Authors:Bogdan Rogowski Pages: 593 - 606 Abstract: Abstract This paper investigated the fracture behavior of a piezoelectro-magneto-elastic medium subjected to electro-magneto-mechanical loads. The bimaterial medium contains a crack which lies at interface and is parallel to their poling direction. One harmonic function, which satisfying all boundary condition of the problem, is introduced. By means of this function, its derivatives physical fields, which appear in both materials of composite, are obtained in exact analytical form. The corresponding semi-permeable crack-face magneto-electric boundary conditions are utilized. Field intensity factors of stress, electric displacement, magnetic induction, cracks displacement, electric and magnetic potentials and the energy release rate are determined. The electric displacement and magnetic induction of crack interior are discussed. Obtained results indicate that the stress field and electric and magnetic fields near the crack tips exhibit square-root singularity. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1158-0 Issue No:Vol. 87, No. 4 (2017)

Authors:Y. H. Gao; S. N. Jiang; D. B. Zhu; H. T. Gao Pages: 607 - 615 Abstract: Abstract A piezoelectric energy harvester, consisting of a long and thin lead zirconate titanate ceramic tube with tangential polarization, is proposed in this paper for scavenging vibration energy. This harvester operates in 3–3 mode while subjected to radial dynamic hydraulic pressure acting at the inner surface of the tube. Based on the linear piezoelectricity theory, the analytical solutions for the output power density of the device and their dependence upon the vibration frequency, the geometrical parameters of the tube, and the impedance of the load circuit are derived. The numerical results indicate the considerably enhanced performances by adjusting the thickness and radius of the ceramic tube. The stress in the ceramic is calculated to ensure that the applied force is within the operational range. The load impedance has a great effect on the performance of the harvester. A wideband energy harvester, which usually consisted of complex architectures in previous research works, is obtained in this pare by just adjusting the value of the load impedance. This opens up a new approach for us to design wideband energy harvesters with simple structures and thus small size, light weight and low cost. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1211-z Issue No:Vol. 87, No. 4 (2017)

Authors:Minzu Liang; Xiangyu Li; Fangyun Lu Pages: 617 - 631 Abstract: Abstract The dynamic fracture and fragmentation of notched rings under explosive loading were modeled to investigate the fragment characteristics (average fragment size and fragment size distribution) and their effects on fragmentation performance. An analytical model of the average fragment size was proposed for dynamic fracture and fragmentation based on energy criteria related to the material properties, strain rates, and notch effect. The theoretical solutions indicated that the notch effect was dominant with the decreased notch spacing. A law for the fragment size distribution was achieved by combining the binomial distribution. The theoretical distribution depended on the notch spacing, and the distribution was approximated by the natural fragmentation of rings with larger notch spacing. Dynamic fracture and fragmentation experiments were also conducted on cylindrical rings made of AISI 1020 steel. The experimental results were compared with the theoretical models. The average fragment sizes of the theoretical solutions agreed well with the experimental results, and the theoretical distribution provided a good description of the experimental data. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1212-y Issue No:Vol. 87, No. 4 (2017)

Authors:Giovanni Incerti Pages: 633 - 645 Abstract: Abstract The dynamic behavior of a servomechanism must be studied as a whole without distinction between its parts, in order to assess correctly the overall performance of the system. For this reason, in many cases of practical interest, it may be useful to analyze the dynamics of a mechatronic device using a mathematical model and a computer simulation software, in order to verify the consequences arising from the modification of a particular parameter of the system. Following this methodological approach, this paper proposes a model for the dynamic analysis of a typical industrial servomechanism characterized by elasticity and backlash in the transmission. The model has been implemented into a software application and it can be used to test, from a theoretical point of view, the dynamic behavior of the device under user-defined operating conditions. The numerical simulations, which can be performed in a short time, may help the designer to optimize the dynamic performance of the servomechanism without performing experimental activities. On the basis of the simulation results, he can then evaluate, for example, whether the presence of the backlash still allows to obtain acceptable acceleration values. The software also allows to verify the effects resulting from different settings of the position regulator, and therefore, it can be helpful to assist the designer during the calibration procedures. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1213-x Issue No:Vol. 87, No. 4 (2017)

Authors:Ming Dai; Peter Schiavone; Cun-Fa Gao Pages: 647 - 665 Abstract: Abstract We propose an innovative numerical scheme (based on complex variable techniques) for the calculation of the effective properties of a composite containing unidirectional periodic fibers in which we additionally incorporate the separate contribution of the ‘interface effect’ between the fibers and the surrounding material. The incorporation of interface effect into the model of deformation allows our model to accommodate the general class of nanocomposite materials, a fast growing area of research and our primary focus in this paper. The composite is loaded by a constant normal strain along the direction parallel to the fibers and by a uniform remote loading in the plane perpendicular to the fibers. Our method is based on the analysis of a representative unit cell with periodic boundary conditions imposed on its edge. Several examples are presented to study the influence of the interface and the volume fraction of the fibers on the effective properties of the composite and the interfacial stress field. We show that when the volume fraction falls below roughly 9%, the interfacial stress distribution recovers effectively to that corresponding to a single fiber with the same interface parameters embedded within an infinite matrix. We find also that if the shear modulus of the fibers exceeds approximately two and a half times that of the matrix, the interface effect is negligible in the determination of the effective properties of the corresponding nanocomposites. Finally, we show that the use of traditional effective medium theories may induce significant errors in the determination of transverse effective properties (in the plane perpendicular to the fibers) of the composite, in particular when the fibers are significantly softer than the matrix. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1215-8 Issue No:Vol. 87, No. 4 (2017)

Authors:Charles Chelem Mayigué; Rodion Groll Pages: 667 - 683 Abstract: Abstract In the present work, the central-upwind schemes proposed by Kurganov et al. (SIAM J Sci Comput 23:707–740, 2001) for hydrodynamics are extended and combined with the divergence cleaning method of Dedner (J Comput Phys 175:645–673, 2002) in order to approximate the equations of the ideal magnetohydrodynamics in a finite volume discretization framework with Gaussian integration. To improve the quality of the solution, the Van Leer interpolation scheme is used. The accuracy and the robustness of the obtained solver are demonstrated through numerical simulations of benchmark problems such as the Brio–Wu shock tube problem, the Orszag–Tang vortex problem and the 2D cloud–shock interaction problem. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1216-7 Issue No:Vol. 87, No. 4 (2017)

Authors:F. F. Real; F. Fontanela; T. G. Ritto; A. Batou; C. Desceliers Pages: 685 - 698 Abstract: Abstract In this paper, a new strategy for modeling uncertainties in the substructures and interfaces of a dynamical system is presented. This strategy is based on (1) the reduction in the dynamical model of each substructure using the Craig–Bampton method and (2) the use of the nonparametric probabilistic approach for the global modeling of uncertainties in each substructure. As an improvement with respect to existing nonparametric methods, the methodology proposed here constructs separated models of uncertainties for the inner and interface degrees of freedom, which allows to control separately the levels of fluctuation induced by these two sources of uncertainties. This methodology is applied for the analysis of the random vibration of a drill-string. Three strategies are compared: (1) a full nonparametric probabilistic approach on all the system, (2) the existing nonparametric probabilistic approach together with the Craig–Bampton substructuring method, and (3) the new nonparametric probabilistic approach proposed here with the separation of the inner and interface degrees of freedom uncertainties. It turns out that, for the same level of uncertainty, the three approaches give similar results, but the new approach gives more flexibility for the control of the probabilistic model. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1217-6 Issue No:Vol. 87, No. 4 (2017)

Authors:Malte Krack; Noha Aboulfotoh; Jens Twiefel; Jörg Wallaschek; Lawrence A. Bergman; Alexander F. Vakakis Pages: 699 - 720 Abstract: Abstract A mechanical system consisting of an elastic beam under harmonic excitation and an attached sliding body is investigated. Recent experimental observations suggest that the system passively (self-)adapts the axial location of the slider to achieve and maintain a condition of self-resonance, which could be useful in applications such as energy harvesting. The purpose of this work is to provide a theoretical explanation of this phenomenon based on an appropriate model. A key feature of the proposed model is a small clearance between the slider and the beam. This clearance gives rise to backlash and frictional contact interactions, both of which are found to be essential for the self-adaptive behavior. Contact is modeled in terms of the Coulomb and Signorini laws, together with the Newton impact law. The set-valued character of the contact laws is accounted for in a measure differential inclusion formulation. Numerical integration is carried out using Moreau’s time-stepping scheme. The proposed model reproduces qualitatively most experimental observations. However, although the system showed a distinct self-adaptive character, the behavior was found to be non-resonant for the considered set of parameters. Beside estimating the relationship between resonance frequency and slider location, the model permits predicting the operating limits with regard to excitation level and frequency. Finally, some specific dynamical phenomena such as hysteresis effects and transient resonance captures underline the rich dynamical behavior of the system. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1218-5 Issue No:Vol. 87, No. 4 (2017)

Authors:Gurmeet Singh; David Kumar; P. M. Mohite Pages: 721 - 736 Abstract: Abstract Epoxy is a widely used thermosetting polymer in various engineering fields to develop composites. Studying its damage and fracture behaviour under various loading conditions is highly important. In this work, a micromechanics-based damage model is developed for understanding the damage initiation and growth in epoxy. To support this damage model, tests are performed for obtaining mechanical properties and to study the damage behaviour of epoxy. Diglycidyl ether of bisphenol A (DGEBA) resin with triethylenetetramine (TETA) hardener in 10:1 ratio are mixed and cured to make the epoxy. To give a physical meaning to damage, the model quantifies the damage as volume fraction of a spherical void in a unit representative volume element (RVE) of epoxy material. Degraded effective properties are computed for damaged RVE using standard mechanics-based micromechanical approach. A second-degree polynomial is established for effective stiffness with damage at any loading instance. This functional form of degraded stiffness in terms of damage is used in constitutive relations. A strain energy- based approach is used to compute thermodynamic forces, a state variable used for the evolution of damage. A damage evolution model is proposed with two material-specific parameters which are determined using experimental tests. The model is implemented by user material subroutine (UMAT) in commercial finite element software, Abaqus/Standard. The proposed model accurately captures the tensile behaviour of the epoxy material and gives capability to simulate an epoxy material’s damage behaviour from its initiation till failure or macrolevel rupture under uniaxial tensile loading. The developed model predicts the behaviour of the material in agreement with experimental results. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1219-4 Issue No:Vol. 87, No. 4 (2017)

Authors:Sergey Sorokin; Radek Kolman; Jan Kopacka Pages: 737 - 750 Abstract: Abstract The boundary integral equations are derived in the framework of the analytical five-mode models for propagation of symmetric and skew-symmetric waves in a straight elastic layer of the constant thickness. The forcing problems for fundamental loading cases are solved with the bi-orthogonality conditions employed. By these means, the Green’s matrices are constructed. The derivation of the Somigliana’s identities for the five-mode models is presented. To exemplify application of the method of boundary integral equations, eigenfrequencies of a layer of the finite length are found for two sets of boundary conditions. In the course of analysis, the essential features and advantages of the method are highlighted. The isogeometric analysis at several approximation levels and the standard finite element software are also used to calculate the eigenfrequencies. The results obtained by alternative methods are shown to be in an excellent agreement with each other. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1220-y Issue No:Vol. 87, No. 4 (2017)

Authors:Yongping Yu; Hongzhi Zhang; Youhong Sun; Weipeng Sun Pages: 751 - 765 Abstract: Abstract The purpose of this paper is to investigate the nonlinear vibration behavior of single and double tapered cantilever beams on the nonlinear foundation and present an alternative analytical method to solve the issue. Unlike other literatures, the admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Analytical approximate solutions in closed and explicit form are obtained by combining the Lagrange method with the Galerkin and Newton linearization method. Compared with the exact (numeric) results, the accuracy of these approximate solutions is presented. The effects of different parameters such as vibration amplitude, and foundation stiff parameters on nonlinear frequencies and displacement response of the tapered beams are easily analyzed, with the brief expressions of the present analytical approximate solutions. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1221-x Issue No:Vol. 87, No. 4 (2017)

Authors:Pravin Bhad; Vinod Varghese; Lalsingh Khalsa Pages: 767 - 781 Abstract: Abstract The present paper deals with an investigation into the thermoelastic effect on the elliptical plate during large deflection while heating with non-stationary temperature distribution. The governing equation for the deflection is formulated with modification within the existing methodology devised by Berger. Thermally induced deflection results and its associated stresses are obtained in terms of Mathieu function of the first kind of order 2n. Furthermore, aforementioned problems can be degenerated into the problems of the circular region by applying limiting conditions. Some results which are derived by means of computational tools are illustrated numerically and depicted graphically. PubDate: 2017-04-01 DOI: 10.1007/s00419-016-1222-9 Issue No:Vol. 87, No. 4 (2017)

Authors:Xiang-Long Peng; Gan-Yun Huang Abstract: Abstract In the paper, by taking advantage of a strain gradient crystal plasticity theory with consideration of dislocation absorption by surfaces, plastic behaviors of thin films with two active slip systems under constrained shear is analytically studied. It is found that the critical loads for the onset of dislocations absorption by surfaces for the two slip systems are size dependent and are greatly affected by the latent hardening in the grain interior, and dislocations absorption by surfaces can significantly change the distributions of the plastic deformation and dislocation density and hence the strain-hardening behaviors. PubDate: 2017-04-12 DOI: 10.1007/s00419-017-1253-x

Authors:Ioannis N. Tsiptsis; Evangelos J. Sapountzakis Abstract: Abstract Toward improving conventional beam elements in order to include distortional effects in their analysis, in this paper, independent parameters have been taken into account. Beam’s behavior becomes more complex, especially for eccentric loading, due to the coupling between warping and distortion. Thus, the importance of including higher-order phenomena in the analysis arises in order to derive accurate results. Due to the fact that more degrees of freedom are employed, the computational cost of the problem is significantly increased. Isogeometric tools (B-splines and NURBS), either integrated in the finite element method or in a boundary element-based method called analog equation method, are employed in this contribution for the static analysis of beams of open or closed (box-shaped) cross sections toward improving computational effort. Responses of the stresses, stress resultants and displacements to static loading have been studied. PubDate: 2017-04-12 DOI: 10.1007/s00419-017-1251-z

Authors:Li Jun; Bao Yuchen; Hu Peng Abstract: Abstract Thermal effects on vibration and buckling behaviors of generally layered composite beams with arbitrary boundary conditions are dealt with in this paper. The composite beam is modeled using third-order shear deformation beam theory in which the Poisson effect is incorporated. A constant temperature change through the beam thickness is assumed. An exact dynamic stiffness matrix is formulated by directly solving the differential equations of motion governing the natural vibration of the composite beams subjected to uniform temperature changes along the beam thickness. Application of the derived dynamic stiffness matrix together with the Wittrick–Williams algorithm to compute the natural frequencies and buckling temperature changes of two particular composite beams is discussed. The correctness and accuracy of the derived dynamic stiffness matrix is evaluated by comparing the present results with the available solutions in literature. The influences of Poisson effect, boundary condition, temperature change, thermal expansion coefficient and material anisotropy on the natural frequencies of the composite beams are studied. PubDate: 2017-04-10 DOI: 10.1007/s00419-017-1250-0

Authors:Yin-lei Huo; Zhong-min Wang Abstract: Abstract The dynamical stability and transverse vibration of the cantilever beam with oscillating length are analyzed in this study. The differential equation of motion with time-dependent coefficients is discretized by the Galerkin method, and then the method of multiple scales for multi-degree of freedom is applied to investigate the parametric resonances of the cantilever beam with oscillating length. The effects of the oscillation amplitude and frequency on the parametric resonance regions and the tip responses are discussed. Tip responses simulation by Runge–Kutta method confirms the parametric resonance regions obtained by multiple scales method. In addition, the ‘jump’ phenomenon on the tip response of the axially oscillating deploying cantilever beam is also discussed. PubDate: 2017-04-06 DOI: 10.1007/s00419-017-1249-6

Abstract: Abstract This paper presents a numerical study of perforation of the aluminium multi-layered targets impacted by steel projectiles in the shape of a ball, nut and nail. For the construction of the protective panels arc-, rectangular-, V- and U-shaped sheets of metal were considered. During the tests the panel thickness was constant at 160 mm. The panels were composed of 1.5-mm-thick aluminium sheets, and the initial speed of debris was \(500~\mathrm{m{/}s}\) . A comprehensive numerical study indicated the shape of the layer that had superior ballistic resistance and the best strength-to-weight ratio. Computational analyses were also used to investigate the influence of thermal softening and strain rate hardening in the Johnson–Cook constitutive model on the ballistic performance of layered targets. The number of layers required to stop the penetrating objects was compared for the rigid and deformable projectiles. Based on the comparative studies, some guidelines for engineering tasks involving exploration of number of possible technical solutions were proposed. PubDate: 2017-04-04 DOI: 10.1007/s00419-017-1247-8

Authors:Alexander Kuzmin Abstract: Abstract We study numerically turbulent flow of the air in a channel with breaks of walls. The flow is supersonic downstream of the break section and in the free stream. Instability of shock waves formed in the channel and in front of the entrance is examined. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate an expulsion/swallowing of the shock waves with variation of the free-stream Mach number. Effects of the upper wall slopes on the shock wave positions and flow bifurcation are examined. PubDate: 2017-04-03 DOI: 10.1007/s00419-017-1248-7

Authors:B. Zhang; J. G. Yu; X. M. Zhang Abstract: Abstract By introducing the double orthogonal polynomial method from the Cartesian coordinate system into the cylindrical coordinate system, this paper investigates the guided wave propagation in cylindrical structures with sector cross-sections. Comparison with available reference results, the validity of the presented method is verified. The corresponding phase velocity dispersion curves, displacement distributions, stress curves and the Poynting vectors are illustrated. The influences of the radius-to-thickness ratio and angular measure on the characteristics of the guided wave are discussed, which gives significant guidance on ultrasonic guided wave nondestructive testing for cylindrical structures with sector cross-sections. PubDate: 2017-03-31 DOI: 10.1007/s00419-017-1237-x

Authors:Feng Yang; Mojia Huang; Jun Liu Abstract: Abstract Most rolled sheet metals are orthotropic aggregates of cubic crystallites. The texture coefficients, characterized by the preferred orientation of the crystallites, are important to set up the yield function. Although the Hosford yield function is more suitable than the Hill yield function for describing both the yielding and plastic deformation of orthotropic material, it suffers from the restriction that the three principal stresses must be coaxial with the orthotropy of materials. This paper proposes the new Hosford yield function for weakly textured sheets of cubic crystal orthotropic metals in any stress state by expanding the introduced orientation-dependent functions to its sixth-order Taylor series expansion. Also, the new yield function, which covers three material parameters and seven texture coefficients, is more general than the existing Hosford yield function. Finally, both the plastic anisotropy of the q-value and the yield stress obtained from the new yield function agree well with experimental results. This yield function can lay a theoretical foundation for analyzing the mechanical properties of metal materials. PubDate: 2017-03-31 DOI: 10.1007/s00419-017-1244-y