Abstract: 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 PubDate: 2020-08-01

Abstract: Abstract In this paper, we examine the transient response of two bonded dissimilar functionally graded magneto-electro-elastic (MEE) layers with multiple interfacial cracks under magneto-electro-mechanical impacts. Material properties of the MEE layers are assumed to vary exponentially in the thickness direction of the layers. However, the rate of material properties gradation are different. First, the analytical solution is developed by considering a dynamic magneto-electro-elastic dislocation with time-dependent Burgers vector be situated at the interface of bonded layers by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the MEE layers containing interfacial cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the field intensity factors and the dynamic energy release rate. The effects of crack spacing and FGM exponent as well as crack interaction are studied. PubDate: 2020-08-01

Abstract: Abstract This article investigates size-dependent nonlinear dynamic modeling and vibration analysis of nanomechanical resonators equipped with piezoelectric layers employing perturbation methods. For nonlinear dynamic modeling, the nanomechanical beam resonator is modeled based on the nonlocal elasticity theory and von-kármán type of nonlinear formulation. Then, the Hamilton’s principle is employed to derive the nonlinear vibration equation of the piezoelectric laminated beam resonator. The Galerkin separation approach is employed to develop the governing equation as a time-dependent nonlinear differential one which is solved by the multiple scales perturbation method. Obtaining an analytical formulation, a detailed study is conducted to investigate the size effects on nonlinear free vibration of the beam at several modes of vibration. The obtained results indicate that the nonlocal parameter causes a reduction effect on the nonlinear frequencies particularly for its higher values and higher modes of vibration. Also, it is observed that the nonlocal effect on the natural frequencies diminishes with an increase in the vibration amplitude. PubDate: 2020-08-01

Abstract: Abstract The trajectory of a ball impacting with an angle on a rigid boundary is recorded with a high-speed camera and the dynamics is reconstructed in a computer. Several experiments are carried out in order to obtain statistical distributions of the trajectory. On the other hand, a continuum model of a viscoelastic material ball simulates the experiment. If the values of the constitutive parameters (e.g. elastic and viscous modulus, friction coefficient, etc.) in the numerical model are correct, the simulated dynamics and the experimental data should match. In this study, the Bayesian inference is applied to identify two constitutive parameters (the friction and viscous coefficients) through statistical measures. The methodology shows to provide a useful tool to solve an inverse problem with a stochastic approach which allows to reference the results in a statistic frame starting from indirect and sparse information. PubDate: 2020-08-01

Abstract: Abstract Precise prediction of collapse pressure is a key role in structural integrity assessment of piping systems. The present study uses an \(\hbox {Al}{-}\hbox {Al}_{\mathrm {2}}\hbox {Cu}\) functionally graded (FG) pipe fabricated through horizontal centrifugal casting technique to empirically investigate its mechanical responses under hydrostatic pressure test. The evolutions of deformations correspond to the external surface of the FG pipe in the axial and hoop directions recorded by strain gauges and data acquisition during pressurization are outlined. Moreover, finite element simulation using user subroutine USDFLD implemented into the commercial software ABAQUS is applied to numerically study the tested FG pipe under similar environmental and loading conditions used in the experimental procedure. Eventually, the experimental results reveal that the final internal pressure and corresponding impact energy of the tested FG pipe fails in a brittle manner are 165 bar and 30.4545 KJ, respectively. Moreover, microstructure observations of the fracture surfaces are performed using scanning electron microscope (SEM). PubDate: 2020-08-01

Abstract: Abstract In this contribution, a constitutive model is proposed for filled rubber-like materials to describe hysteresis. The model is based on the network decomposition concept. Rubber matrix is decomposed into purely elastic and deformable networks. The Gent model is considered to model the purely elastic network. The deformable network is simulated by using the freely jointed chain concept, a probability density function of the chain length and the network alteration theory. Damage in a network is assumed as a debonding of polymer chains from filler surface, which evolves with respect to the chain length over the set of available chains. In the consecutive loading cycles, a new network rearrangement is accounted for the characterization of the hysteresis behavior. Debonded chains in the damaged network are considered to rebond up to the point of the permanent set. The model contains seven material parameters and was successfully tested on the sequential cyclic uniaxial tensile test data of filled rubbers having different filler concentrations. PubDate: 2020-08-01

Abstract: Abstract This work proposes a new constitutive model that takes into account the asymmetry of Ti–6Al–4V, its microstructural state and its pronounced anisotropy in order to improve the use of this titanium alloy in biomechanics and aeronautics in particular. The choice of the stress directions and their effect on shaping procedures in light of accounting the effect of heat treatment on the behavior of Ti–6Al–4V, hardness and microstructural defects is important. The fracture surfaces of a material specimen subjected to traction/compression is examined using scanning electron microscope. An appropriate choice of the model is necessary through experimental validation. The use of this alloy in the biomechanical field brings into consideration several factors such as different solicitations and uniaxial loads, and tension-compression asymmetry...as well as in the aeronautical field other factors such as material strength and ductility in shaping under certain heat treatment are considered. PubDate: 2020-08-01

Abstract: Abstract Instead of the traditional method of utilizing the extremal values of Rayleigh quotient, in this research we develop an upper bound theory to determine the natural frequencies in a linear space of boundary functions. The boundary function will have the following restrictions: boundary conditions are satisfied, fourth-order polynomial at least with unit leading coefficient. It proves that the maximum value of Rayleigh quotient in terms of kth-order boundary function builds a good upper bound when the \((k - 3)\)th-order natural frequency is approximated. There are four boundary conditions of the beam, so the fourth-order boundary function is unique without having any parameter. On the contrary, the kth-order boundary function has \(k-4\) free parameters, which leave us a chance to optimize them. We employ the orthogonality to derive the higher-order optimal boundary functions from the lower-order optimal boundary functions exactly, which are constructed sequentially by starting from the fourth-order boundary function. We examine the upper bound theory for uniform beams under three types of supports, and the single- and double- tapered beams under cantilevered support. Comparison is made between the first four natural frequencies with the exact/numerical ones, which proves the usefulness of the upper bound theory. PubDate: 2020-08-01

Abstract: Abstract In this paper, the buckling and free vibration of a Mindlin plate with a side crack are presented considering a uniaxial in-plane compressive or tensile load. The side crack is through the thickness of the plate. In the Ritz method, a series of corner functions are incorporated into the admissible functions which consist of the modified characteristic functions. With this treatment, one can describe the singularity in stress near the tip of the crack as well as the discontinuities in both displacement and bending rotations across the crack. The buckling loads and natural frequencies are solved through eigenvalue problems considering the existence of the crack. The effects of location, length and orientation of the crack on the buckling and free vibration of the loaded plate are demonstrated. The coupling effect of the crack and the in-plane load on the vibrational characteristics of the plate is analyzed with varying parameters. It is shown that the influences of the tensile and compressive preloads are enhanced by the crack, and the tensile preload can cause the low-order frequency to increase with the growing crack. PubDate: 2020-08-01

Abstract: Abstract High-Q micromechanical resonators have been studied intensively because of the tunable performance and the associated potential applications. Nevertheless, some designs experience long relaxation times which hinder fast switching applications. We investigate an open-loop control, an intentional and confined time-periodic variation, that is capable of reducing the transient time allowing rapid switching times. The physical phenomenon is described in detail and analysed using a singular perturbation technique. Analytical conditions are developed for designing future experimentation. The control is proven numerically for an exemplary micromechanical resonator. PubDate: 2020-08-01

Abstract: Abstract An efficient and nonlinear form-finding method is proposed for symmetric cable–strut structures with complex geometry or many nodes. Expressed in the symmetry-adapted coordinate system, the first block matrix of the symmetry-adapted tangent stiffness matrix is extracted using the full symmetry subspace, which is much smaller-sized and associated with the first irreducible representation of a symmetry group. Then, this stiffness submatrix and the principle of minimum potential energy are adopted for the fast but stable convergence of the initial configuration to the stable configuration. During the form-finding process, the generalized inverse of a matrix and modification for the minimum eigenvalues are employed, to guarantee the positive definiteness of the stiffness submatrix. The form-finding process can start from an arbitrary initial configuration, whereas only certain symmetry group, and the connectivity pattern and the initial lengths of the members should be given in advance. A few numerical examples are illustrated to show the efficiency and accuracy of the form-finding method for cable–strut structures with complex geometry and different symmetry. PubDate: 2020-08-01

Abstract: Abstract A new linear yield criterion in terms of principal stresses is developed for the purpose of overcoming the analytical difficulty of mechanical parameters when using the nonlinear Mises yield criterion. This developed yield criterion is established through the parabola interpolation method and the mathematical averaging method, which can be called as the mean influence factor yield criterion, or called MIF yield criterion for short. The yield locus of the criterion on the \(\pi \)-plane is an equilateral and non-equiangular dodecagon, lies between the Tresca and TSS loci, and is very close to the locus of the Mises yield criterion. By comparing with the classical yield criteria, the MIF yield criterion varies linearly with the Lode parameter and has a good accuracy with experimental data. Moreover, based on the flow rule and the geometric projection of the principle stress components, the specific plastic work rate of the yield criterion is also derived. The criterion and its specific plastic work rate are used to solve the limit load of a simply supported circular plate and the forging of a rectangular bar, and both the corresponding analytical solutions are obtained. The theoretical results for the limit load and the forging force are in good agreement with the simulation and experimental data, respectively, and are more accurate than the results calculated from other yield criteria. PubDate: 2020-08-01

Abstract: Abstract Due to the large surface/interface-to-volume ratio, surface/interface effect in nanomaterials begins to play an important role in changing the constitutive law seen in classical elasticity theory. This work investigates the size-dependent elastic field of nano-inhomogeneity due to interface and interphase effect, respectively. Closed-form solution to the elastic field of nano-inhomogeneity with interface and interphase effect is found. For comparison, the numerical result of InAs/GaAs system is provided as an example, which demonstrates that interface and interphase effect could have significant influence on the elastic field of nano-inhomogeneity. The continuity/discontinuity of the elastic field of nano-inhomogeneity with interface and interphase effect is discussed in detail. It is verified both numerically and analytically that the elastic field from interphase effect tends to converge to that from interface effect when the interphase thickness shrinks to zero. Furthermore, all results converge to the classical solution at positions far away from the interfacial region, so it is unnecessary to distinguish interface or interphase effect at positions far away from the interfacial region in practical situations. PubDate: 2020-07-11

Abstract: Abstract Based on the Hamilton’s principle, a nonlinear mathematical model of the cantilever-type piezoelectric energy harvester with a tip mass is systematically derived under parametric and external excitations. The proposed model accounts for geometric and electro-mechanical coupling nonlinearities, damping nonlinearity and the inextensibility condition of beam. Using the Galerkin approach, the proposed model is converted into the electro-mechanical coupling Mathieu–Duffing equations. Analytical solutions of the frequency–response curves are presented by the multiple scales method. Nonlinear characteristics of the energy harvesters are explored under parametric excitation and hybrid parametric and external excitations. Analytical results provided new insights into the effects of tip mass and nonlinear damping on the performance of the energy harvester. The results show that with the tip mass increasing, the frequency–response curves of the energy harvester change from the nonlinear hardening type to the nonlinear softening type and the operating bandwidth and the output voltages of the energy harvester enlarge. For parametrical excitation, variation of the quadratic damping does not alter the initial threshold of the harvesters and the position of two transcritical bifurcation points of the frequency–response curves. The initiation threshold decreases with the tip mass increasing. Hybrid parametric and external excitations enhance the bandwidth and output voltage of the energy harvester, which will probably be used as an ideal way to improve the performance of the energy harvesting system. PubDate: 2020-07-11

Abstract: Abstract The problem of vibrations generated in a homogeneous and isotropic elastic half-space by spatially concentrated forces, known in Seismology as (part of) the Lamb problem, is formulated here in terms of Helmholtz potentials of the elastic displacement. The method is based on time Fourier transforms, spatial Fourier transforms with respect to the coordinates parallel to the surface (in-plane Fourier transforms) and generalized wave equations, which include the surface values of the functions and their derivatives. This formulation provides a formal general solution to the problem of forced elastic vibrations in the homogeneous and isotropic half-space. Explicit results are given for forces derived from a gradient, localized at an inner point in the half-space, which correspond to a scalar seismic moment of the seismic sources. Similarly, explicit results are given for a surface force perpendicular to the surface and localized at a point on the surface. Both harmonic time dependence and time \(\delta \) -pulses are considered (where \(\delta \) stands for the Dirac delta function). It is shown that a \(\delta \) -like time dependence of the forces generates transient perturbations which are vanishing in time, such that they cannot be viewed properly as vibrations. The particularities of the generation and the propagation of the seismic waves and the effects of the inclusion of the boundary conditions are discussed, as well as the role played by the eigenmodes of the homogeneous and isotropic elastic half-space. Similarly, the distinction is highlighted between the transient regime of wave propagation prior to the establishment of the elastic vibrations and the stationary-wave regime. PubDate: 2020-07-11

Abstract: Abstract In this paper, we investigate the problem for a classical piezoelectric vibration energy harvester. Exact theoretical solution to the problem is derived and compared to the solutions proposed in the literature. Asymptotic expansions of the solution are explored in the hope of finding a plausible simpler approximation of the solution and corresponding output performance measures. Dependence of the output performance measures upon the electromechanical coupling factor is therefore studied. Some tips are then provided for the design of piezoelectric energy harvester. PubDate: 2020-07-08

Abstract: Abstract The paper presents a new method for the identification of joint friction, reductor self-locking and gear backlash parameters. The method was developed using an existing hexapod robot. During the process, the motor driving currents given by the model and measured on the real device were observed and compared. Initially, the current curves showed specific differences. After the analysis of these deviations, their causes were identified as joint friction, reductor self-locking and gear backlash. The parameters of these phenomena were determined using swarm optimization. As a result of this process, a validated model was obtained. The mentioned mechanical properties were identified using a step-by-step method, in which one property aided in the discovery of another. The robot model was created in a MATLAB/Simulink environment, using the Simscape Multibody Toolbox. PubDate: 2020-07-01

Abstract: 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. PubDate: 2020-07-01

Abstract: 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. PubDate: 2020-07-01

Abstract: Abstract This paper focuses on the effects of the boundary wall thickness and the velocity power index parameters on a steady 2D mixed convection flow along a vertical semi-infinite moving plate with non-uniform thickness. The effects of diffusion on the velocity, temperature and concentration fields with power-law temperature and concentration distributions at the plate surface are also analyzed. A shooting technique is adopted to obtain dual solutions for the system of nonlinear coupled ordinary differential equations. The significant impacts on the boundary layer development along the boundary surface have been noticed due to the non-flatness of the moving surface. It is noted that the velocity, temperature and concentration profiles admit dual solutions for certain range of unsteadiness parameter. Both, upper and lower branch, solutions are presented to display the effects of the boundary wall thickness and the velocity power index on the flow, thermal and concentration fields. A stability analysis is performed to determine the existence of dual solutions. PubDate: 2020-07-01