Authors:Zai-lin Yang; Chong-qun Zhang; Guan-xi-xi Jiang; Pei-lei Yan; Yong Yang Abstract: The complex function method is applied in the solution of the scattering problem for an irregularly shaped boundary in an infinite inhomogeneous elastic medium, which is deduced from the scattering problem in a homogeneous one. The potential function of the scattering wave which is generated by the irregularly boundary is obtained by applying the complex function method in the inhomogeneous medium. The reduced Helmholtz equation with variable coefficients is solved by separation of variables. Then, the potential function is expressed as the complex domain functions series. By truncating a set of infinite algebraic equations, the coefficient of the series are determined. In order to verify the validity of this method, the wave equation in a inhomogeneous medium is degenerated to the equation with constant coefficients. The domain function is discussed. The dynamic stress concentration factor around an elliptical cavity is calculated in an exponentially inhomogeneous medium. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1876-6

Authors:H. B. Zhao; H. Feng; F. Liu; Y. W. Liu; P. H. Wen Abstract: A theoretical model is developed to investigate the effects of the nanoscale twin and the dislocation pileup at the twin boundary on crack blunting in nanocrystalline materials. In the model, the nanoscale twin as a stress source approximately equals a quadrupole of wedge disclination. Using the complex variable method, the complex form expressions of the stress field and the force field are derived. The critical stress intensity factors (SIFs) for the first dislocation emission from the crack tip are calculated. The effects of the dislocation pileup, disclination strength, twin size, twin orientation, twin position and crack length on the critical SIFs are discussed in detail. Moreover, the shielding/anti-shielding effect produced by the twin, the dislocation pileup at the twin boundary and the first dislocation emitted on the crack tip is discussed. The results show that both the twin and the dislocation pileup at the twin boundary would suppress the dislocation emission from the crack tip. The suppressive effect induced by the dislocation pileup at the twin boundary is much stronger that that by the twin. Meanwhile, the emission angle has a significant effect on the mode I shielding/anti-shielding effect on the crack tip a. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1874-8

Authors:L. Cveticanin; M. Zukovic; D. Cveticanin Abstract: In this paper the energy harvester device with piezoelectric element is considered. In the device the mechanical energy of vibration is transformed into electric energy. The mechanical part of the system contains an oscillator which is coupled with a motor. The motor–oscillator system is of non-ideal type. Namely, the motion of the oscillator is affected by the motor excitation, but the oscillator also has an influence on the motion of the motor. In the paper the influence of nonlinear properties of the oscillator and of the piezoelement is considered. Analytical procedure based on averaging is developed. Special attention is given to averaging of the harvested energy of the system. The influence of the linear and of the nonlinear coupling piezoelectric parameter is considered. The Sommerfeld effect is treated. The region of unstable solutions is reduced by increasing the value of the nonlinear piezoelectric parameter. The analytically obtained solutions are compared with numerically obtained ones. They are in good agreement. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1878-4

Authors:Shahriar Dastjerdi; Mohammad Abbasi; Leila Yazdanparast Abstract: In this research, the nonlinear local and nonlocal analysis of an annular sector plate is studied and solved based on a new modified higher-order shear deformation theory. Due to the shortcomings of HSDT in the two-dimensional nonlinear analysis, it is modified by eliminating the defects, and a comprehensive theory is presented for analyzing the mechanical behavior of an annular sector sheet in general form. The strain field is developed by considering the von Karman assumptions and also the nonlocal theory of Eringen from which the classical local analysis can be deduced conveniently by neglecting the small-scale effects. Whereas the annular sector plate is assumed, the sector, annular/circular, rectangular and solid circular plates can be simulated. Afterward, the nonlocal constitutive equations are derived and solved by using the two-dimensional SAPM (Dastjerdi et al. in Compos B Eng 98, 78–87, 2016). Moreover, a combination of the extended Kantorovich method and one-dimensional SAPM is applied. Since the presented theory is relatively new and similar studying was not available in order to compare the results, a comparison is done with the results of lower-order theories. Finally, the effect of various parameters, such as boundary conditions, different theories, nonlocal and local analyses, loading and the size of the plate, on the mechanical behavior of an annular sector plate are investigated. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1872-x

Authors:D. V. Dung; Pham Minh Vuong Abstract: In this paper, FGM toroidal shell segments surrounded by elastic foundation and subjected to uniform external pressure are investigated by analytical method. A novelty of the study is that the Reddy’s third-order shear deformation shell theory (TSDT) with von Karman geometrical nonlinearity combined with deflection function selected with three terms is used to investigate the nonlinear stability of thicker FGM toroidal shell segments. In addition, the thermal element in the shell is also taken into account. The FGM shell is a convex and concave toroidal shell segment. It is a general form for a circular cylindrical shell. Closed-form expressions for determining the static critical external pressure load and postbuckling load–deflection curves are obtained. Effects of temperature field, foundations, material and dimensional parameters on the stability of shells are considered. This paper also shows that the use of TSDT to analyze the nonlinear stability of thicker toroidal shell segments is necessary and more suitable. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1888-2

Authors:M. Mete Ozturk; A. Bhattacharyya Abstract: With a view toward contributing to the state of the art in the research on shape memory alloy memory storage devices, the thermal response of a shape memory alloy (SMA) thin film during a complete cycle of heating and cooling is computationally addressed in this communication. The ultimate objective is to provide a better understanding of shape memory alloys within the context of the characteristics of thermally activated phase-transforming materials as candidate materials for memory devices. In this study, the effect of the current density, thickness of the SMA thin film, convection and boundary conditions on the transformation of the SMA thin film are investigated. In particular, we study the effect of pulse heating as that is important for memory devices. A comparison is made between the cyclic response time of a an SMA unit cell and an Ovonic unit memory (OUM) cell. The total cycle time for the SMA cell and the OUM cell is 0.7 and 60 ns, respectively. The total energy consumption per cycle for the SMA cell and the OUM cell is 0.441 and 37.8 pJ, respectively. While the response of the SMA cell is almost two orders of magnitude better than the OUM cell, we want to strike a cautionary note that the results for the SMA cell are computational and those for the OUM cell are experimental in nature. Regardless, we hope that the outcomes for the SMA cell will provide some motivation for research in SMA-based memory devices. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1879-3

Authors:Petr Tovstik; Tatiana Tovstik Abstract: A study is carried out of a thin plate of constant thickness made of linearly elastic material which is transversally isotropic and heterogeneous in the thickness direction. Asymptotic expansions in powers of the relative plate thickness are constructed, and the bending equation of second-order accuracy (the SA model) is delivered. The results of the SA model are compared with the Kirchhoff–Love classical model and with the Timoshenko–Reissner (TR) model, as well as with the exact solution. To this end, some problems for a functionally gradient plate bending, and for a multi-layer plate bending and free vibration are solved and analysed. The range of plate heterogeneity, for which the error of the approximate models is small, is established. The TR model and the SA model are proved to yields results close to each other and the exact results for a very broad range of heterogeneity. That is why the generalized TR model for one-layered homogeneous transversely isotropic plate is proposed. Parameters of this model are chosen so that the results are close to the exact results and the results by the SA model. For the Navier boundary conditions, the analytical solution of 3D problems for a rectangular heterogeneous plate is constructed. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1880-x

Authors:Abdolreza Pasharavesh; M. T. Ahmadian; H. Zohoor Abstract: As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and adding concentrated tip masses where both result in a sensitivity enhancement as well. Therefore, according to the amplitude and frequency of applied excitations and physical parameters of the harvester, large amplitude motions can occurr in these systems. In this study, nonlinear dynamics of a piezoelectric harvester under large amplitude vibrations is investigated. To that end first of all an accurate comprehensive fully coupled electromechanical nonlinear model is extracted through a constrained Hamilton’s variational principle. A semi-analytical approach implementing the perturbation method of multiple scales is used to solve the governing coupled nonlinear differential equations of the model and analyze the primary and superharmonic resonances. Results indicate that as excitation grows, the output power response curves are right bended leading to enhancement of the harvester bandwidth. At primary resonance a second-order harmonic of the excitation frequency is present in the output voltage as a consequence of both nonlinear curvature and inertia due to shortening effect. Furthermore, the existence of superharmonic resonances makes it possible to extract considerable amounts of power at fractions of natural frequency which is very beneficial in MEMS-based harvesters with generally high resonance frequencies. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1864-x

Authors:Shishir Gupta; Neelima Bhengra Abstract: This paper presents an outcome of the broader effect to assess the importance of magnetoelasticity, compressive and tensile initial stress in soil dynamics. Haskell’s matrix technique is employed to investigate the SH-wave propagation in a multilayered magnetoelastic orthotropic (MMO) medium. The dispersion relation for the total ( \(n-1\) ) layers lying over a half-space is obtained in a closed form. Special cases are derived for both the single and double layers, and the obtained relations are found to be in good agreement with the Classical Love wave equation. Based on the finite difference technique, a stability analysis is performed to reduce the escalation of errors to make it stable and convergent. The expression for the phase and group velocities is attained by this technique when the SH-wave propagates across the MMO medium. Numerical computations and graphical exhibition have been carried out to show the effects of different values of the magnetoelastic coupling parameter, compressive and tensile initial stresses and courant number on the phase and group velocities. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1884-6

Authors:Pankaj Kumar; Anirvan DasGupta; Ranjan Bhattacharyya Abstract: In this paper, a study of bulk wave propagation in a layered half-space and the corresponding surface motion characteristics is reported. Two different types of layer material, namely elastic and viscoelastic, are considered. In both cases, the half-space is modeled as an elastic medium. The displacement functions are obtained for the free surface material point motion. In general, the free surface material point motion in a layered half-space is elliptical with certain aspect ratio and orientation. The aspect ratio and orientation depend upon the incident wave and medium properties. The effects of various parameters of the viscoelastic media on the material point motion are studied. The dependence of phase velocity and quality factor on frequency is derived using the creep function of the viscoelastic medium. The effects of various controllable parameters on the characteristics of surface displacement and material point motion are presented and discussed. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1868-6

Authors:M. Mohammadzadeh-Keleshteri; S. Samie-Anarestani; A. Assadi Abstract: In this study, considering surface and bulk residual stresses, size- and orientation-dependent nonlinear bending, large amplitude vibration and postbuckling of single-crystalline nanoplates with cubic anisotropy are studied. Based on the first-order shear deformation plate theory, von-Karman geometrical nonlinearity and Gurtin-Murdoch theory, the model is formulated. In order to discretize the governing equations along with different combinations of boundary conditions, the generalized differential quadrature method is used and then a direct iterative method (Picard) is employed to solve the nonlinear system of equations. The presented results reveal that when thickness of the nanoplate increases, especially at high orientation and anisotropicity, ignoring shear deformation could cause some noticeable errors in the response of nonlinear bending, large amplitude vibration and postbuckling of nanoplates. Moreover, although orientation has a very direct effect on large amplitude vibration of nanoplates, it is observed that at a specific amplitude, the natural frequencies are independent from the orientation. The results of this study show that geometrical nonlinearity could be ignored in analyzing large amplitude vibration and postbuckling of highly anisotropic nanoplates in the [110] direction. PubDate: 2017-06-17 DOI: 10.1007/s00707-017-1862-z

Authors:Minsung Kim; Jintai Chung Abstract: In this paper, a new dynamic model for a pulley–belt system is proposed, in which the system considers not only the deflection of a belt but also the rigid-body motion of pulleys. This paper focuses on the effects of the rigid-body motion, which determines the dynamic characteristics of the pulley–belt system with spring supports. To this end, by using Hamilton’s principle, four linear governing equations of motion and eight boundary conditions are derived. The Galerkin method is used to discretize the equations of motion. The eigenvalue problems are solved to analyze the natural frequencies and mode shapes that are affected by the rigid-body motion of the system. The natural frequency loci veering and mode exchange are investigated for different moving velocities of the belt and various values of the spring constant. In addition, the beat phenomena in the upper and lower belts are also analyzed. Based on these analyses, we show that the natural frequency veering and beat phenomena are caused by a coupling effect between the rigid-body motion and belt deflection in the pulley–belt system. PubDate: 2017-06-07 DOI: 10.1007/s00707-017-1882-8

Authors:Xu Wang; Peter Schiavone Abstract: We investigate the time-dependent deformations of multilayered isotropic elastic cylindrical panels with interfacial diffusion and rate-dependent sliding under thermomechanical loads. The state-space approach is found to be extremely effective for the analysis of a cylindrical panel composed of an arbitrary number of layers. We show that when a particular condition is met, the thermal loading will not induce any thermal stresses in the cylindrical panel. To demonstrate our results, we present the evolving displacements and stresses in a three-layered panel induced by sinusoidal temperature variation and normal traction applied to its upper surface. In addition, we present all 198 relaxation times corresponding to a 100-layered panel. PubDate: 2017-06-07 DOI: 10.1007/s00707-017-1886-4

Authors:Esmaeal Ghavanloo Abstract: In this study, we investigate the axisymmetric deformation of a geometrically imperfect circular graphene sheet subjected to a uniform radial load using nonlocal elasticity theory. Due to the imperfection of the graphene sheet, an inhomogeneous version of Bessel’s equation is derived as a nonlocal governing equation of the system. Closed-form expressions are obtained to predict the deformations of the graphene sheet as functions of the radius, small-scale coefficient, initial imperfection, and bending rigidity of the graphene sheet. Furthermore, relations are proposed to determine critical radial loads. The present model indicates that it is necessary to include the effect of an initial imperfection as well as the small-scale effect. PubDate: 2017-06-07 DOI: 10.1007/s00707-017-1891-7

Authors:C. L. Li; Q. Han; Y. J. Liu Abstract: This paper considers elastic wave propagation in seven-wire parallel strands. Under a transverse distributed force, the stress state of seven-wire strands is derived from the Hertzian theory, which is regarded as the prestress state for the dynamic analysis. According to the wave finite element method, the elastodynamic equation with prestress is discretized corresponding to harmonic wave motion. Firstly, the results are verified by the semi-analysis finite element method. Then, dispersion properties in seven-wire parallel strands are computed and compared to those of double cylindrical rods. Besides, the results from parallel strands and helical strands indicate that wave propagation in the former is significantly different from that in the latter. For the deep understanding of wave characteristics, the displacement vectors are used to identify the propagating modes. It is found that there is only one torsional-like mode which rotates with a twist center in the whole region. Meanwhile, it is found that the variation of prestress has large influence on the torsional-like mode for low frequencies, but little on propagating modes for high frequencies. In addition, there appears the notch frequency and the effect of prestress on it is discussed in detail. The notch frequency decreases with the rising of the prestress in a certain range. PubDate: 2017-06-07 DOI: 10.1007/s00707-017-1860-1

Authors:Mingshi Wang; Qinghua Qin; T. J. Wang Abstract: The dynamic response of physically asymmetric rectangular sandwich plates with metal foam core subjected to blast loading is investigated analytically and numerically. The so-called ‘bounds’ of analytical solutions for the maximum central deflection of back face-sheets and the structural response time are obtained, respectively, by employing the yield criteria for an asymmetric sandwich structure including core compression. Furthermore, an improved membrane mode analysis considering the ‘residual’ bending moment for asymmetric sandwich plates is presented and the membrane mode solutions are given. It is shown that there is a good agreement between the theoretical predictions and the numerical results. Based on the analytical formulae, optimal design charts are constructed to maximize the impulsive resistance of physically asymmetric sandwich plates for a given mass. Finally, the performances of optimally designed sandwich plates with various face-sheet material combinations are discussed. PubDate: 2017-06-07 DOI: 10.1007/s00707-017-1870-z

Authors:Gongxi Zhang; Hailong Wang; Shengping Shen Abstract: The thermal growth of the oxide scale between the ceramic coating and substrate due to high-temperature oxidation is regarded as the dominating cause for the failure of the ceramic/substrate system, for example the thermal barrier coating. Based on the irreversible evolution equations, the growth strain in the oxide scale is formulated by considering the coupling effects of stress and chemical reaction during isothermal oxidation. A model which accounts for the growth strain, thermal expansion strain, and viscoplastic effect is developed for the stress analysis of the oxide scale. Numerical results reveal that there is a significant gradient in the oxide scale with the maximum compressive stress at the oxide/substrate interface and the minimum compressive stress at the ceramic/oxide interface, and the stress in the oxide scale is larger than those in the ceramic coat and bond coat. The effects of the growth strain, viscoplasticity, chemomechanical coupling, and chemical reaction on the stresses are numerically discussed. PubDate: 2017-06-03 DOI: 10.1007/s00707-017-1887-3

Authors:Jena Jeong; Hamidréza Ramézani; Nordine Leklou Abstract: In the present paper, the original micro-dilatation theory or the so-called void elasticity and classical elasticity have been firstly implemented as the cement paste and aggregates, respectively. The effect of crystallization pressure driven by the delayed ettringite formation across the cement-based materials has been computed and studied via the micro-dilatation theory and the Monte Carlo simulation. The micro-mechanically motivated crystallization pressure is computed by means of the microscale constitutive parameter of the micro-dilatation theory to obtain the current porosity and assess the swelling deformations herein. Two-phase material assumption, i.e., cement paste and aggregates, has been taken into account. Due to the fact that the crystallization pressure strongly depends on the irregular pore shapes and heterogeneous supersaturation conditions, the Monte Carlo simulation has been successfully achieved to predict the current porosity and crystallization-based stress tensor. The preliminary numerical outcomes fairly agreed with the experimental observations coming from scanning electronic microscope. PubDate: 2017-06-03 DOI: 10.1007/s00707-017-1863-y

Authors:Wei Wang; Liping Liu Abstract: Our understanding of nonlinear dynamics critically hinges on rigorous closed-form solutions to nonlinear wave equations; few closed-form solutions have been achieved for physics-based interaction models beyond one-dimensional space. In this paper, we investigate the dynamics of a two-dimensional lattice with harmonic, weakly nonlinear, and strongly nonlinear interactions. Assuming nearest neighbor interaction, we derive the continuum approximation of the discrete system in the long-wavelength regime while keeping the Hamiltonian structure of the system. For a hexagonal lattice with nontrivial shear resistance, we surprisingly find that solitary wave solutions exist in certain directions related to the underlying symmetries of the lattice. The properties of the solitary waves are also studied by numerical simulations of the original discrete system. Besides being of fundamental scientific interest, the solitary wave solutions in nonlinear hexagonal lattices are anticipated to have applications in the design of shock absorbers, acoustic lens, or nondestructive structural testing devices, among many others. PubDate: 2017-06-03 DOI: 10.1007/s00707-017-1881-9

Authors:Sk. M. Subhani; S. Maniprakash; A. Arockiarajan Abstract: Composite structures which show magneto-electric (ME) coupling behavior have a wide range of engineering applications. In this work, a composite structure comprising of a ferroelectric and a magnetostrictive material is taken for investigation. First, the nonlinear responses of the ferroelectric material and the magnetostrictive material are studied separately by experiments. In order to predict the nonlinear response, a thermodynamically consistent macroscopic model is proposed for the ferroic materials. Model parameters are then estimated from the experimental data, and the simulated results based on the proposed model are presented. Results from the theoretical model are in agreement with the experimental data. Subsequently, a homogenization procedure is introduced to find out the nonlinear response of a layered ME composite structure, and the obtained results are discussed. PubDate: 2017-06-03 DOI: 10.1007/s00707-017-1889-1