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The ‘Ziegler paradox’, concerning the destabilizing effect of damping on elastic systems loaded by nonconservative positional forces, is addressed. The paper aims to look at the phenomenon in a new perspective, according to which no surprising discontinuities in the critical load exist between undamped and damped systems. To show that the actual critical load is found as an (infinitesimal) perturbation of one of the infinitely many sub-critically loaded undamped systems. A series expansion of the damped eigenvalues around the distinct purely imaginary undamped eigenvalues is performed, with the load kept as a fixed, although unknown, parameter. The first sensitivity of the eigenvalues, which is found to be real, is zeroed, so that an implicit expression for the critical load multiplier is found, which only depends on the ‘shape’ of damping, being independent of its magnitude. An interpretation is given of the destabilization paradox, by referring to the concept of ‘modal damping’, according to which the sign of the projection of the damping force on the eigenvector of the dual basis, and not on the eigenvector itself, is the true responsible for stability. The whole procedure is explained in detail for discrete systems, and successively extended to continuous systems. Two sample structures are studied for illustrative purposes: the classical reverse double-pendulum under a follower force and a linear visco-elastic beam under a follower force and a dead load.  相似文献   

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We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the linear frequency band while they are either end-localized or end-avoided for frequencies outside the linear frequency band. The analytical solutions are resonant at particular frequencies, which compose the frequency dispersion relation of the finite system.  相似文献   

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颗粒离散元模拟中的阻尼系数标定   总被引:2,自引:0,他引:2       下载免费PDF全文
离散元模型中所采用的阻尼系数是不确定的,经常凭主观经验设定.为了使得物理模型与现实中的颗粒动力学属性符合更好,通过采用声频采样技术对物理模型中的阻尼系数进行标定,得出与实验符合的阻尼系数应为0.5左右.利用标定后的阻尼系数模拟了一元颗粒在圆柱形容器里的随机堆积过程,得到最终的堆积密度为0.625,与经典的实验结果一致.研究证明,在得到模型阻尼系数的同时,也确认了数值模型的正确性和用声频采样技术进行高精度碰撞时间检测的可行性. 关键词: 颗粒堆积 阻尼系数标定 声频采样 离散元法  相似文献   

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The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that non-linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.  相似文献   

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A Fokker Planck collisional model is used to study the time evolution of Bernstein linear wave echoes. It is shown that a very small amount of collision destroys efficiently the upper echoes.  相似文献   

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This paper is concerned with the experimental evaluation of the performance of viscous damping identification methods in linear vibration theory. Both existing and some new methods proposed by the present authors [A.S. Phani, J. Woodhouse, Viscous damping identification in linear vibration, Journal of Sound and Vibration 303 (3–5) (2007) 475–500] are applied to experimental data measured on two test structures: a coupled three cantilever beam with moderate modal overlap and a free–free beam with low modal overlap. The performance of each method is quantified and compared based on three norms and the best methods are identified. The role of complex modes in damping identification from vibration measurements is critically assessed.  相似文献   

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A unified approximation method is derived to illustrate the effect of electro-mechanical coupling on vibration-based energy harvesting systems caused by variations in damping ratio and excitation frequency of the mechanical subsystem. Vibrational energy harvesters are electro-mechanical systems that generate power from the ambient oscillations. Typically vibration-based energy harvesters employ a mechanical subsystem tuned to resonate with ambient oscillations. The piezoelectric or electromagnetic coupling mechanisms utilized in energy harvesters, transfers some energy from the mechanical subsystem and converts it to an electric energy. Recently the focus of energy harvesting community has shifted toward nonlinear energy harvesters that are less sensitive to the frequency of ambient vibrations. We consider the general class of hybrid energy harvesters that use both piezoelectric and electromagnetic energy harvesting mechanisms. Through using perturbation methods for low amplitude oscillations and numerical integration for large amplitude vibrations we establish a unified approximation method for linear, softly nonlinear, and bi-stable nonlinear energy harvesters. The method quantifies equivalent changes in damping and excitation frequency of the mechanical subsystem that resembles the backward coupling from energy harvesting. We investigate a novel nonlinear hybrid energy harvester as a case study of the proposed method. The approximation method is accurate, provides an intuitive explanation for backward coupling effects and in some cases reduces the computational efforts by an order of magnitude.  相似文献   

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Phase transition from the over-damping to under-damping states is a ubiquitous phenomenon in physical systems. However, what kind of symmetry is broken associated with this phase transition remains unclear. Here, we discover that this phase transition is determined by an anti-parity-time(anti-PT) symmetry hidden in a single damping linear resonator, which is significantly different from the conventional anti-PT-symmetric systems with two or more modes. We show that the breaking of the anti-PT sy...  相似文献   

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We study the influence of the elastic degrees of freedom of a one-dimensional spin-chain with ferromagnetic Heisenberg coupling in situations, where the magnetic dynamics can be described by a Sine-Gordon model. Compatibility of the Sine-Gordon approach with spin-lattice coupling is shown, and CsNiF3 and domain wall motion are discussed as concrete physical realizations. As a consequence of the spin-lattice interaction a soliton-phonon coupling arises, which destroys the formal Lorentz invariance of the Sine-Gordon system. The influence of this coupling on the soliton dynamics is investigated. It results in a dynamic damping of the soliton motion, which in general is not of viscous type. Moreover, the influences of the soliton-phonon coupling on the phonon dispersion are estimated and possible experimental consequences are discussed.Project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt financed by special funds of the Deutsche Forschungsgemeinschaft  相似文献   

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Transverse feedback systems for suppression of transverse coherent beam oscillations are used in modern synchrotrons for preventing the development of transverse instabilities and damping residual beam oscillations after injection. Information on damper systems for the Large Hadron Collider (LHC; CERN, Geneva) and the accelerator complex FAIR (GSI, Darmstadt) is presented. The project for the LHC is being performed at the Laboratory of Particle Physics of the Joint Institute for Nuclear Research in collaboration with CERN. The information concerning the state of the project and the plans of its completion at the LHC is given. The results of the first design activity on transverse damping systems at the SIS100 and SIS300 synchrotrons, to be created in the framework of the new international project FAIR, are presented.  相似文献   

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Dissipation of mechanical vibration energy at contact interfaces in a structure, commonly referred to as interface damping, is an important source of vibration damping in built-up structures and its modeling is the focus of the present study. The approach taken uses interface forces which are linearly dependent on the relative vibration displacements at the contact interfaces.The main objective is to demonstrate a straightforward technique for simulation of interface damping in built-up structures using FE modeling and simple, distributed, damping forces localized to interfaces where the damping occurs.As an illustration of the resulting damping the dissipated power is used for evaluation purposes. This is calculated from surface integrals over the contact interfaces and allows for explicit assessment of the effect of simulated interface forces for different cases and frequencies. The resulting loss factor at resonance is explicitly evaluated and, using linear simulations, it is demonstrated that high damping levels may arise even though the displacement differences between contacting surfaces at damped interfaces may be very small.  相似文献   

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It is shown that conservation laws of energy and momentum contain often sufficient information on various weakly nonlinear interactions. The changes in the temporal development of an explosive instability or its stabilization due to the linear damping of the interacting waves are discussed in more detail.Nademlýnská 600, Praha 9, Czechoslovakia.  相似文献   

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李新霞  唐翌 《物理学报》2006,55(12):6556-6561
利用分子动力学方法,研究了阻尼对一维体系热传导性质的影响.研究结果表明,当体系的可积性因阻尼的引入而被破坏时,在一维谐振子晶格体系中也能够形成线性的温度分布.弱阻尼对非可积体系的温度分布和热导率的影响是一种微扰,而对于可积体系是一种性态的改变.在强阻尼条件下,由于体系能量的过度耗散,体系中呈现出凹形的温度分布和收敛的热导率. 关键词: 非线性动力学 一维体系 能量传输 阻尼  相似文献   

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The transmission efficiency, frequency and amplitude alteration have been measured by a simple technique of coupled oscillators with a frequency gradient and in a system of non-Newtonian fluid in the form of corn-flour slime. The system of coupled oscillators was found to exhibit preferential energy transfer towards the low frequency end with the reverse propagation severely damped. Energy transfer in all directions was damped in the non-Newtonian fluid in comparison with water. Also the damping in non-Newtonian fluids works only after a lower limit for input amplitude. While most of the previous studies focussed on dissipation of energy within shock-absorbing systems, we demonstrate the contribution of re-distribution of energy reaching the output end to achieve shock absorbing.   相似文献   

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We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states. The usefulness of this general concept is demonstrated by quantifying correlations of interacting electrons in the Hubbard model and in a series of transition-metal oxides using dynamical mean-field theory.  相似文献   

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