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171.
172.
利用拉格朗日方程,导出了多节摆系统的运动微分方程.根据三对角阵的性质,给出了振动系统的特征多项式和特征矢量的递推公式,并以三节摆为例,说明了结果的应用,用此方法验证了<力学与实践>2002年第24期<多自由度振动系统的简正坐标和简正振动模式>一文中的结果. 相似文献
173.
In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated. 相似文献
174.
175.
C. W. Lim 《Acta Mechanica Solida Sinica》2011,24(6):484-494
The torsional static and dynamic behaviors of circular nanosolids such as nanoshafts, nanorods and nanotubes are established based on a new nonlocal elastic stress field theory. Based on a new expression for strain energy with a nonlocal nanoscale parameter, new higher-order governing equations and the corresponding boundary conditions are first derived here via the variational principle because the classical equilibrium conditions and/or equations of motion can- not be directly applied to nonlocal nanostructures even if the stress and moment quantities are replaced by the corresponding nonlocal quantities. The static twist and torsional vibration of circular, nonlocal nanosolids are solved and discussed in detail. A comparison of the conventional and new nonlocal models is also presented for a fully fixed nanosolid, where a lower-order governing equation and reduced stiffness are found in the conventional model while the new model reports opposite solutions. Analytical solutions and numerical examples based on the new nonlocal stress theory demonstrate that nonlocal stress enhances stiffness of nanosolids, i.e. the angular displacement decreases with the increasing nonlocal nanoscale while the natural frequency increases with the increasing nonlocal nanoscale. 相似文献
176.
In this paper, an optimal criterion is presented for adaptive Kalman filter in a control system with unknown variances of
stochastic vibration by constructing a function of noise variances and minimizing the function. We solve the model and measure
variances by using DFP optimal method to guarantee the results of Kalman filter to be optimized. Finally, the control of vibration
can be implemented by LQG method. 相似文献
177.
稳定受迫振动中的能量转换 总被引:2,自引:0,他引:2
将强迫分解成超前位移π/2和位移相同或反相的两个分量,通过对两分力作功的定量计算,可以方便地讨论受迫振动中的能量转换,并能对共振作出较的物理解释。 相似文献
178.
This paper is concerned with the simultaneous maneuver and vibration control of a flexible spacecraft. The problem is solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of vibration, as well as of perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies bang-bang control. On the other hand, the first-order control is a time-dependent linear quadratic regulator including integral feedback and prescribed convergence rate.This research was sponsored by USAF/ASD and AFOSR Research Grant F33615-86-C-3233 monitored by Drs. A. K. Amos and V. B. Venkayya, whose support is greatly appreciated. 相似文献
179.
The time averaged frame subtraction technique is improved by subtracting two Bessel fringe patterns at two different force levels. The technique enables significant enhancement of fringe contrast and increased measurement sensitivity. The contrast and sensitivity of the fringes obtained at different force ratios are investigated. Both theoretical and experimental results are presented. 相似文献
180.
A. I. Egorov 《Computational Mathematics and Mathematical Physics》2008,48(6):912-917
The observability problem for beam vibrations described by a fourth-order partial differential equation with various boundary conditions is considered. Dynamic observability problems are solved in terms of boundary conditions and observations of the beam state at certain fixed instants of time. 相似文献