Authors:Mohammad Shishesaz; Mohammad Hosseini; Khosro Naderan Tahan; Amin Hadi Abstract: Abstract In this paper, the thermoelastic behavior of a functionally graded nanodisk is studied based on the strain gradient theory. It is assumed that the nanodisk thickness is constant, and a power-law model is adopted to describe the variation of functionally graded material properties. Furthermore, the nanodisk angular acceleration is taken to be zero while it is subjected to an axisymmetric loading. Also, it is assumed that any variation in temperature occurs only in the radial direction. The equilibrium equation and the boundary conditions are deduced from Hamilton’s principle. The obtained results are compared with those of classical theory. These results show that both theories predict the same trend for the variation in radial displacements. The differences between the stresses obtained from classical and strain gradient theories are clearly highlighted. Increasing the value of the material inhomogeneity parameter, n, considerably affects the magnitudes and the corresponding peak values of the high-order stress \(\bar{\tau }_{rrr}\) . Any rise in temperature at the outside radius has a direct effect on the total stresses and radial displacements in the nanodisk. Also, the effects of external load at the inner and outer radii on radial displacement as well as stress components are fully investigated. PubDate: 2017-08-01 DOI: 10.1007/s00707-017-1939-8

Authors:Olivian Simionescu-Panait; Iulian Ana Abstract: Abstract The transverse-horizontal wave propagating in a semi-infinite piezoelectric solid with hexagonal symmetry subject to initial electromechanical fields is investigated in this paper. The electromechanical boundary value problem is solved, and the phase velocity, the displacement, and the electric potential are obtained. For a metallized boundary surface, the dependency of the solution on the initial fields for several piezoelectric crystals is analyzed. These results may be proved useful to model the propagation of waves in anisotropic piezoelectric structures subject to a bias, serving as a benchmark for further numerical and experimental approaches. PubDate: 2017-07-31 DOI: 10.1007/s00707-017-1931-3

Authors:A. Alibeigloo; A. Rajaee Piteh Noee Abstract: Abstract In this paper, static and free vibration analysis of a sandwich cylindrical shell is performed using theory of elasticity formulation. The core layer is made of functionally graded material with material properties varying along the thickness direction according to a simple power law. For the case of simply supported boundary conditions, equations of motion and equilibrium equations are solved analytically by applying a state-space technique along the radial direction and Fourier series expansion along the axial and circumferential direction. When boundary conditions are not simply supported, a semi-analytically solution is performed by using the differential quadrature method along the axial direction. The present approach is validated by comparing the obtained numerical results with those published in the available literature. Moreover, effects of boundary conditions, graded direction, mid-radius to thickness and length to mid-radius ratios on bending and vibration behavior are considered. PubDate: 2017-07-31 DOI: 10.1007/s00707-017-1914-4

Authors:B. S. Dandapat; S. Maity; S. K. Singh Abstract: Abstract The development of a two-layer thin film over a rough non-uniformly rotating disk with constant air shear is analyzed under the consideration of planar interface and free surface. von Kármán’s similarity variables are applied to transform the guiding Navier–Stokes equations into a set of coupled unsteady nonlinear partial differential equations. These equations with moving boundary conditions are solved using the finite difference method. Here, it is found that the azimuthal roughness slows down the film thinning rate and the radial roughness enhances the thinning rate slightly. Also, the effect of air shear on film thinning is discussed. For different types of rotation, effects on the flow due to azimuthal roughness, radial roughness, and air shear remain the same. PubDate: 2017-07-29 DOI: 10.1007/s00707-017-1933-1

Authors:Roberta De Luca; Salvatore Rionero Abstract: Abstract Via the longtime behavior of the perturbations to thermal conduction solution \(m_0\) , the nonlinear longtime behavior of Navier–Stokes fluid mixtures filling horizontal rotating layers uniformly heated from below and salted by one salt—either from above or below—is investigated. Via the existence of \(L^2\) -absorbing sets, it is shown that the perturbations to \(m_0\) are ultimately bounded. The onset of steady or oscillatory convection is analyzed. Via a Linearization Principle (Rionero in Rend Lincei Mat Appl 25:1–44, 2014) it is shown that the linear theory captures completely the physics of the problem since the linear stability implies the nonlinear global asymptotic stability in the \(L^2\) -norm. PubDate: 2017-07-28 DOI: 10.1007/s00707-017-1943-z

Authors:Zai-lin Yang; Guan-xi-xi Jiang; Bai-tao Sun; Yong Yang Abstract: Abstract Based on the complex function method and a multipolar coordinate system, scattering of shear waves by a cylindrical inclusion in an anisotropic (orthotropic) half space is studied. In order to find the solution of shear waves, the governing equation is transferred into its normalized form. Then, the scattering wave in the half space and the standing wave in the inclusion are deduced. Different incident wave angles and anisotropies are considered to obtain the reflected wave. Then, the unknown coefficients in scattering wave and standing wave are found by utilizing the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. The results demonstrate that the distribution of the DSCF is influenced by the anisotropy of the half space, and the value of the DSCF is mainly affected by the wave numbers ratio and the shear modulus ratio. PubDate: 2017-07-28 DOI: 10.1007/s00707-017-1941-1

Authors:Hamidreza Kazemi; Farzad Shahabian; Seyed Mahmoud Hosseini Abstract: Abstract The stochastic meshless local Petrov–Galerkin method is employed for dynamic analysis of cylinders made of fully saturated porous materials with considering uncertainties in the constitutive mechanical properties. The porous cylinder is assumed to be under shock loading. To approximate the trial functions in the radial point interpolation method, the radial basis functions are utilized. The Monte Carlo simulation is used to generate the random fields for mechanical properties. The results are obtained for various random variables, which are simulated by uniform, normal and lognormal probability density functions with various coefficients of variation (COV), changing from 0 to 20%. The obtained results from the presented stochastic analysis are compared to those obtained from analysis with considering deterministic mechanical properties. The results show that the uncertainty in mechanical properties has a significant effect on the structural responses, especially for big values of COVs. PubDate: 2017-07-28 DOI: 10.1007/s00707-017-1898-0

Authors:A. M. Hussein Abstract: Abstract A method introduced by Yehia (J Phys A Math Gen 32:7565–7580, 1999 , for example) for generalizing known results of the problem of the motion of a rigid body is extended here to take magnetization by rotation (Barnett–London effect) into account. In the general case of anisotropic ferromagnets, the equations of motion are proved to be covariant under a one-parameter family of transformations which generalize the problem by inserting a parameter, with a definite physical meaning, into the dynamical equations. As an example, we generalize a particular solution of the problem of the motion of a gyrostat in a central field of attraction. It turns out that the generalized solution represents a new particular solution of the problem of the motion by inertia of a rigid body in an ideal incompressible fluid. PubDate: 2017-07-28 DOI: 10.1007/s00707-017-1937-x

Authors:Liping Tang; Jianguo Wang Abstract: Abstract A distributed-parameter model of cantilevered piezoelectric beam with a dynamic magnifier has been proposed for the efficient analysis of a piezoelectric energy harvester, but there appears no beam model suitable for a piezoelectric energy harvester with tip mass offset and a dynamic magnifier. To deal with tip mass offset, the size effect of tip mass offset on the kinetic equation and boundary condition has been considered. A modified model of cantilevered piezoelectric energy harvester with tip mass offset and a dynamic magnifier has been developed by using the generalized Hamilton’s principle. Analytical formulation of the eigenfunction and natural frequency of the modified model have been presented. The modified model has been demonstrated by parametric studies. The results obtained show that the harvesting power can be dramatically enhanced with proper selection of the design parameters of the dynamic magnifier and tip mass offset. The tip mass offset significantly affects the accuracy of the analysis. It is observed that even a small change in tip mass geometry results in a substantial change of energy harvester performance, not only to change the resonant frequency but also to affect the strain distribution along the energy harvester length. The modified model is more suitable for the harvester with tip mass offset and dynamic magnifier. PubDate: 2017-07-28 DOI: 10.1007/s00707-017-1910-8

Authors:Azadeh Bakhshandeh; Bahram Navayi Neya; Parvaneh Nateghi Babagi Abstract: Abstract In this research, by using displacement potential functions, the exact solution is presented for free vibration analysis of simply supported rectangular transversely isotropic plates with constant thickness. The displacement components of the plate are written in terms of displacement potential functions, and the governing differential equations are derived by the substitution of the displacement components in Navier’s equations. The two governing partial differential equations of fourth and second order are solved using the separation of variables method and satisfying the exact boundary conditions. Having no simplifying assumptions for the strain or stress distribution in the plate thickness, the obtained results in this paper are applicable to any arbitrary plate thickness with no limitation on its thickness ratio. Due to absence of available research on thick transversely isotropic plates, the obtained results are compared with other analytical works for thin and moderately thick plates and the finite element method for thick plates, showing remarkable agreement. Accurate natural frequencies are presented for different ranges of thickness ratio and aspect ratio and different materials. It is observed that with increasing thickness the ratio and aspect ratio of the plate, the non-dimensional natural frequencies decrease and increase, respectively. In addition, comparative results of isotropic material and four different transversely isotropic materials also illustrate that the shear modulus in transverse direction has important influence on the vibrational behavior of plates. PubDate: 2017-07-28 DOI: 10.1007/s00707-017-1916-2

Authors:A. A. Elmandouh Abstract: Abstract We consider the motion of a charged rigid body about a fixed point carrying a rotor that is attached along one of the principal axes of the body. This motion occurs under the action of the resultant of the uniform gravity field and the homogeneous magnetic field. The equations of motion are formulated, and they are presented by means of the Hamiltonian function in the framework of the Lie–Poisson system. These equations of motion have six equilibrium solutions. The sufficient conditions for instability for these equilibria are studied by utilizing the linear approximation method, while the sufficient conditions for stability are presented by means of the energy-Casimir method. For certain configuration of the body, the regions of Lyapunov stability and instability are determined in the plane of some parameters. Furthermore, we clarify that the regions of Lyapunov stability are a portion of the regions of linear stability. PubDate: 2017-07-26 DOI: 10.1007/s00707-017-1927-z

Authors:Fumio Narita; Koji Shikanai; Yasuhide Shindo; Kotaro Mori Abstract: Abstract This paper investigates the cyclic fatigue behavior in giant magnetostrictive materials with a crack under magnetic fields. Fatigue tests were performed in three-point bending with single-edge precracked-beam specimens, and the number of cycles to failure under sinusoidal mechanical loads and magnetic fields was obtained. A finite element analysis was also carried out, and the energy release rate was calculated. The effect of magnetic fields on the maximum energy release rate versus number of cycles to failure curve was then discussed. In addition, fracture surfaces were examined by scanning electron microscopy and laser microscopy to correlate with fatigue characteristics. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1925-1

Authors:Sergei Alexandrov; Woncheol Jeong Abstract: Abstract The objective of the present paper is to provide an efficient method for finding steady planar ideal plastic flows of anisotropic materials. The method consists of determining two mappings between coordinate systems. One of these mappings is between principal lines-based and characteristics-based coordinate systems, and the other is between Cartesian- and characteristics-based coordinate systems. Thus, the mapping between the Cartesian- and principal lines-based coordinate systems is given in parametric form. It is shown that the boundary value problem of finding the mapping between the principal lines-based and characteristics-based coordinate systems can be reduced to the solution of a telegraph equation where two families of characteristics are curved and to the evaluation of ordinary integrals where one family of characteristics is straight. In either case, after solving this problem the problem of finding the mapping between the Cartesian- and characteristics- based coordinate systems can be reduced to the evaluation of ordinary integrals. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1915-3

Authors:Juergen Schoeftner Abstract: Abstract This contribution focuses on bending moment tracking in slender beam-type structures that are equipped with piezoelectric actuators. Bending moments are associated with the axial stress, which is the dominant stress component of laterally excited beam structures. If the maximum value exceeds a certain tensile stress limit, the structures will crack or be irreparably damaged. In the present contribution, a piezoelectric bimorph beam is considered and it is investigated in which manner the piezoelectric actuation devices have to be distributed along the beam length, such that a certain bending moment distribution is obtained. This is called bending moment tracking. First, the basic equations of a piezoelectric bimorph beam are recalled and the differential equations for the bending moment are derived. Then a positive semi-definite integral depending on the error of the bending moment is defined, which is the difference between the actual and the desired bending moment. The results of the derivations are conditions for the eigencurvature due to the piezoelectric actuation, such that a certain bending moment distribution is achieved. Approximate solutions for the eigencurvature are also presented for the lower- and for the high-frequency domain. The theory is verified by a support-excited piezoelectric bimorph. First, the frequency response curves for the deflection, the bending moment and the axial stresses are calculated. Then the responses due to a sinusoidal excitation are computed, showing that the suggested control algorithm enables the reduction of the bending moment and also of the axial stress in a satisfactory manner. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1918-0

Authors:Michael Osipenko; Yuri Nyashin; Anton Kasatkin Abstract: Abstract The unilateral contact of two closely hanging chains (heavy inextensible strings) under the action of gravity and small horizontal loading is considered. Each chain has one end fixed and the other free. The chains have different lengths; the linear densities of the chains may be variable. The horizontal loading slightly deflects the chains from the vertical line, so that the system is geometrically linear. The basic problem is to find the shapes of the chains. This problem is reduced to the problem of finding the density of the forces of interaction between the chains. The accurate formulation of the latter contact problem is propounded. The unknown density of the contact forces is assumed to be the sum of piecewise continuous (and one-sided continuous) function and delta functions describing the concentrated forces. The uniqueness of the solution of the problem is proved. The analytical solution is constructed in some special cases. The following contact patterns are found out: contact at one point, contact along the full length of the shorter chain, contact along a part of the shorter chain, contact at a point and along a part of the shorter chain. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1904-6

Authors:Zhong Chen; Mehrdad Negahban Abstract: Abstract Functional grading (FG) around the crack tip is studied to improve the load capacity in parts made of graded interpenetrating polymer networks (IPN). To calculate the capacity, the stress intensity factor at the crack tip is calculated by blending the displacement correlation technique and finite element solutions. This process is integrated into an optimization process that uses linear scaling to obtain optimal material grading in a fixed domain around the crack tip. The process is demonstrated using a known poly(methyl methacrylate)/polyurethane IPN system for the case of internal and edge cracks. The FG-IPN parts obtained by this optimization show substantially improved load capacity compared to both optimal uniform plates, and plates with simple toughening of the region around the crack. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1911-7

Authors:A. S. Rezaei; A. R. Saidi Abstract: Abstract In the present article, the buckling of a fluid-infiltrated porous plate is investigated using Mindlin plate theory and an analytical procedure. A cosine rule for the pore distribution across the plate thickness is assumed with a coefficient defining porosity level. The governing stability equations are rewritten in terms of four auxiliary functions and decoupled with the aid of some mathematical manipulations. The decoupled partial differential equations are solved analytically by assuming simply supported radial edges for the plate. The critical buckling loads are calculated by considering fluid-saturated and fluid free conditions for the interconnected network of pores for different sector angles, thickness–radius ratios, coefficients of plate porosity, aspect ratios, and boundary conditions. It is found that the pore fluid compressibility affects the buckling load significantly. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1908-2

Authors:G. Y. Zhang; X.-L. Gao; Z. Y. Guo Abstract: Abstract A non-classical model for an orthotropic Kirchhoff plate embedded in a viscoelastic medium is developed by using an extended version of the modified couple stress theory and a three-parameter foundation model. The equations of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton’s principle. The new plate model contains three material length scale parameters to capture the microstructure effect, one damping coefficient to account for the viscoelastic damping effect, and two foundation moduli to represent the foundation effect. The current non-classical orthotropic plate model includes the isotropic plate model incorporating the microstructure effect and the classical elasticity-based orthotropic plate model as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported orthotropic plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate predicted by the current model is smaller than that predicted by the classical model, and the difference is large when the plate thickness is small but diminishes as the thickness becomes large. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. In addition, the damping ratio predicted by the new plate model is lower than that predicted by the classical plate model, and the difference is diminishing as the plate thickness increases. These predicted trends of the size effect at the micron scale agree with those observed experimentally. Furthermore, it is quantitatively shown that the presence of the foundation enlarges the plate natural frequency. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1906-4

Authors:D. Ieşan Abstract: Abstract This paper is concerned with the deformation of a chiral elastic bar subjected to a thermal field. The bar is composed of two different materials welded together along the surface of separation. The behavior of chiral materials is of interest for the investigation of bones and auxetic materials. We study the deformation of isotropic chiral materials by using the equilibrium theory of Cosserat thermoelasticity. The temperature variation is assumed to be a polynomial in the axial coordinate. It is shown that a plane thermal field, in contrast with the result predicted by the theory of achiral materials, produces torsional effects. The solution of the problem could be used to investigate the behavior of bone implants and other compound cylinders. The method is applied to the case of a circular bar reinforced by a longitudinal circular rod. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1900-x

Authors:Saad Essa; Hakan Argeso Abstract: Abstract Analytical solutions are developed for the analysis of elastic polar orthotropic functionally graded annular disks rotating with constant angular velocity. The formulations are carried out by presuming a state of plane stress and small deformations. The elasticity moduli and thickness are varied radially by a nonlinear function controlled by three parameters, while the radial variation of density may be defined by any form of continuous function. Poisson’s ratios are taken to be constant. Annular disks having traction-free inner and outer surfaces, and annular disks mounted on a circular rigid shaft having traction-free outer surface are studied separately. The analytical solutions are verified numerically by the use of a computational model based on the nonlinear shooting method. An analysis that inspects the effects of the degree of orthotropy is presented. Elastic limit angular velocities are determined according to Hosford’s yield criteria. Stress, displacement and strain profiles are compared within the elastic range. PubDate: 2017-07-25 DOI: 10.1007/s00707-017-1896-2