Authors:Péter L. Várkonyi Pages: 785 - 799 Abstract: We investigate the dynamics of finite degree-of-freedom, planar mechanical systems with multiple sliding, unilateral frictional point contacts. A complete classification of systems with 2 sliding contacts is given. The contact-mode-based approach of rigid body mechanics is combined with linear stability analysis using a compliant contact model to determine the feasibility and the stability of every possible contact mode in each class. Special forms of non-stationary contact dynamics including “impact without collision” and “reverse chattering” are also investigated. Many types of solution inconsistency and indeterminacy are identified and new phenomena related to Painlevé’s non-existence and non-uniqueness paradoxes are discovered. Among other results, we show that the non-existence paradox is not fully resolvable by considering impulsive contact forces. These findings contribute to a growing body of evidence that rigid body mechanics cannot be developed into a complete and self-consistent theory in the presence of contacts and friction. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1165-1 Issue No:Vol. 87, No. 5 (2017)

Authors:Wojciech Sawczuk; Grzegorz M. Szymański Pages: 801 - 815 Abstract: Increasing the speed of trains forces the application of a greater braking power, i.e. the capability of the brake system of rapidly absorbing and dispersing the stored heat energy. The instability of operation results from the occurrence of vibrations on the friction component, which affects the efficiency of the braking process. In practice, it means that when braking, the vehicle variable friction resistance may lead to an uneven braking process. The effects of such changes can be manifested in the form of vibrations with high input amplitude. The vibrations generated by the working components are distributed throughout the vehicle, which also adversely affects the driving comfort. The purpose of this paper is to determine the resonant frequencies of selected components of the railway disc brake. This paper presents a method of assessing the thickness of the brake pads of a railway disc brake based on the results of parameterization of the time-frequency map a(t, f) of vibrations generated by the brake components. Methods of time-frequency analysis were suggested as a tool of time-frequency selection of the vibration signal. The authors described an algorithm of the method and presented an example illustrating the application of the synchronously averaged short-time Fourier transform for the extraction of the signal components related to the braking process. As a result of parameterization of the map a(t, f) signal parameters, values covariant with the thickness of the disc brake were obtained. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1202-0 Issue No:Vol. 87, No. 5 (2017)

Authors:Grzegorz Kudra; Jan Awrejcewicz Pages: 817 - 828 Abstract: Some special cases of a larger class of smooth models of the resultant friction force occurring on a planar contact area are developed and presented. These models are constructed under assumptions of classical Coulomb’s law of friction on each element of contact and instantaneous transition between two modes: fully developed sliding and rigid stick state without local slips and deformations of the contact area. They are able to model cases of different values of static and kinetic friction factors. The considered models are very effective tools for fast and reliable numerical simulations of mechanical systems with frictional contacts. They are applied in modelling and numerical analysis of a special kind of mechanical system, i.e. a kind of a pendulum with special frictional driving. The rotational joint of the pendulum is elastically suspended in the motion plane. The pendulum is driven by circular frictional contact with a rotating disk. Examples of self-excited bifurcation and chaotic dynamics as well as stick–slip behaviour of the pendulum are presented. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1182-0 Issue No:Vol. 87, No. 5 (2017)

Authors:Yury Selyutskiy; Rinaldo Garziera; Luca Collini Pages: 829 - 839 Abstract: One of the most destructive effects of earthquakes upon buildings and other constructions is due to horizontal displacement of the ground. This paper proposes a simplified approach to describe behavior of tower-like structures in such conditions. For this aim, a plane-parallel motion of a rigid body over horizontal plane with dry friction is considered. It is assumed that the plane performs harmonic oscillations in horizontal direction. In order to describe collisions between the body and the supporting plane, Routh hypothesis is used. Influence of body aspect ratio and characteristics of the supporting plane acceleration on the behavior of the body is studied. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1214-9 Issue No:Vol. 87, No. 5 (2017)

Authors:Grażyna Sypniewska-Kamińska; Roman Starosta; Jan Awrejcewicz Pages: 841 - 852 Abstract: The externally excited and damped vibration of the double pendulum in the vertical plane are considered. The pendulum can collide many times during the motion with a motionless obstacle having the rough surface. The double pendulum colliding with this object has been modeled as a piecewise smooth system constrained by the unilateral constraint. In the relatively long time between the collisions, the differential equations govern the motion of the pendulum. When the contact with the obstacle appears, the pendulum exhibits a discontinuous behavior. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson’s hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Therefore, the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space. The angular velocities of both pendulum parts as well as the reaction forces at the joints of the system, which change in stepwise manner, have been presented in the paper. PubDate: 2017-05-01 DOI: 10.1007/s00419-017-1230-4 Issue No:Vol. 87, No. 5 (2017)

Authors:Valter Böhm; Tobias Kaufhold; Igor Zeidis; Klaus Zimmermann Pages: 853 - 864 Abstract: The use of mechanically compliant tensegrity structures in mobile robotics is an attractive research topic. The mechanical properties and therefore the locomotion performance of mobile robots based on these structures can be adjusted reversibly during locomotion. In the present work, a rolling mobile robot, based on a simple tensegrity structure, consisting of two rigid disconnected curved members connected to a continuous net of eight prestressed tensioned members with pronounced elasticity, is considered. Pure rolling uniaxial locomotion and also planar locomotion can be realized with small control effort, induced by the movement of two internal masses. After kinematic considerations, the nonlinear equations of motion are derived and transient dynamic analyses are performed, to study the system behavior. Also the dependency of the rolling movement behavior on structural and actuation parameters is discussed. The uniaxial and planar locomotion performance of the system are verified experimentally. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1183-z Issue No:Vol. 87, No. 5 (2017)

Authors:F. Clementi; S. Lenci; G. Rega Pages: 865 - 880 Abstract: Two approximate solutions for the nonlinear free oscillations of a planar Timoshenko beam are compared to each other. The beam has an axial spring that permits to consider different boundary conditions, from axially free (which has a softening nonlinear behaviour) to perfectly axially restrained (which has a hardening nonlinear behaviour). The first approximation is analytical and is obtained by the asymptotic development method, while the second is numerical and is obtained by the finite element method. The comparison is made in terms of backbone curves describing the dependence of the (nonlinear) frequency on the oscillation amplitude. Very good agreement is found, for both slender and thick beams, and for varying stiffness of the end spring. This is a cross-check verification of the reliability of both approximate solutions. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1159-z Issue No:Vol. 87, No. 5 (2017)

Authors:Paweł Fritzkowski Pages: 881 - 892 Abstract: The paper is devoted to transverse in-plane vibrations of a beam which is a part of a symmetrical triangular frame. A mathematical model based on the Hamilton principle, formulated for large deflections of the beam subjected to dynamic axial excitation, is presented. An approximate nonlinear ordinary differential equation for the vibration amplitude is derived by means of the Galerkin method. Dynamics of the system is studied numerically for the two cases: harmonic and pulsating load. Various values of the model parameters, including the excitation amplitude and frequency, are considered. The amplitude is taken to be below or above the static critical load. The regions of stable and unstable solutions are determined in parameter planes by evaluation of the maximal Lyapunov exponent. The results are compared to the case of the abbreviated (linear) dynamical system. The stable and unstable beam responses are analysed and classified. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1156-2 Issue No:Vol. 87, No. 5 (2017)

Authors:Manuel Braz-César; Rui Barros Pages: 893 - 904 Abstract: Although building structures can be perceived as a combination of primary frames in two orthogonal directions, they are three-dimensional systems that usually present a very complex dynamic behavior due to irregular geometric configurations, in particular due to plant stiffness or mass eccentricities. This asymmetric geometry results in coupled lateral–torsional motion produced by wind and seismic loading with consequences in the design of lateral and corner columns. A considerable amount of research effort has been devoted to develop structural control systems to reduce the effects of plan asymmetries and to improve the dynamic behavior of these buildings. This paper presents a numerical analysis of a semi-active control system with MR dampers designed to reduce lateral–torsional responses of a plan asymmetric building structure excited by El Centro NS earthquake ground motion. A parametric study comprising passive and semi-active control modes is given to demonstrate the effectiveness of the proposed control system with respect to uncontrolled case. The numerical results prove the efficiency of the semi-active control system and its potential use in mitigating coupled lateral–torsional structural responses. PubDate: 2017-05-01 DOI: 10.1007/s00419-016-1191-z Issue No:Vol. 87, No. 5 (2017)

Authors:Edoardo Patelli; Yves Govers; Matteo Broggi; Herbert Martins Gomes; Michael Link; John E. Mottershead Pages: 905 - 925 Abstract: Deterministic model updating is now a mature technology widely applied to large-scale industrial structures. It is concerned with the calibration of the parameters of a single model based on one set of test data. It is, of course, well known that different analysts produce different finite element models, make different physics-based assumptions, and parameterize their models differently. Also, tests carried out on the same structure, by different operatives, at different times, under different ambient conditions produce different results. There is no unique model and no unique data. Therefore, model updating needs to take account of modeling and test-data variability. Much emphasis is now placed on what has become known as stochastic model updating where data are available from multiple nominally identical test structures. In this paper two currently prominent stochastic model updating techniques (sensitivity-based updating and Bayesian model updating) are described and applied to the DLR AIRMOD structure. PubDate: 2017-05-01 DOI: 10.1007/s00419-017-1233-1 Issue No:Vol. 87, No. 5 (2017)

Authors:Jinyu Zhou; Wujun Chen; Bing Zhao; Shilin Dong Abstract: For a structure with given shape, to acquire feasible pre-stress states without changing its predefined shape is the main purpose of force finding as a crucial step in structural designs, since mechanical behaviors of cable-strut structures are highly sensitive to their pre-tensioning levels. One of practical ways to initial force designs is double singular value decomposition (DSVD), the essence of which is visual inspections of symmetry properties that could be arbitrary and time consuming due to its manual grouping. To reduce the iteration times of finding a proper group division, a grouping scheme was developed by utilizing the distributed static indeterminacy as a symmetry indicator that represents both geometric and stiffness symmetry. The existing DSVD method was subsequently modified using the proposed scheme that could provide an initial group classification being helpful to decrease the undesirable numbers of pre-stress states. Finally, two examples were investigated to verify the validity and accuracy of the modified method, and then it was applied in an enormous stadium with saddle-shaped roof structure showing good agreement with results obtained by a conventional approach. PubDate: 2017-05-15 DOI: 10.1007/s00419-017-1257-6

Authors:Mostafa Mohammadian; Mehdi Akbarzade Abstract: In the current paper, a powerful approximate analytical approach namely the global residue harmonic balance method (GRHBM) is proposed for obtaining higher-order approximate frequency and periodic solution of nonlinear conservative oscillatory systems arising in engineering problems. The proposed method has a main difference with other traditional harmonic balance methods such that the residual errors obtained in pervious order approximation are used in the present one. Comparison of the obtained results with the exact and numerical solution as well as well-known analytical methods such as Hamiltonian approach, Max–Min approach, variational approach, and He’s amplitude–frequency formulation reveals the correctness and usefulness of the GRHBM. It is shown that the results are valid for different values of system parameters and both small and large amplitudes. Hence, the method can be easily applied to other strongly nonlinear conservative oscillatory systems. Furthermore, using the obtained analytical expressions, the effect of amplitude and system parameters on nonlinear frequency is studied. PubDate: 2017-05-10 DOI: 10.1007/s00419-017-1252-y

Authors:Friedrich Pfeiffer; Johannes Mayet Abstract: Chain fountains are known since long time, and many efforts have been taken to model and to explain the dynamics of such a chain fountain. A chain consists of many small elements starting from an inertial container, forms this specific arc and comes to an inertial position again after a rather long vertical distance. As the chain elements are all connected by a bearing-type structure, they all have to move with the same velocity v. In the following we shall consider only the stationary case and not the evolution from a state of rest to the fountain with velocity v. Most models known use the idea of a continuous model. In the following we shall apply multibody theory in addition by modeling each bead with its connections separately. Results confirm the approach. PubDate: 2017-05-10 DOI: 10.1007/s00419-017-1260-y

Authors:Jun-Hyok Ri; Hyon-Sik Hong Abstract: Linear matching method has been widely used for the numerical analysis of limit and shakedown. It has been proved theoretically that linear matching method could offer the monotonically reducing sequence of upper bound. Nevertheless, it still remains open whether linear matching method can obtain the conversed and reliable lower bound or not. Thus, an elastic compensation method is used generally for the evaluation of lower bound, but limit analysis using linear matching method and elastic compensation method needs double iterative computations. Moreover, the convergence can be checked only after the computation is finished because linear matching method and elastic compensation method cannot be performed simultaneously. From this, we propose a simple method in order to improve the numerical solution of lower bound by linear matching method. The Young’s modulus varying spatially is determined in every iteration such that not only the stress state lies on the yielding surface but also the strain state does not exceed a certain value of reference strain, leading to the evaluation of lower bound based on the strain state but not the stress one. The proposed method can improve the numerical solution of lower bound by linear matching method without any affection on the upper bound. ANSYS UserMat is used for implementing the current method. The limit analysis is performed like the general elastic finite element analysis in ANSYS. Some numerical examples are considered in order to confirm the effectiveness of proposed approach. Numerical examples showed the validity and improvement of numerical accuracy of our approach. It should be mentioned that our approach can predict the lower bound and upper one simultaneously within the framework of only linear matching method without using the elastic compensation method. PubDate: 2017-05-08 DOI: 10.1007/s00419-017-1258-5

Authors:Stefan Hartmann; Rose Rogin Gilbert Abstract: Material parameter identification using constitutive models of elasticity, viscoelasticity, rate-independent plasticity and viscoplasticity has a long history with regard to homogeneous and inhomogeneous deformations. For example, uniaxial tensile tests, pure shear tests, torsion experiments of thin-walled tubes or biaxial tensile tests are used to obtain the material parameters by solving the inverse problem. Frequently, the parameters are determined by numerical optimization tools. In this paper, we investigate some very basic single- and two-layered examples regarding identifiability, because these tests are the basis for more complex geometrical and physical nonlinear problems. These simple examples are the uniaxial tensile/compression case, biaxial tensile tests of a cruciform specimen, torsion of a thin-walled tube, a thick-walled tube under internal pressure and the indentation test. For the thick-walled tube under internal and external pressure with an axial pre-strain with several layers, an analytical solution is provided directly suitable for programming. The aim is to get an understanding whether some problems lead to non-identifiable parameters. PubDate: 2017-05-08 DOI: 10.1007/s00419-017-1259-4

Authors:Marko Vukasović; Radoslav Pavazza; Frane Vlak Abstract: An approximate analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear is presented. The solution based on the classical Vlasov’s thin-walled beam theory is modified for thin-walled laminated composite beams with orthotropic and symmetrical lay-up. It is shown that the beam subjected to torsion with influence of shear, caused by couples in the cross section planes, is also subjected to bending due to shear in the plane orthogonal to the plane of symmetry. If the cross section has two axes of symmetry, the beam will be subjected only to torsion with influence of shear. The expressions for the displacements and normal stresses are derived in closed analytic form. The material influence on shear is defined by factor that depends on the fibre orientations. Simply supported and clamped beams subjected to distributed couples are considered. Illustrative examples are provided, and the results for the displacements and stresses show very good agreement between analytical ones and numerically obtained results utilizing three-dimensional shell finite elements. PubDate: 2017-05-02 DOI: 10.1007/s00419-017-1256-7

Authors:Alla V. Ilyashenko; Sergey V. Kuznetsov Abstract: For a plane crack of arbitrary loading in a medium with arbitrary elastic anisotropy analytic expressions are derived allowing computing stress intensity factors by the corresponding displacement intensity factors. The relation between both intensity factors is derived for media with arbitrary elastic anisotropy. Comparison with the expressions for a plane crack in isotropic medium is outlined. PubDate: 2017-04-26 DOI: 10.1007/s00419-017-1255-8

Authors:Huizheng Chen; Lei Hou; Yushu Chen Abstract: This paper is focused on the relationship between rigid body translation and rigid body precession in a squeeze film damper–rigid-rotor system with unsymmetrical stiffness supports. Two cases are considered: the precession motion non-resonance and internal resonance when translation motion occur primary resonant. In the first case, the amplitudes of translation and precession can be connected with an integration parameter about rotor parameters such as geometric size, stiffness, and mass. Some combination of system parameters will make the amplitudes of precession motion reach the same magnitude of the amplitudes of translation motion, so this integration parameter become an index to reflect the precessional motion degree, it is can be used to judge the feasibility of neglecting processional motion and simplifying asymmetry rotor as reasonable symmetry model. In the second case, the translation motion and precessional motion are strongly coupled, the vibration energy transfer between two kind of motion and the system occur internal resonant, which is possible appear in the rotor with cantilever disk. Each of case may appear nonlinear phenomenon, which is closely related with system parameters. The bifurcation analysis by using singularity methods is carried out to delimit the range of applicative operation parameters to avoid harmful phenomenon in unsymmetrical rotor system. The results of this paper provide a theoretical foundation for the convenient model simplification judgment and parameters optimization of the squeeze film damper-unsymmetrical rotor systems. PubDate: 2017-04-26 DOI: 10.1007/s00419-017-1254-9

Authors:Xiang-Long Peng; Gan-Yun Huang 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