Broadband locally resonant beams containing multiple periodic arrays of attached resonators

The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators. Complex Bloch wave vectors are calculated to quantify the wave attenuation performance of band gaps. It is shown that a locally resonant beam with multiple arrays of damped resonators can achieve much broader band gaps, at frequencies both below and around the Bragg condition, than a locally resonant beam with only a single array of resonators, although the two systems have the same total resonator masses.     

Dynamic stability of pretwisted columns under periodic axial loads

This paper deals with the parametric instability of pretwisted columns subjected to static and periodic axial loads. The governing equations of the problem are reduced to time domain by applying Galerkin's method. The instability regions are determined with the procedure proposed by Hsu. The analysis includes free vibration and static buckling of the column as special cases. Although the method is quite general, numerical calculations are carried out only for a simply supported column. Free vibration frequencies, static buckling loads and the coefficients of the instability regions are obtained for various values of the pretwisting angle and those of the cross sectional rigidity ratio of the column.     

一类非线性动力系统的稳定性及周期运动

根据“库仑扭秤”实验的原理提出了一个非线性动力系统模型,分析了其稳定性及其周期运动．     

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.     

具有一般广义阻尼力和强迫周期力的相对转动非线性动力学模型的周期解

研究了一类具有一般广义阻尼力和强迫周期力项的相对转动非线性动力学模型的周期解问题.讨论了对应自治系统的周期解问题.运用Mawhin重合度理论,得到了该模型的周期解存在惟一性结果,推广了已有的结果,并且列举了具体的例子来说明结果的新颖性.     

The dynamic stability resonant cavity design of two rod Nd:YAG laser

The stability of the higher output power with high-quality beams is very important parameter in material processing. This paper presents using the S parameter and Gauss beam parameters matching to design efficient resonant cavity of two-rod Nd:YAG. The fundamental mode beam radius in rod, fundamental mode beam radius on the mirror, beam quality factor, and the value of the degree of the symmetry of the TEM00 mode volume as a function of the between neighbor rods distance, laser rod end face to mirror distance, and input power are simulated. The design method of resonant cavity is illustrated and compared with previously published experimental measurements for different pump power and the length of the cavity parameters and a good agreement has been found.     

Dynamic stability of linearly varying thickness viscoelastic rectangular plate with crack and subjected to tangential follower force

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory, the differential equations of linearly varying thickness viscoelastic plate with crack and subjected to uniformly distributed tangential follower force in the Laplace domain are established, and the expression of the additional rotation induced by the crack is given. The complex eigenvalue equations of linearly varying thickness viscoelastic plate constituted by elastic behavior in dilatation and the Kelvin-Voigt laws for distortion with crack and under the action of uniformly distributed tangential follower force are obtained by the differential quadrature method. The generalized eigenvalue under different boundary conditions is calculated, and the curves of real parts and imaginary parts of the first three order dimensionless complex frequencies versus uniformly distributed tangential follower force are obtained. The effects of the aspect ratio, the thickness ratio, the crack parameters and the dimensionless delay time on the dynamic stability of the viscoelastic plates are analyzed.     

On the stability of the three classes of Newtonian three-body planar periodic orbits

Currently,the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Suvakov and Dmitra sinovi[Phys Rev Lett,2013,110:114301]using the gradient descent method with double precision.In this paper,these reported orbits are checked stringently by means of a reliable numerical approach(namely the"Clean Numerical Simulation",CNS),which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification.It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time,and are thus most possibly unstable at least.It is suggested to carefully check whether or not these seven unstable orbits are the so-called"computational periodicity"mentioned by Lorenz in 2006.This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.     

Temperature dependence of the stability of written bits in a magnetic hard-disk medium investigated by magnetic force microscopy

The thermal stability of written bits in a magnetic hard-disk medium has been investigated with a magnetic force microscope (MFM), which was equipped with an in situ heating system capable of heating the medium up to 300 °C. It is shown that both the annealing temperature and the duration have significant effect on the decay of the MFM signal. No signal decay is observed when annealing for 30 min up to temperatures of 200 °C. The MFM signal decays rapidly with increasing temperature, for temperatures over 200 °C. Repeated annealing at 280 °C with a duration below 10 min does not cause any signal decay.