Authors:Mikhail E. Semenov; Andrey M. Solovyov; Mikhail A. Popov; Peter A. Meleshenko Pages: 517 - 524 Abstract: A mathematical model of an unstable system in the form of inverted coupled pendulums is developed and simulated. Dynamics of such a system is investigated, and the stability zones are identified in the explicit form. The algorithm of stabilization of the pendulums near the vertical position is constructed and verified. PubDate: 2018-04-01 DOI: 10.1007/s00419-017-1323-0 Issue No:Vol. 88, No. 4 (2018)

Authors:H. R. Majidi; M. R. Ayatollahi; A. R. Torabi Pages: 587 - 612 Abstract: The aim of the present study is to assess the suitability of the extended finite element method (XFEM) combined with the cohesive zone model (CZM) and also the incremental method together with the maximum tangential stress (MTS) criterion in predicting the fracture load and crack trajectory of key-hole notched brittle components subjected to mixed mode I/II loading with negative mode I contributions. For this purpose, a total number of 63 fracture test results, reported recently in the literature on the key-hole notched Brazilian disk (Key-BD) specimens made of the general-purpose polystyrene (GPPS) under mixed mode I/II loading with negative mode I contributions, are first collected. Then, the experimentally obtained fracture loads of the tested GPPS specimens are theoretically predicted by means of XFEM combined with CZM. Additionally, the crack trajectory in the tested Key-BD specimens is predicted by using both XFEM combined with CZM and the incremental method combined with MTS criterion. Finally, it is shown that both the fracture load and the crack trajectory could successfully be predicted by means of the two proposed methods for different notch geometries. PubDate: 2018-04-01 DOI: 10.1007/s00419-017-1329-7 Issue No:Vol. 88, No. 4 (2018)

Authors:Lifeng Ma; Biao Wang; Alexander M. Korsunsky Pages: 613 - 627 Abstract: Analytical solution for a rigid line inclusion embedded in an infinite-extended plane under non-uniform loading is still a challenging problem in inclusion mechanics, which has both theoretical and applied significance in material engineering. In this paper, by directly employing Kolosov–Muskhelishvili stress potentials, a rigid line inclusion interacting with a generalized singularity is addressed in the framework of plane deformation, with the help of the superposition principle. It should be pointed out that the generalized singularity in this study can represent a point force, an edge dislocation, a point moment, a point nucleus of strain, and even remote uniform load, etc. The solutions can be used as kernel functions for integral equation formulations of rigid line inclusion–substrate system models using the Green’s function method. With this framework, stress field and stress intensity factors at the line inclusion ends are analyzed. The application of the solutions is demonstrated with two simple examples: (i) the rigid line inclusion under remote loading is studied, and it is strictly confirmed with rigorous proof that the remote shear load will not arouse stress concentration; (ii) a rigid line inclusion interacting with a dislocation is investigated, and the full solution is given. These examples also partially validate the general solution derived this study. PubDate: 2018-04-01 DOI: 10.1007/s00419-017-1330-1 Issue No:Vol. 88, No. 4 (2018)

Authors:Sandipan Nath Thakur; Chaitali Ray; Subrata Chakraborty Abstract: Laminated composite shells are widely used as structural components in important aerospace, marine, automobile engineering structures. Thus, appropriate evaluation of sensitivities of responses like deflection, frequency, buckling etc. due to changes in design variables is of great importance for efficient and safe design of such structures. The present paper deals with a comprehensive sensitivity analysis of laminated composite shells using \({C}^{0 }\) finite element with more accurate theoretical model based on higher-order shear deformation theory (HSDT). The sensitivity analysis of deflection and natural frequency with respect to important design parameters such as material parameters, angle of fiber orientation, radius of curvature, density of materials and external load is presented. Furthermore, sensitivity-based importance factor for each parameter is obtained so that the most important parameters affecting the shell responses can be readily identified. The response sensitivities obtained by the proposed formulation are compared with those obtained by the finite difference procedure. An extensive parametric study has been carried out considering different variables to understand the performance of laminated shell. PubDate: 2018-04-26 DOI: 10.1007/s00419-018-1380-z

Authors:Ranita Roy; Soumen De; B. N. Mandal Abstract: The problem of water wave scattering by three thin vertical barriers present in infinitely deep water is investigated assuming linear theory. Out of the three, two outer barriers are partially immersed and the inner one is fully submerged and extends infinitely downwards. Havelock’s expansion of water wave potential along with inversion formulae is employed to reduce the problem into a set of linear first-kind integral equations which are solved approximately by using single-term Galerkin approximation technique. Very accurate numerical estimates for the reflection and transmission coefficients are then obtained. The numerical results obtained for various arrangements of the three vertical barriers are depicted graphically in several figures against the wavenumber. These figures exhibit that the reflection coefficient vanishes at discrete wavenumbers only when the two outer barriers are identical. Few known results of a single submerged wall with a gap, single fully submerged barrier extending infinitely downwards, and two barriers partially immersed up to the same depth in deep water are recovered as special cases. This establishes the correctness of the method employed here. PubDate: 2018-04-25 DOI: 10.1007/s00419-018-1382-x

Authors:A. Nasrnia; F. Haji Aboutalebi Abstract: In brittle or quasi-brittle materials, mechanical fracture phenomenon occurs suddenly and without any warning. Therefore, prediction of brittle materials failure is an essential challenge confronting design engineers. In this research, using the conventional finite element method (CFEM) and extended finite element method (XFEM) based on linear elastic fracture mechanics, rupture behavior of U-notch specimens under mixed mode loadings are numerically and practically studied. As the main contribution and objective of the current study, two different fracture criteria established on CFEM and six various criteria founded on XFEM are employed to numerically predict load carrying capacity and crack initiation angle of the U-notch samples. Also, the load carrying capacity and crack initiation angle are experimentally obtained from tensile tests of the U-notch instances under planar mixed mode loading to verify the simulation results. The empirical results are compared with the corresponding estimated values achieved by CFEM and XFEM methods which permit to assess the accuracy of the mentioned criteria in predicting the load carrying capacity and crack initiation angle of U-notch coupons subjected to mixed mode loadings, as the novelty of the investigation. The comparison shows that although both the CFEM and XFEM can properly predict the load carrying capacity and crack initiation angle, applying the XFEM in addition to reduce the computational costs and mesh sensitivity is more precise. Besides, a comparison between the XFEM results denotes that stress-based models are significantly more accurate than strain-based types in predicting the load carrying capacity and crack initiation angle of the U-notch instances under mixed mode loading. PubDate: 2018-04-24 DOI: 10.1007/s00419-018-1381-y

Authors:Wei Liu; Lichun Bian Abstract: In this paper, a three-layer model is proposed for the composite with an ellipsoidal inclusion core surrounded successively by the interphase and matrix phase, respectively. The elastic properties of composites are investigated, and the existence of interphase between inclusion and matrix is taken into account. The overall composite materials can be treated statistically as a transversely isotropic solid for the case of aligned axisymmetric ellipsoidal inclusions. The main novelty in the present scheme resides in the consideration of the existence of interphase surrounding the multiple types of aligned ellipsoidal inclusions, and the interactions between inclusions and interphase are taken into account. The influence of some factors, such as the particle shape, the particle size and the interphase thickness, on longitudinal and transversal Young’s modulus is analyzed. The obtained solutions are shown to agree well with the theoretical ones in the existing literature. PubDate: 2018-04-23 DOI: 10.1007/s00419-018-1384-8

Authors:Nguyen Van Khang; Nguyen Sy Nam; Nguyen Van Quyen Abstract: A computer algebraic approach for linearization of the equations of constrained multibody systems is discussed in this paper. Based on linearized differential equations, the Newmark method is applied to calculate steady-state periodic vibrations of the parametric vibration of constrained dynamical models. The numerical calculation is also demonstrated on a model of a mechanism with elastic connecting link. PubDate: 2018-04-20 DOI: 10.1007/s00419-018-1376-8

Authors:Ehsan Torkan; Mostafa Pirmoradian; Mohammad Hashemian Abstract: Elastodynamic behavior analysis of structures under moving loads is of great interest in most engineering fields. In this study, dynamic instability due to parametric and external resonances of simply supported thin rectangular plates on an elastic foundation under successive moving masses is investigated as a linear time-periodic problem. Effects of all components of moving mass inertia are considered in the analysis. The governing partial differential equation of motion is transformed to a set of ordinary differential equations using the Galerkin method. A comprehensive study of resonance conditions is carried out for two cases: (1) the masses move on a rectilinear path parallel to the longitudinal edges of the plate, and (2) a sequence of moving masses along the diagonal of the plate. Homotopy perturbation method (HPM) is employed as a semi-analytical method to obtain stable and unstable zones in a parameters space in additions to external resonance curves. In order to validate the HPM results, Floquet theory is applied to the state-space equations. A good agreement between two methods is observed. The results of this study are useful for the design of road pavements resting on foundation soil, slab-type bridges, airport pavements, and decks of ships on which aircrafts land. PubDate: 2018-04-18 DOI: 10.1007/s00419-018-1379-5

Authors:H. S. Bauomy; A. T. EL-Sayed Abstract: This study focused on the vibration behavior of a modified vertical conveyor system. The calculated system is exhibited by 2-degree-of-freedom counting quadratic and cubic nonlinearities among both external and parametric forces. Technique of multiple scales connected to gain approximate solutions and study stability of measured structure. All resonances from mathematical solution are extracted. The performance of the system is measured by means of Runge–Kutta fourth-order process (e.g., ode45 in MATLAB). Moreover, two simultaneous resonance cases of this system have been studied analytically and numerically. Stability of acquired numerical solution discovered via frequency response equations. Influences contained by important coefficients scheduled frequency response curves of the considered structure are studied inside numerical results. Methodical results obtained in this work agreed well through the numerical outcome. The description outcome is matched up to available recently published articles. PubDate: 2018-04-16 DOI: 10.1007/s00419-018-1375-9

Authors:Emmanuel Rigaud; Pierre-Henri Cornuault; Benoît Bazin; Emmanuel Grandais-Menant Abstract: This paper focuses on the numerical analysis of the vibroacoustic behavior of an electric window-lift gear motor for automotive vehicle which consists of a DC motor and a worm gear. A dynamic modeling of the gear motor is proposed. The excitation sources correspond to radial electromagnetic forces applied to steel stator, electromagnetic input torque fluctuation, rotor mechanical imbalance, worm gear static transmission error and mesh stiffness fluctuations and gear wheel eccentricity. Parametric equations of motion are solved using an iterative spectral method. It allows the computing of the vibroacoustic response of the system, taking account of the interaction between the mesh stiffness fluctuation and the other excitations. The simulation results are validated from comparison with experimental vibroacoustic measurements performed with a specific test bench. Spectrograms of the dynamic response show components corresponding to the harmonics of the excitation spectra, as well as lateral components arising around the mesh frequency and the input torque fluctuation frequency. This spectral enrichment is generated by the interaction between the mesh stiffness fluctuation and the other excitations. The lateral components contribute little to the overall level of the vibroacoustic response, but they may have a significant impact on the quality of noise radiated directly by the gear motor or indirectly by its supporting structure. Finally, the weights of the different excitation sources to the spatial-average mean-square velocity of the radiating surface and the equivalent global dynamic force transmitted to the supporting structure are compared. PubDate: 2018-04-06 DOI: 10.1007/s00419-018-1378-6

Authors:George A. Gazonas; Raymond A. Wildman; David A. Hopkins; Michael J. Scheidler Abstract: We consider several one-dimensional impact problems involving finite or semi-infinite, linear elastic flyers that collide with and adhere to a finite stationary linear viscoelastic target backed by a semi-infinite linear elastic half-space. The impact generates a shock wave in the target which undergoes multiple reflections from the target boundaries. Laplace transforms with respect to time, together with impact boundary conditions derived in our previous work, are used to derive explicit closed-form solutions for the stress and particle velocity in the Laplace transform domain at any point in the target. For several stress relaxation functions of the Wiechert (Prony series) type, a modified Dubner–Abate–Crump algorithm is used to numerically invert those solutions to the time domain. These solutions are compared with numerical solutions obtained using both a finite-difference method and the commercial finite element code, COMSOL Multiphysics. The final value theorem for Laplace transforms is used to derive new explicit analytical expressions for the long-time asymptotes of the stress and velocity in viscoelastic targets; these results are useful for the verification of viscoelastic impact simulations taken to long observation times. PubDate: 2018-04-06 DOI: 10.1007/s00419-018-1372-z

Authors:Chuanzong Sun; Yushu Chen; Lei Hou Abstract: In this paper, the nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact are investigated. A novel framework is proposed, in which the sophisticated geometrical structure is considered by finite solid element method and efficient model order reduction is applied to the model. The validity and efficiency of the reduced-order model are verified through critical speed and eigen problems. Its stable and unstable solutions are calculated by means of the assembly technique and the multiple harmonic balance method combined with the alternating frequency/time domain technique (MHB–AFT). The accurate frequency amplitudes are obtained accordingly for each harmonic component. The stabilities of the solutions are checked by the Floquet theory. Through the numerical computations, some complex nonlinear phenomena, such as combined frequency vibration, hysteresis, and resonant peak shifting, are discovered when the rub-impact occurs. The results also show that the control parameters of mass eccentricity, rub-impact stiffness, and rotational speed ratio make significant but different influences on the dynamical characteristics of the system. Therefore, a key innovation of this paper is the marriage of a hybrid modeling method—accurate modeling technique combined with model order reduction and solution method—highly efficient semi-analytic method of MHB–AFT. The proposed framework is benefit for parametric study and provides a better understanding of the nonlinear dynamical behaviors of the real complicated dual-rotor aero-engine with rub-impact. PubDate: 2018-04-06 DOI: 10.1007/s00419-018-1373-y

Authors:Amin Ghadami; Mehdi Behzad; Hamid Reza Mirdamadi Abstract: Damage detection in uniform structures has been studied in numerous previous researches. However, damage detection in non-uniform structures is less studied. In this paper, a damage detection algorithm for identifying rectangular notch parameters in a stepped waveguide using Lamb waves is presented. The proposed algorithm is based on mode conversion and scattering phenomena because of interaction of Lamb wave modes with defects. The analysis is divided into two steps: notch localization and notch geometry detection. The main advantage of this method is its ability to detect all of the notch parameters in a waveguide with arbitrary number of step discontinuities. The method is applied to a numerical example and the results show that it can successfully identify the notch location, depth, and width in a multi-step plate. PubDate: 2018-04-06 DOI: 10.1007/s00419-018-1355-0

Authors:Alla V. Ilyashenko; Sergey V. Kuznetsov Abstract: The exact solutions of the linear Pochhammer–Chree equation for propagating harmonic waves in a cylindrical rod are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of wave polarization on the free surface due to variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear speed ( \(c_2\) ) all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer–Chree wave can propagate at \(c_2\) phase speed. PubDate: 2018-04-04 DOI: 10.1007/s00419-018-1377-7

Authors:Carmine M. Pappalardo; Domenico Guida Abstract: This paper is focused on the development of a numerical procedure for solving the system identification problem of linear dynamical models that mathematically describe multibody mechanical systems. To this end, an input–output representation of the time evolution of a general mechanical system based on a sequence of matrices referred to as Markov parameters is employed. The set of Markov parameters incorporate the state-space matrices that allow for describing the dynamic behavior of a general mechanical system considering the assumption of structural linearity. The system Markov parameters are defined by means of a discretization process applied to the analytical description of a mechanical system, and therefore, they are difficult to obtain directly from observable measurements. However, a state observer can be introduced in order to define a set of observer Markov parameters that can be readily recovered from input–output experimental data. The observer Markov parameters obtained by using a least-square approach allow for computing in a recursive manner the system Markov parameters as well as another discrete sequence of matrices referred to as observer gain Markov parameters. Subsequently, the system and observer gain Markov parameters identified from observable input–output data are used for constructing a sequence of generalized Hankel matrices from which a state-space model of the mechanical system of interest can be extracted. This fundamental step of the identification procedure is performed in the algorithm elaborated in this work employing a numerical procedure which relies on the use of the Moore–Penrose pseudoinverse matrix obtained by means of the singular value decomposition. In the paper, the principal analytical and numerical aspects of the proposed identification algorithm are described in detail. Furthermore, a numerical example based on a simple vehicle model is discussed in order to verify by means of numerical experiments the effectiveness of the identification procedure developed in this work. PubDate: 2018-04-04 DOI: 10.1007/s00419-018-1374-x

Authors:Ahmad Paknejad; Gholamhossein Rahimi; Hamed Salmani Abstract: The study of vibrational energy harvesting using piezoelectric patch integrated on isotropic beam-like or plate-like thin structures has received significant attention over the past decade. Multilayer orthotropic composite plates are widely used in aerospace, automotive and marine applications, where they can be considered as host structures for vibration-based energy harvesting. In this paper, an exact analytical solution and numerical validation of a piezoelectric energy harvester structurally integrated to a thin multilayer orthotropic plate are presented. Electroelastic model of the thin multilayer composite plate with the piezoelectric patch harvester is developed based on a distributed parameter modeling approach with classical laminate plate theory assumptions for all-four-edge-clamped (CCCC) boundary condition. Closed-form steady-state expressions for coupled electrical outputs and structural vibration response are derived under harmonic transverse force excitation in the presence of a resistive load. Analytical electroelastic FRFs related to the voltage output as well as vibration response to force input are derived and generalized for different boundary conditions of host plate. The results of numerical and analytical models from multiple vibration modes are compared first for validating the analytical model with a case study employing a thin PZT-5A piezoceramic patch attached on the surface of a multilayer orthotropic composite CCCC plate. For this purpose, finite-element analysis is carried out by using ANSYS mechanical APDL software. Then, it is important to specify parameters in energy harvesting model, so positioning of piezoceramic patch harvester and excitation point force on the voltage output FRFs is discussed through an analysis of dynamic strain distribution on the overall plate surface. In addition, the effects of various composite laminate plates with different stacking sequences as host structures on generated power are discussed in details as well. PubDate: 2018-04-04 DOI: 10.1007/s00419-018-1363-0

Authors:H. Roy; S. Chandraker Abstract: In the past, many researchers developed rotor models using either lump system or finite element approach, where material damping played a crucial role in dynamic behaviour. Such damping in any rotating structure triggers instability at the supercritical range. In most of the literatures, material damping has been incorporated either by frequency-independent hysteretic damping or frequency-dependent viscous damping, but these models are insufficient to estimate the dynamic characteristics of the system. The motivation for using general viscoelastic model arises from a need to capture the influence of both types of damping. Such type of modelling is done through operator-based constitutive relationship. The numerator and denominator of material modulus are a polynomial of differential time operator, and polynomial coefficients are known as a viscoelastic parameter. The operator-based constitutive relationship is further utilized to bring down higher-order equations of motion by using two different techniques, i.e. (a) analytical approach and (b) finite element approach.The shaft damping is tackled in such a manner that the dissipation effects can be considered through all coordinates. The significance of both approaches is explained with the help of stability and response analysis at various disc positions. PubDate: 2018-04-04 DOI: 10.1007/s00419-018-1370-1

Authors:Jia-Hao He; Hsin-Haou Huang Abstract: This paper presents a metamaterial plate (metaplate) consisting of a periodic array of holes on a homogeneous thin plate with slot-embedded resonators. The study numerically proves that the proposed model can generate a complete vibrational bandgap in the low-frequency range. A simplified analytical model was proposed for feasibly and accurately capturing the dispersion behavior and first bandgap characteristics in the low-frequency range, which can be used for initial design and bandgap study of the metaplate. A realistic and practical unit metaplate was subsequently designed to verify the analytical model through finite element simulations. The metaplate not only generated a complete vibrational bandgap but also exhibited excellent agreement in both analytical and finite element models for predicting the bandgap characteristics. This study facilitates the design of opening and tuning bandgaps for potential applications such as low-frequency vibration isolation and stress wave mitigation. PubDate: 2018-04-04 DOI: 10.1007/s00419-018-1371-0

Authors:F. D. Fischer; G. A. Zickler; J. Svoboda Abstract: As outlined in the previous paper, an eigenstrain state due to an interstitial atom, acting as misfitting inclusion in the crystal lattice, may interact with a load stress state and/or a stress state due to a defect. Since the interstitial atoms can be assembled in a cylinder, as in the established case of a so-called Cottrell cloud, the according stress state can be investigated by a cylindrical inclusion with a general eigenstrain state. Both eigenstrain components belonging to the antiplane shear, however, were not dealt with in the past. According stress and deformation equations are now offered in analytical form in this addendum. PubDate: 2018-04-02 DOI: 10.1007/s00419-018-1367-9