Authors:Hui Cheng; Tian You Fan; Hao Wei Pages: 1363 - 1372 Abstract: Abstract In view of the same model of fivefold and tenfold symmetry quasicrystals, with the same boundary and the same initial conditions, we have obtained a lot of results by phonon–phason dynamics and hydrodynamics and have performed a detailed comparative analysis. The quantitative results on mass density, viscosity velocities, phonon displacements, phason displacements, phonon stresses, phason stresses, and viscosity stresses and their time–space variations help us to understand the motion of solid quasicrystals. The analysis for octagonal and dodecagonal quasicrystals can be easily extended to other two-dimensional quasicrystals and three-dimensional icosahedral quasicrystals. These results reveal that the phonon field is dominated; moreover, the coupling between phonon and phason fields is important for the studied dynamic process, and these two elementary excitations are the main figures in the dynamic process. In contrast, the effects of the compressibility and viscosity are very weak, and they make almost no contribution to the dynamic process. For this dynamic process, the hydrodynamics and phonon–phason dynamics are equivalent, and the hydrodynamics can be simplified by phonon–phason dynamics for solid quasicrystals. PubDate: 2017-04-01 DOI: 10.1007/s00707-016-1779-y Issue No:Vol. 228, No. 4 (2017)

Authors:Yanxun Zhou; Yimin Zhang; Guo Yao Pages: 1393 - 1406 Abstract: Abstract This paper’s purpose is to investigate the stochastic dynamic behavior of a tapered cantilever beam, taking into account the deterioration of its performance during the working process. The equation of motion of the tapered beam is established by using Lagrange’s equation. By applying the assumed mode method, the equation of motion of the beam is discretized into a series of coupled linear time-varying ordinary differential equations. To describe the deterioration of the performance of the tapered cantilever beam, the mass and stiffness deteriorations of the beam are modeled by two independent Gamma processes. Based on the stochastic perturbation method, the response of the linear continuous system with stochastic parameters is investigated by superimposing the discretized modes. In the numerical simulation, the validity of the present study is confirmed, the effects of the cone angle (tapered ratio) of the tapered beam and the frequency of the external force on the response of the tapered cantilever beam are investigated, and the influences of the parameters of the two Gamma processes on the variance of the response are also discussed. PubDate: 2017-04-01 DOI: 10.1007/s00707-016-1764-5 Issue No:Vol. 228, No. 4 (2017)

Authors:Yasuhide Shindo; Fumio Narita; Yuhei Goto Pages: 1407 - 1413 Abstract: Abstract This paper studies analytically and experimentally the cryogenic static fatigue behavior of cracked piezoelectric ceramics under electric fields. The crack was created normal to the poling direction. Static fatigue tests were carried out in three-point bending with the single-edge precracked-beam specimens at room temperature and liquid nitrogen temperature (77 K), and times-to-failure under different mechanical loads and electric fields were obtained. Plane strain finite element analysis using temperature-dependent material properties of piezoelectric ceramics was also performed, and the energy release rate for the permeable crack model was calculated. The effects of electric field and temperature on the energy release rate versus lifetime curve are discussed. PubDate: 2017-04-01 DOI: 10.1007/s00707-016-1782-3 Issue No:Vol. 228, No. 4 (2017)

Authors:Iman Shojaei; Ali Kaveh; Hossein Rahami; Reza Shirazi; Babak Bazrgari Pages: 1445 - 1456 Abstract: Abstract Some near-regular mechanical systems involve global irregularities, wherein a large number of degrees of freedom are affected by irregularity. However, no efficient solution for such global near-regular systems has yet been developed. In this paper, methods for static and dynamic analyses/reanalyses of these systems are established using graph product rules combined with matrix analysis and linear algebra. Also, these methods are generalized to systems with nonlinear behavior. The developed formulations allow reduction in computational time and storage compared to those of conventional methods. As a practical example of a global near-regular mechanical system, a subject-specific finite element mechanical model of the human spine is developed and presented. PubDate: 2017-04-01 DOI: 10.1007/s00707-016-1778-z Issue No:Vol. 228, No. 4 (2017)

Authors:Yi Zhang Pages: 1481 - 1492 Abstract: Abstract Herglotz proposed a generalized variational principle through his work on contact transformations and their connections with Hamiltonian systems and Poisson brackets, which provides an effective method to study the dynamics of nonconservative systems. In this paper, the variational problem of Herglotz type for a Birkhoffian system is presented and the differential equations of motion for the system are established. The invariance of the Pfaff–Herglotz action under a group of infinitesimal transformations and its connection with the conserved quantities of the system are studied, and Noether’s theorem and its inverse for the Herglotz variational problem are derived. The variational problem of Herglotz type for a Birkhoffian system reduces to the classical Pfaff–Birkhoff variational problem under classical conditions. Thus, it contains Noether’s theorem for the classical Birkhoffian system as a special case. And since Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics, the results we obtained contain Noether’s theorem of Herglotz variational problems for Hamiltonian systems and Lagrangian systems as special cases. In the end of the paper, we give two examples to illustrate the application of the results. PubDate: 2017-04-01 DOI: 10.1007/s00707-016-1758-3 Issue No:Vol. 228, No. 4 (2017)

Authors:Min He; Lihua Zhang; Zhong Huang; Qishen Wang Pages: 1511 - 1524 Abstract: Abstract The semi-inverse method was used to solve the inverse problem of the vibration of a symmetric rod with two elastic supports. We discuss when the linear density function of the symmetric rod with two elastic supports is a symmetric polynomial function how to construct the axial stiffness of the symmetric rod with two elastic supports for the same symmetric polynomial function, when the symmetric or anti-symmetric mode and the corresponding circular frequency are known. We discuss the axial stiffness of a symmetric rod with two free ends and two fixed ends that was constructed from the symmetric mode or anti-symmetric mode and the associated linear density function. PubDate: 2017-04-01 DOI: 10.1007/s00707-016-1783-2 Issue No:Vol. 228, No. 4 (2017)

Authors:V. M. Bhojawala; D. P. Vakharia Abstract: Abstract The current work presents an accurate closed-form model to Microelectro Mechanical System designers for computing static pull-in voltage of electrostatically actuated microbeams with clamped–clamped end condition. The model incorporates the effect of Casimir force including correction for finite conductivity. The Euler–Bernoulli beam equation is adapted considering the effects of mid-plane stretching, residual stress, fringing field and Casimir force to derive the governing differential equation for electrostatically actuated microbeams. The Galerkin method is used with a multimodes reduced-order model to solve the governing differential equation of microbeams. The results obtained using the reduced-order model are further compared with the solution of the boundary value problem and are validated with published numerical and experimental results. The results of the current work indicate that at least three modes in reduced-order model are essential for the prediction of pull-in voltage of microbeams which have a large value of mid-plane stretching parameter. In order to develop a closed-form relation, dimensionless parameters are used to plot the curves of pull-in voltage versus various parameters such as axial force due to residual stress, Casimir force, fringing field, Casimir force including finite conductivity correction, and mid-plane stretching. Based on the relationship observed in the plotted curves for the independent effect and interaction effects of these parameters on static pull-in voltage, a closed-form model is proposed for the computation of static pull-in voltage. Optimised coefficients of the proposed model are determined using nonlinear regression analysis. An adjusted R \(^2\) value equal to 0.99909, a P value equal to zero, and \({\chi }^2\) tolerance equal to \(1\times 10^{-9}\) obtained by statistical analysis exhibit the precision of fitted data, significance of model, and convergence of the fit, respectively. The proposed model is validated by comparing the results of the model with results of boundary value problem solutions, results predicted from reduced-order model and other several reported numerical and experimental results. The proposed model is robust enough for calculating the static pull-in voltage under different conditions with maximum error of 3% when compared to reported experimental and numerical results. PubDate: 2017-04-18 DOI: 10.1007/s00707-017-1843-2

Authors:J. L. Jiang; D. J. Huang; B. Yang; W. Q. Chen; H. J. Ding Abstract: Abstract This paper presents three-dimensional elasticity solutions for an annular sector plate made of transversely isotropic functionally graded material (FGM) subjected to concentrated forces \(\left( X,Y,0 \right) \) or couples \(\left( M_X,M_Y,M_Z\right) \) applied at one of its radial edges. The elastic coefficients can vary arbitrarily through the plate thickness. The analysis was based on the assumed forms of displacements for bending of an FGM plate (Mian and Spencer in J Mech Phys Solids 4:2283–2295, 1998), in which the four analytical functions were constructed properly. Appropriate boundary conditions and end conditions similar to those in the classic plate theory were employed to determine the unknown constants contained in the analytical functions so as to accomplish the analysis. When the material coefficients are all constant, the obtained analytical solutions can be degenerated into those for a homogeneous transversely isotropic annular sector plate, which have never been reported before. The solutions may be further reduced to those for a homogeneous isotropic annular sector plate, among which the ones for concentrated couples \(\left( M_X ,M_Y,0 \right) \) are also new to the literature. PubDate: 2017-04-18 DOI: 10.1007/s00707-017-1839-y

Authors:Kadry Zakaria; Sameh A. Alkharashi Abstract: Abstract The purpose of this study is to establish the temporal stability of two bounded thin films flow of a viscous fluid inside a permeable inclined channel. Based on the long-wave theory, an integral boundary layer model for the film thickness, the volumetric flow rate, and the surface charge are derived. The driving force for the instability under an electric field is an electrostatic force exerted on the free charges accumulated at the interface. The linear stability analysis for the leaky dielectric model is performed, and a cubic dispersion relation is obtained by the normal mode technique using suitable boundary and interface conditions. The numerical calculations of the linear analysis reveal that our model is unstable for a small Reynolds number, and for higher numbers, the system becomes stable in nature. The dielectric constant ratio has a stabilizing influence, in which the inverse behavior is found for increasing the electrical conductivity. For the perfect dielectric case, the nonlinear stability is carried out. The analytical solution of stationary waves is discussed by introducing the linearized instability of the fixed points and Hopf bifurcation. It is found that the viscosity ratio and the permeability parameter have an opposite effect on the existence of the fixed points. A specified case of the stationary wave, namely Shkadov wave, is investigated. PubDate: 2017-04-17 DOI: 10.1007/s00707-017-1847-y

Authors:Yang Sun; Ang Li; Xiang Ren; Yi Lu; Mabao Liu Abstract: Abstract Analytical solutions for interfacial diffusion-induced creep rate and stress relaxation in metal matrix particulate composites are developed under triaxial loading. Based on the Eshelby inclusion theory, the driving forces for interface diffusion and interface slip are obtained, respectively, and the relationship between them is clarified. The effects of the triaxial loading, the volume fraction of the inclusion, and the modulus ratio of the inclusion and matrix on the creep rate and stress relaxation are analyzed. In addition, the error caused by the scale effect is corrected by fitting the finite element results with the nonlinear least square method. The present solutions provide an important reference for various engineering applications of metal matrix particulate composites. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1832-5

Authors:Jiemin Xie; Shuaiqi Fan; Xuedong Chen; Yuantai Hu Abstract: Abstract In this study, a coupling dynamic model on an acoustic wave sensor system, consisting of a thickness-shear mode quartz crystal resonator (QCR) and an array of surface nanowires (NWs), has been established including the surface effects of NWs. The governing equations of NWs are derived from the Timoshenko beam theory in consideration of shear deformation and rotary inertia. The electrical admittance is described directly in terms of the physical properties of the surface NWs from an electrically forced vibration analysis. The effects of residual surface tension \(\tau _{0}\) and surface elasticity \(E_\mathrm{s}\) of NWs on the admittance spectra and vibration modes of the compound QCR system are examined, and some useful results are obtained, which will be helpful to the design of nanosized beams loaded acoustic wave sensors and some related applications. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1845-0

Authors:Yu. A. Chirkunov Abstract: Abstract The problem of scattering of sound waves by a local inhomogeneity in an anisotropic medium with a spherical stratification is studied for a linear acoustic model. Natural oscillations of the external medium are considered with a help of intertwining operators for the differential operator of the basic equation. We show that there exist local inhomogeneities (domains) for which there is no scattered field, induced by a falling on these inhomogeneities acoustic field, created by external compactly distributed sources. It means that these inhomogeneities cannot be detected by the acoustic field generated by external compactly distributed sources. The main characteristics of these nonscattering inhomogeneities are studied. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1849-9

Authors:Hai-Bing Yang; Ming Dai; Cun-Fa Gao Abstract: Abstract This work presents a complex variable-based scheme to calculate the anti-plane shear properties of a porous structure containing periodic holes under uniform (anti-plane shear) loadings. The scheme is featured by practically arbitrary shapes of the holes and the surface effects (resulting from surface elasticity) incorporated on each hole’s boundary. Numerical examples are given to verify the feasibility of our scheme and to study the influence of the hole shape and surface effects on the stress concentration around the holes and the effective (longitudinal) shear moduli of the structure. It is shown that the stress concentration around periodic holes can be treated approximately as that around a single hole (for the same hole size and surface shear modulus) when the hole volume fraction is less than 7%. It is also found that for (reasonably) given surface shear modulus, hole volume fraction and hole size, the structure containing periodic circular holes can achieve larger effective shear moduli but lower sensitivity of effective shear moduli to the surface effects, as compared with those containing periodic regular polygonal holes. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1848-x

Authors:Ranislav M. Bulatovic Abstract: Abstract A criterion which contains necessary and sufficient conditions for spectral stability, flutter and divergence instability of circulatory systems is formulated. The conditions are expressed via the properties of a quadratic form with the coefficients expressed by means of the traces of powers of the non-conservative stiffness matrix. As corollaries, this general algebraic result leads to a number of stability conditions known in the literature. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1841-4

Authors:François Nicot; Jean Lerbet; Félix Darve Abstract: Abstract Although the concept of the second-order work criterion dates back to the middle of the past century, its physical meaning often continues to be debated. Recent papers have established that a certain class of instabilities, related to the occurrence of an outburst in kinetic energy, could be properly detected by the vanishing of the second-order work. This manuscript attempts to extend the second-order work formalism to boundary value problems. For this purpose, the role of the boundary stiffness tensor (relating external forces and displacement components) is put forward in the occurrence of instability by divergence. Omitting body forces, a global method is then given to compute the second-order work terms directly. The capability of this formalism is finally demonstrated in the context of engineering issues. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1844-1

Authors:Jianfeng Zhao; Jinlin Liu; Guozheng Kang; Linan An; Xu Zhang Abstract: Abstract Nanocomposites have shown excellent mechanical and physical properties; however, their properties are seriously affected by the nucleation of misfit defects at the interfaces between the inclusion and the matrix. Based on the energy rule, the nucleation criteria for a misfit extended dislocation dipole (MEDD) and a misfit screw dislocation dipole (MSDD) are analytically given. Furthermore, we systematically investigate the effects of the geometrical and mechanical factors, such as the radius of the inclusion, the misfit strain, the shear modulus ratio and the stacking fault energy, on the competitive nucleation between MEDD and MSDD. It is found that the stacking fault energy has a decisive effect on the competitive nucleation of MEDD and MSDD. The critical stacking fault energy for the nucleation transferring from MSDD to MEDD increases with the increase of the shear modulus ratio and decrease of the misfit strain, while it is almost not affected by the inclusion radius. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1840-5

Authors:George Z. Voyiadjis; Peter I. Kattan Abstract: Abstract Refinements and generalizations of the decomposition of the damage variable are presented within the framework of continuum damage mechanics. It is assumed that damage in a solid is due mainly to cracks and voids. The classical decomposition of the damage variable into a damage part due to cracks and another damage part due to voids is examined and extended consistently and mathematically. This is further elaborated upon by considering a solid with three types of defects: cracks, voids, and a third defect that is unspecified. Initially, the decomposition issues are carried out in one dimension using scalars. But this is generalized subsequently for the general case of three-dimensional deformation and damage using tensors. Finally, the special case of plane stress is illustrated as an example. It is shown that in the case of plane stress, two explicit decomposition equations are obtained along with a third implicit coupling equation that relates the various “crack” and “void” damage tensor components. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1836-1

Authors:Michael Baumgart; Andreas Steinboeck; Martin Saxinger; Andreas Kugi Abstract: Abstract A quasi-static model of axially moving steel strips in a continuous hot-dip galvanizing line is presented. The model provides the bending line of the strip and takes into account the history of elasto-plastic deformation. The numerical integration of the material model of elasto-plastic deformation is algorithmically separated from the solution of the boundary value problem of the bending line by pre-computing sets of one-dimensional candidate relations between the strip curvature and the bending moment. Using this model, the influence of different roll positions in the zinc bath on the mean displacement of the strip at the gas wiping dies and the maximum lateral curvature of the strip (crossbow) can be efficiently calculated and analyzed. PubDate: 2017-04-11 DOI: 10.1007/s00707-017-1824-5