure component, such as wing, tail, fuselage, and etc Based on the offered method for weight estimation of MAVs, the weight estimation of a fixed wing MAV with inverse Zimmerman planform and a flapping wing MAV named “Thunder I” are experimentally shown This developed methodology gives guidelines for weight estimation and determination of the structural weight percentages in order to design and fabricate efficient fixed and flapping wing MAVs

Design and kinematic optimization of a novel underactuated robotic hand exoskeleton

Abstract: This study presents the design and the kinematic optimization of a novel, underactuated, linkage-based robotic hand exoskeleton to assist users performing grasping tasks. The device has been designed to apply only normal forces to the finger phalanges during flexion/extension of the fingers, while providing automatic adaptability for different finger sizes. Thus, the easiness of the attachment to the user’s fingers and better comfort have been ensured. The analyses of the device kinematic pose, statics and stability of grasp have been performed. These analyses have been used to optimize the link lengths of the mechanism, ensuring that a reasonable range of motion is satisfied while maximizing the force transmission on the finger joints. Finally, the usability of a prototype with multiple fingers has been tested during grasping tasks with different objects.

Viscoelastic frictional properties of rubber-layer roller bearings (RLRB) seismic isolators

Abstract: This paper deals with the behavior of a rubber-layer roller bearing (RLRB) isolation system. This system consists of steel cylinders interposed between steel plates padded with high damping rubber layers. When the cylinders start to roll, a partial decoupling is achieved between the superstructure response and the ground motion. However, the presence of rubber layers in RLRB isolators aims at dissipating part of the seismic energy, thus reducing the relative motion between the base and the superstructure (building). To better understand this phenomenon, we proceeded to a mechanistic study of the viscoelastic contact interaction between the rolling cylinders and the rubber layers. The analysis is led in the framework of continuum mechanics and linear viscoelasticity by means of a numerical strategy, belonging to the class of boundary element methods, able to take into account the viscoelastic layer thickness. The results show that, depending on the design parameters, a strong reduction of the viscoelastic friction can be achieved, useful to uncouple the motion of the superstructure from the motion of the base and then of the ground, without negatively affecting the amount of energy dissipation per unit time. The simulations allow determining the optimal sizes and dimensions to the component parts of the isolator.

A model of imperfect interface with damage

Abstract: In this paper two models of damaged materials are presented. The first one describes a structure composed by two adherents and an adhesive which is micro-cracked and subject to two different regimes, one in traction and one in compression. The second model is a model of interface derived from the first one through an asymptotic analysis, and it can be interpreted as a model for contact with adhesion and unilateral constraint. Simple numerical examples are presented.

In-plane vibration analysis of plates in curvilinear domains by a differential quadrature hierarchical finite element method

Abstract: Free in-plane vibration analysis of plates is carried out by a differential quadrature hierarchical finite element method (DQHFEM). The NURBS (Non-Uniform Rational B-Splines) patches of geometries were first transformed into differential quadrature hierarchical (DQH) patches, and then the elastic field was discretized by the same DQH basis. The DQHFEM solved the compatibility problem caused by different parametrization of neighbouring patches of isogeometric analysis using NURBS. And mesh refinement in DQHFEM does not propagate from patch to patch. The DQHFEM matrices also have the embedding property as the hierarchical finite element method (HFEM). In-plane vibration analyses of plates of several planforms showed that the DQHFEM is similar as the fixed interface mode synthesis method that can analyse a structure using a few nodes on the boundary of substructure elements and only several clamped modes inside each substructure element, but the DQHFEM does not need modal analysis and is of high accuracy. The accuracy and convergence of the DQHFEM were validated through comparison with exact and approximate results in literatures and computed by the authors.

Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory

Abstract: In this paper, vibration features of variable thickness rectangular viscoelastic nanoplates are studied. In order to consider the small-scale and the transverse shear deformation effects, governing differential equations and relevant boundary conditions are adopted based on the nonlocal elasticity theory in relation to first-order shear deformation theory of plates. The numerical solution for the nanoplate vibration frequencies is proposed applying the differential quadrature method, as a simple, effective and precise numerical tool. The present formulation and solution method are validated showing their fast convergence rate and comparison of results, in limited cases, using the available literature. Excellent agreement between the obtained and available results is observed. The effects of structural damping coefficient, boundary conditions, aspect ratio, nonlocal and variable thickness parameters on viscoelastic nanoplates vibration behaviour are studied in detail.

Planetary gearbox with localised bearings and gears faults: simulation and time/frequency analysis

Abstract: Planets bearings of planetary gear sets exhibit high rate of failure; detection of these faults which may result in catastrophic breakdowns have always been challenging. The objective of this paper is to investigate the planetary gears vibration properties in healthy and faulty conditions. To seek this goal a previously proposed lumped parameter model (LPM) of planetary gear trains is integrated with a more comprehensive bearing model. This modified LPM includes time varying gear mesh and bearing stiffness and also nonlinear bearing stiffness due to the assumption of Hertzian contact between the rollers/balls and races. The proposed model is completely general and accepts any inner/outer race bearing defect location and profile in addition to its original capacity of modelling cracks and spalls of gears; therefore, various combinations of gears and bearing defects are also applicable. The model is exploited to attain the dynamic response of the system in order to identify and analyze localized faults signatures for inner and outer races as well as rolling elements of planets bearings. Moreover, bearing defect frequencies of inner/outer race and ball/roller and also their sidebands are discussed thoroughly. Finally, frequency response of the system for different sizes of planets bearing faults are compared and statistical diagnostic algorithms are tested to investigate faults presence and growth.

Homogenized modeling for vascularized poroelastic materials

Abstract: A new mathematical model for the macroscopic behavior of a material composed of a poroelastic solid embedding a Newtonian fluid network phase (also referred to as vascularized poroelastic material), with fluid transport between them, is derived via asymptotic homogenization. The typical distance between the vessels/channels (microscale) is much smaller than the average size of a whole domain (macroscale). The homogeneous and isotropic Biot’s equation (in the quasi-static case and in absence of volume forces) for the poroelastic phase and the Stokes’ problem for the fluid network are coupled through a fluid-structure interaction problem which accounts for fluid transport between the two phases; the latter is driven by the pressure difference between the two compartments. The averaging process results in a new system of partial differential equations that formally reads as a double poroelastic, globally mass conserving, model, together with a new constitutive relationship for the whole material which encodes the role of both pore and fluid network pressures. The mathematical model describes the mutual interplay among fluid filling the pores, flow in the network, transport between compartments, and linear elastic deformation of the (potentially compressible) elastic matrix comprising the poroelastic phase. Assuming periodicity at the microscale level, the model is computationally feasible, as it holds on the macroscale only (where the microstructure is smoothed out), and encodes geometrical information on the microvessels in its coefficients, which are to be computed solving classical periodic cell problems. Recently developed double porosity models are recovered when deformations of the elastic matrix are neglected. The new model is relevant to a wide range of applications, such as fluid in porous, fractured rocks, blood transport in vascularized, deformable tumors, and interactions across different hierarchical levels of porosity in the bone.

Validation of a drill string dynamical model and torsional stability

Abstract: This paper proposes a lumped parameter model for the torsional vibration of a drill string, with a nonlinear friction torque representing the bit-rock interaction. This model is sufficient to analyze torsional instability (stick-slip oscillations). In the first part of the paper, field data with 50 Hz sample rate are used to fit the bit-rock interaction curve. With the identified bit-rock interaction model, the response of the proposed computational model is compared with the bit speed (field data), showing a good agreement. In the second part of the paper, the numerical model is used to construct a torsional stability map (rotational speed at the top vs. weight-on-bit). It should be remarked that the field data available in this paper is precious, due to its high frequency rate, and that the proposed model, although neglecting axial an lateral vibrations, can effectively tackle the problem of torsional stability.

Elasto-plastic contact of rough surfaces: a mixed-lubrication model for the textured surface analysis

Abstract: An improved asperity contact model for two rough surfaces with misalignment is presented in this study. The contact model is statistical and can account for the elasto-plastic behavior of interacting asperities. By combining the improved asperity contact model and the average flow Reynolds equation together, a mixed-lubrication model is developed to understand the effect of surface texturing. By comparing with the results of the purely elastic asperity contact model, it is found that the improved asperity contact model can predict the contact force and actual contact area more accurately, particularly under high load conditions. Moreover, comparing with the elasto-plastic model with an equivalent rough surface against a plane, the improved contact model can consider the effect of permitting misalignment of two rough surfaces. This is beneficial for analyzing the performance of the textured piston ring/liner system, especially when asperities contact and wear happen.