Authors:P. Geng; J. Z. Xing; X. X. Chen Pages: 365 - 384 Abstract: Abstract The maximum strength ratio and more uniform strength for all layers can be achieved by variation of winding angle of filament-wound (FW) vessel. The deformation and stresses of a thick-walled cylinder with multi-angle winding filament under uniform internal pressure are proposed. The stresses of each orthotropic unit of fiber layers, as well as longitudinal stress along the fiber direction, transverse stresses perpendicular to the fiber direction and shear stress in the fiber layer are derived analytically. An optimization model of FW closed ends vessel under uniform internal pressure subjected to Tsai–Wu failure criterion to maximize the lowest strength ratio through thickness with optimal variation of winding angle is built. Two optimization methods are adopted to find the optimized winding angle sequence through different ways, and their combination led to more efficient algorithm is suggested. The research shows that the material utilization and working pressure can be increased by proper winding angle variation, and several optimization winding angle sequence schemes are found for different thickness ratios cylindrical vessels with two typical composite materials E-glass/epoxy and T300/934, which are useful for many applications of FW vessel design and manufacture. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1198-5 Issue No:Vol. 87, No. 3 (2017)

Authors:G. B. Muravskii Pages: 405 - 425 Abstract: Abstract An approximate method is presented, using (with suitable corrections) only the compliance’s poles that are located nearly positive real axis in the complex frequency plane, for solving transient vibration problems containing different damping mechanisms. For determination of poles and its residues, a new method based on consideration of known values of a function in the vicinity of a pole is suggested which allows achieving a required accuracy due to an iteration process. Simple and sufficiently accurate approximate formulas are obtained for treatment mechanical systems with different damping mechanisms under the action of impulse loads. A particular attention is paid to the model, which can be considered as a correction of the ideal hysteretic model. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1200-2 Issue No:Vol. 87, No. 3 (2017)

Authors:Ioannis G. Raftoyiannis; George T. Michaltsos Pages: 427 - 437 Abstract: Abstract A procedure for deriving the complete equations of motion to compute an isolator’s displacement due to strong ground motion is applied to structures isolated with friction pendulum systems. The resulting equations, which contain the vertical inertia forces, were studied to estimate the influence of these forces on the isolator’s behavior. The nonlinear equation is solved employing the technique of successive approximations. The results obtained showed that the influence of the vertical inertia forces on structural response is negligible for the case of a long-distance ground motion, while becoming significant for a near-source ground motion. On the other hand, very small values of the isolator’s radius R cause an increase of the aforementioned influence. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1201-1 Issue No:Vol. 87, No. 3 (2017)

Authors:Zineeddine Louna; Ibrahim Goda; Jean-François Ganghoffer; Salah Benhadid Pages: 457 - 477 Abstract: Abstract We construct in the present paper the effective growth response of trabecular bone, based on micromechanical analyses at the scale of a representative volume element consisting of individual trabeculae defining the representative unit cell (RUC). From a fundamental perspective, we adopt the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the surface remodeling of the individual trabeculae, the averaging of which leads to a net growth at the mesoscopic scale of the RUC. The effective model for the growing unit cell relies on an average kinematics which has been formulated in terms of the effective growth velocity gradient and effective elastic rate of deformation tensor, both functions of the rate of the effective density and stress applied over the RUC. The evaluation of the relation between the average rate of growth tensor and elastic growth rate versus the external stress applied to the RUC is obtained from a split of the average rate of growth tensor into its spherical and deviatoric parts, each of which being related to the corresponding applied stress quantities. The effective growth model is written for three different loading conditions as a polynomial relation between the components of the rate of growth tensor and similar components of the stress tensor under planar conditions, with a nonlinear function of the effective density as a weighting factor. The developed methodology is quite general and is applicable to any choice of the RUC morphology representative of the internal bone architecture. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1204-y Issue No:Vol. 87, No. 3 (2017)

Authors:Weiqin Yu; Fangqi Chen; Na Li; Tianbo Wang; Shouwei Zhao Pages: 479 - 487 Abstract: Abstract Through both analytical and numerical approaches, stability and bifurcation dynamics are studied for a nonlinear controlled system subjected to parametric excitation. The controlled system is a typical case of a two-degree-of-freedom system composed of a parametrically excited pendulum and its driving device. Three types of critical points for the modulation equations are considered near the principle resonance and internal resonance, which are characterized by a double zero and two negative eigenvalues, a double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues, respectively. With the aid of normal form theory, the stability regions for the initial equilibrium solutions and the critical bifurcation curves are obtained analytically, which exhibit some new dynamical behaviors. A time integration scheme is used to find the numerical solutions for these bifurcations cases, which confirm these analytical predictions. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1205-x Issue No:Vol. 87, No. 3 (2017)

Authors:Ping Wang; Qiang Yi; Caiyou Zhao; Mengting Xing; Jian Tang Pages: 503 - 519 Abstract: Abstract This paper presents the results of a study concerning the band-gap behaviours and formation mechanisms of periodic track structures. Based on the band-gap theories introduced from phononic crystal which concentrates on the elastic wave propagation in periodic structures, the railway track can be regarded as a novel locally resonant phononic crystal. The band-gaps are found by using the transfer matrix method combined with Bloch theorem, and the attenuation factors in band-gaps are also obtained firstly. Then, band-gap behaviours of periodic track structures are investigated with various parameters such as stiffness of rail pad, fastening spacing and thermal force in rail. Bounding frequencies and width of band-gaps are closely related to the parameters of track structures, resulting from the various wave motion modes at the bounding frequencies. Moreover, it has been found that Bragg band-gaps and locally resonance band-gaps coexist in periodic track structures. And formation mechanisms of band-gaps in periodic track structures can be explained by the Bragg scattering mechanism and locally resonance mechanism. The theoretical analysis is verified by the frequency response functions calculated through the finite element models at last. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1207-8 Issue No:Vol. 87, No. 3 (2017)

Authors:Xiaojing Sun; Xinyu Gong; Diangui Huang Pages: 521 - 554 Abstract: Abstract In the recent decades, biomimetic robots have attracted scientific communities’ attention increasingly, as people try to learn from nature in which exist astonishing and uniquely evolved mechanisms shown by very species. Dragonfly, as such one example, demonstrates unique and superior flight performance than most of the other insect species and birds. Researchers are obsessed with the aerodynamic characteristics of an in-flight dragonfly as two pairs of independently controlled wings provide them with an unmatchable flying performance and robustness. In this paper, an extensive review of recent studies related to the flight aerodynamics of dragonflies has been conducted. The main research findings about effect of the motion parameters and body attitude on the resulting aerodynamic forces and power requirements in different flight modes of a dragonfly are summarized. Particular attention is given to functional characteristics of dragonfly wings and the importance of mutual interaction between forewing and hindwing for its flyability. This article aims to bring together current understandings of dragonfly aerodynamics and thus has certain reference value to design and control of dragonfly-inspired biomimetic devices. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1208-7 Issue No:Vol. 87, No. 3 (2017)

Authors:L. Auersch Pages: 555 - 574 Abstract: Abstract The dynamics of unisolated and isolated ballast tracks have been analysed by multi-beam models for the track and by a layered half-space model for the soil. The solution is calculated in frequency–wavenumber domain and transformed back to space domain by a wavenumber integral. This is a faster method compared to other detailed track–soil interaction methods and almost as fast as the widely used Winkler soil method, especially if the compliances of the soil have been stored for repeated use. Frequency-dependent compliances and force transfer functions have been calculated for a variety of track and soil parameters. The ballast has a clear influence on the high-frequency behaviour, whereas the soil is dominating the low-frequency behaviour of the track. A layering of the soil may cause a moderate track–soil resonance, whereas more pronounced vehicle–track resonances occur with elastic track elements like rail pads, sleeper pads and ballast mats. Above these resonant frequencies, a reduction in the excitation forces follows as a consequence. The track deformation along the track has been analysed for the most interesting track systems. The track deformation is strongly influenced by the resonances due to layering or elastic elements. The attenuation of amplitudes and the velocity of the track–soil waves change considerably around the resonant frequencies. The track deformation due to complete trains have been calculated for different continuous and Winkler soils and compared with the measurement of a train passage showing a good agreement for the continuous soil and clear deviations for the Winkler soil model. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1209-6 Issue No:Vol. 87, No. 3 (2017)

Authors:Panagiotis Koutsovasilis Pages: 575 - 592 Abstract: Abstract The modelling and simulation process of high-speed rotor dynamics is a rather essential task that should accompany the virtual prototype development of exhaust gas turbochargers. The system’s nonlinear nature originates primarily in the oil-film concentrated in the journal bearings, which relates to the associated gyroscopic forward and backward modes. This study focuses on linear rotor dynamics and the impact of the bearing stiffness variation on the shape alternation of gyroscopic modes, which cannot be observed in the typical critical speed maps or Campbell diagrams. The mode degeneration is investigated with the help of the modal assurance criterion according to two principles: first, quantify the shape alternation of the associated modes on the basis of the average bearing stiffness from literature, and second, compare the consecutive modes against each other, either forward or backward. The latter reveals that the aforementioned degeneration leads to a jump with respect to the mode shape into the next occurring mode although it is still being registered as a system whirl that belongs to the previous natural frequency. The investigation is extended over a wide range of turbocharger frame sizes demonstrating that both the mode degeneration and jump occur independently of the assembly dimensions, thus offering an alternative insight on the possible form of the occurring rotor-bearing oscillations arising from motor excitation, aero-loads or self-excited vibrations due to oil-whirl. PubDate: 2017-03-01 DOI: 10.1007/s00419-016-1210-0 Issue No:Vol. 87, No. 3 (2017)

Abstract: Abstract Newton’s law of motion is derived from Kepler’s laws of planetary motion. This is achieved by applying a simple system identification method using numerical data from the planet’s orbits in conjunction with the inverse square law for the attractive force between celestial bodies and the concepts of the derivative and differential equation. The identification procedure yields the differential equation of motion of a body under the action of an applied force as stated by Newton. Moreover, the employed procedure, besides validating the inverse square law, permits the evaluation of the gravitational mass (standard gravitational parameter), paving thus the way for establishing Newton’s law of universal gravitation. As the employed mathematical tools and the theory were available before 1686, we are allowed to state that the equation of motion for a body with constant mass could have been established from Kepler’s law of planetary motion, before Newton had published his law of motion. PubDate: 2017-03-28

Abstract: Abstract This paper considers the free vibrations of the non-uniform axially functionally graded cantilever beam with a tip body. It is assumed that the mass center of the tip body is eccentrically displaced in both axial and transverse direction relative to the beam tip. All considerations are carried out within the Euler–Bernoulli beam theory. The in-plane transverse and axial deformations of the beam are considered. It is shown that there is a coupling between the axial and transverse deformations of the cantilever beam due to the tip body mass center eccentricity in the transverse direction. An universal, numerically efficient rigid element method which is able to analyze the cantilever beam with any law of changes of the geometric parameters of the cross section or the characteristics of the material along the beam was formed. Theoretical considerations are accompanied by numerical examples. There is a good agreement of the results obtained with the results available in the literature. PubDate: 2017-03-23

Abstract: Abstract This paper presents new regularized boundary integral equations (BIEs) for elastic displacement gradients in three dimensions and then combines them by the generalized Hooke’s law to calculate the boundary stress. In the new regularized BIEs, two special tangential vectors are designed with the normal vector to construct a transformation system. Based on this system, the displacement gradient in any direction can be transformed into a linear combination of the normal gradient and tangential gradients along the two special vectors. Moreover, a theorem related to some integral properties of the fundamental solution is introduced. Finally, the regularized indirect BIEs are developed by using the above-mentioned technique of linear combination and theorem. The proposed method has some advantages over the direct boundary element method, such as the relaxed continuity requirement of density function, no hypersingular integral, and being available to calculate the displacement gradient in any direction. The numerical implementation of the developed integral equation is provided, and the accuracy and convergence of the approach are also illustrated through four numerical examples. PubDate: 2017-03-23

Authors:Gergana Nikolova; Jordanka Ivanova; Frank Wuttke; Petia Dineva Abstract: Abstract The interface fracture behaviour of a bi-material poroelastic plate with normal to the interface surface-breaking pre-crack with crack-tip approaching the interface subjected to time-harmonic uniaxial uniform load is considered. A viscoelastic isomorphism to Biot’s dynamic poroelasticity is applied to describe the soil material properties, thus replacing the original two-phase poroelastic material by a single-phase viscoelastic one of Kelvin–Voigt type. A viscoelastic shear-lag model for one-dimensional stress–strain state with analytically derived solution for the length of the delamination zone along the interface is proposed. The parametric analysis demonstrates that the debonding length is sensitive to the following key factors: (a) frequency and magnitude of the applied load; (b) material and geometric characteristics; (c) soil porosity as respected soil type; and (d) soil saturation—dry or saturated soils. PubDate: 2017-03-14 DOI: 10.1007/s00419-017-1241-1

Authors:F. Hache; N. Challamel; I. Elishakoff; C. M. Wang Abstract: Abstract This paper investigates both stability and vibration of nonlocal beams or plates in the presence of compressive forces. Various nonlocal structural models have been proposed to capture the inherent scale effects of lattice-based beams or plates. These nonlocal models are either based on continualization of the difference equations of the original lattice problem (labeled as continualized nonlocal models), or developed from phenomenological nonlocal approaches such as Eringen’s type nonlocality. Considered herein are several continualization schemes that lead to either fourth or sixth order spatial governing differential or partial differential equation. Even if the new continualized nonlocal plate models differ in their mathematical description, they appear to furnish very close macroscopic results as shown from asymptotic expansion arguments. The continualized nonlocal beam and plate models and the phenomenological approaches are also introduced from variational arguments. The key role of boundary conditions is shown especially for Eringen’s nonlocal model that is not necessarily variationally based. For each of them, the buckling load and the natural frequencies are determined for simply supported beams and plates and compared to their counterparts obtained from the lattice model. The small length scale coefficient of the nonlocal beam or plate models is intrinsically constant and problem independent for the continualized approaches, whereas it is calibrated for the phenomenological models based on the equivalence with the reference microstructured model and consequently, depends on the load, the buckling or vibration mode or the aspect ratio. It is found that the nonlocal continualized approaches are more efficient than the nonlocal phenomenological ones. For beam problems, continualized nonlocal and phenomenological approaches such as Eringen’s nonlocal theory can become the same. However, for plate problems, phenomenological approaches may differ significantly from continualized nonlocal ones; thereby offering one the opportunity to have a new class of two-dimensional nonlocal models. PubDate: 2017-03-13 DOI: 10.1007/s00419-017-1235-z

Authors:Wang Xu; Zhenzhen Tong; Dalun Rong; A. Y. T. Leung; Xinsheng Xu; Zhenhuan Zhou Abstract: Abstract A finite element discretized symplectic method is presented for the determination of modes I and II stress intensity factors (SIFs) for cracked bimaterial plates subjected to bending loads using Kirchhoff’s theory and symplectic approach. The overall plate is meshed by conventional discrete Kirchhoff theory elements and is divided into two regions: a near field which contains the crack tip and is enhanced by the symplectic series expansion and a far field which is far away from the crack tip. Based on the analytical solutions of global displacement, numerous degrees of freedom are transformed to a small set of undetermined coefficients of the symplectic series through a displacement transformation, while those in the far field remain unchanged. The SIFs can be obtained directly from coefficients of eigensolution (Re \(\mu < 1\) ), and no post-processing or special singular element are required to develop for extracting the SIFs. Numerical examples are presented and compared with existing results to demonstrate the efficiency and accuracy of the method. PubDate: 2017-03-13 DOI: 10.1007/s00419-017-1239-8

Authors:Wolfgang E. Weber; George D. Manolis Abstract: Abstract This work addresses the evaluation of the displacement field in an elastic matrix due to the presence of an embedded homogeneous inclusion under time-harmonic SH-wave loads. We consider the bond between the circular cylindrical inclusion and the surrounding matrix of infinite extent to be partly damaged in the circumferential direction. The material of both inclusion and matrix is modelled as homogeneous, isotropic, and linearly elastic. An analytical approach is introduced here for describing the scattering of SH-waves by inclusions with partly damaged bond. Subsequently, a numerical example serves to illustrate the methodology, which can be extended to the scattering of SV/P-waves in a straightforward manner. PubDate: 2017-03-10 DOI: 10.1007/s00419-017-1238-9

Authors:Ivan Jeník; Petr Kubík; František Šebek; Jiří Hůlka; Jindřich Petruška Abstract: Abstract Two alternative methods for the stress–strain curve determination in the large strains region are proposed. Only standard force–elongation response is needed as an input into the identification procedure. Both methods are applied to eight various materials, covering a broad spectre of possible ductile behaviour. The first method is based on the iterative procedure of sequential simulation of piecewise stress–strain curve using the parallel finite element modelling. Error between the computed and experimental force–elongation response is low, while the convergence rate is high. The second method uses the neural network for the stress–strain curve identification. Large database of force–elongation responses is computed by the finite element method. Then, the database is processed and reduced in order to get the input for neural network training procedure. Training process and response of network is fast compared to sequential simulation. When the desired accuracy is not reached, results can be used as a starting point for the following optimization task. PubDate: 2017-03-07 DOI: 10.1007/s00419-017-1234-0

Authors:Guowei Zhao; Jianming Du; Zhigang Wu Abstract: Abstract In this study, we reconstructed a dynamic model of a rotating cantilever beam for which the geometric stiffening term was obtained by accounting for the longitudinal shrinkage caused by the transverse deflection of the beam. Previous investigations focused on kinetic energy but neglected strain energy. For this study, we retained these strain energy coupling terms. We used Hamilton’s principle to derive the complete coupling model. Taking the effect of steady-state axial deformation into account, we obtained the transverse equation of motion and the coupling general characteristic equation. Unlike previous models, this model incorporates not only the geometric stiffening effect but also the geometric softening effect. In relevant numerical examples, as the angular velocity increases, the bending frequency gives rise to geometric stiffening in line with the results obtained in previous studies. When the angular velocity reaches and exceeds a critical value, the bending frequency produces a geometric softening phenomenon. PubDate: 2017-03-02 DOI: 10.1007/s00419-017-1231-3

Authors:L. H. Zheng; Z. Liu; M. L. Chen; Y. T. Zhu Abstract: Abstract A vibration quarter-carbody model of a roller coaster running on a spatial trajectory is derived based upon the motion parameters, vertical acceleration, angular velocity, angular attitude, and transient position. These motion parameters are acquired from an ADAMS virtual prototype. The vibration response of the carbody is obtained by solving the differential equations with variable coefficients. Besides, the validity of both the ADAMS virtual prototype and the vibration model is verified by the simulated results versus the actually measured ones. Furthermore, a method, called as space frequency characteristics, is proposed to investigate the relation between the carbody vibration and the motion parameter of roller coaster, which reveals that the carbody vibration is related to its transient position and the influence of the randomness of the motion parameters on the vibration is eliminated. This research is supposed to be helpful for the fault diagnosis of roller coaster by considering both the vibration and motion signals. PubDate: 2016-12-24 DOI: 10.1007/s00419-016-1206-9