This paper investigates the influence of inerter on the natural frequencies of vibration systems. First of all, the natural frequencies of a single-degree-of-freedom (SDOF) system and a two-degree-of-freedom (TDOF) system are derived algebraically and the fact that the inerter can reduce the natural frequencies of these systems is demonstrated. Then, to further investigate the influence of inerter in a general vibration system, a multi-degree-of-freedom system (MDOF) is considered. Sensitivity analysis is performed on the natural frequencies and mode shapes to demonstrate that the natural frequencies of the MDOF system can always be reduced by increasing the inertance of any inerter. The condition for a general MDOF system of which the natural frequencies can be reduced by an inerter is also derived. Finally, the influence of the inerter position on the natural frequencies is investigated and the efficiency of inerter in reducing the largest natural frequencies is verified by simulating a six-degree-of-freedom system, where a reduction of more than 47 percent is obtained by employing only five inerters. 相似文献
This paper introduces a new chaos generator, a switching piecewise-linear controller, which can create chaos from a three-dimensional linear system within a wide range of parameter values. Basic dynamical behaviors of the chaotic controlled system are investigated in some detail. (c) 2002 American Institute of Physics. 相似文献
The study of nonlinear vibrations/oscillations in mechanical and electronic systems has always been an important research area. While important progress in the development of mathematical chaos theory has been made for finite dimensional second order nonlinear ODEs arising from nonlinear springs and electronic circuits, the state of understanding of chaotic vibrations for analogous infinite dimensional systems is still very incomplete.
The 1-dimensional vibrating string satisfying on the unit interval is an infinite dimensional harmonic oscillator. Consider the boundary conditions: at the left end , the string is fixed, while at the right end , a nonlinear boundary condition , takes effect. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. We formulate the problem into an equivalent first order hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary condition. Since the solution of the first order hyperbolic system depends completely on this nonlinear relation and its iterates, the problem is reduced to a discrete iteration problem of the type , where is the nonlinear reflection relation. We say that the PDE system is chaotic if the mapping is chaotic as an interval map. Algebraic, asymptotic and numerical techniques are developed to tackle the cubic nonlinearities. We then define a rotation number, following J.P. Keener , and obtain denseness of orbits and periodic points by either directly constructing a shift sequence or by applying results of M.I. Malkin to determine the chaotic regime of for the nonlinear reflection relation , thereby rigorously proving chaos. Nonchaotic cases for other values of are also classified. Such cases correspond to limit cycles in nonlinear second order ODEs. Numerical simulations of chaotic and nonchaotic vibrations are illustrated by computer graphics.
In this paper, a new algorithm is proposed, which uses only local information to analyze community structures in complex networks. The algorithm is based on a table that describes a network and a virtual cache similar to the cache in the computer structure. When being tested on some typical computer-generated and real-world networks, this algorithm demonstrates excellent detection results and very fast processing performance, much faster than the existing comparable algorithms of the same kind. 相似文献
The equi-luminance of color stimulus in normal subjects is characterized by L-cone and M-cone activation in retina. For the protanopes and deuternopes, only the activations of one relevant remaining cone type should be considered. 相似文献
Since the Laplacian matrices of weighted networks usually have complex eigenvalues, the problem of complex synchronized regions should be investigated carefully. The present Letter addresses this important problem by converting it to a matrix stability problem with respect to a complex parameter, which gives rise to several types of complex synchronized regions, including bounded, unbounded, disconnected, and empty regions. Because of the existence of disconnected synchronized regions, the convexity characteristic of stability for matrix pencils is further discussed. Then, some efficient methods for designing local feedback controllers and inner-linking matrices to enlarge the synchronized regions are developed and analyzed. Finally, a weighted network of smooth Chua's circuits is presented as an example for illustration. 相似文献
