Analysis and Experiment on Dynamic Stability of Steel Structures Subjected to Dynamic In-Plane Force

采用解析和试验相结合的方法，对索、桥等钢结构在面内动荷载作用下的动力稳定性进行了分析。结果如下。(1)研究了垂度扁拉索在轴向周期力作用下的动力稳定性问题。被调查的。索的运动方程用伽辽金法求解。不稳定区域首先提出了各种垂跨比和波速比。利用非线性索理论得到了不稳定运动的幅值。(2)分析了面内对称时变荷载作用下斜拉索通过分叉时的反对称响应。采用伽辽金法求解索在对称力作用下的面内非线性运动方程。首先给出了出现反对称响应的频率范围。然后，利用Runge-Kutta-Gill方法计算了不稳定区域内的非线性对称响应和相应的反对称响应 ...更多信息 方法在特定的垂跨比下，对称响应和反对称响应之间存在非线性耦合。反对称反应。(3)本文研究了梁在正弦时变轴向力作用下，在各种边界条件和载荷条件下的动力不稳定区域和响应幅值。对于固定-自由梁，考虑了保守力和跟随力。首先讨论了由小挠度理论得到的动力失稳区域，并由梁的非线性理论得到了由挠度引起的轴力和梁的非线性曲率引起的失稳运动的幅值。(4)研究了在径向边缘受面内动力矩作用的环形扇形板的动力稳定性问题。应用伽辽金法将基本方程化为一组常微分方程，再利用谐波平衡法将其转化为特征值问题。系统的稳定性可直接由特征值的真实的部分的符号来判定。(5)研究了环形扇形板在等时变矩和反向时变矩作用下的非线性动力失稳问题。本文用伽辽金法分析了基于Berger近似方程的环扇形板大挠度运动方程。所得到的方程的时间变量是通过使用龙格-库塔-吉尔方法集成。各种边界条件，阻尼力和静态力矩的数值结果。(6)给出了固支梁在对称力作用下反对称响应的实验结果，并与理论结果进行了比较。对移动荷载作用下钢桥的竖向和横向振动进行了测试和讨论。少

Dynamic stability of steel structures such as cables and bridges subjected to in-plane dynamic load is analyzed by using analytical and experimental approaches. The results are as follows.(1) Dynamic stability of a flat sag cable subjected to an axial periodic force is investigated. The investigated. The equation of motion of the cable is solved by the Galerkin method. Unstable regions are presented first for various sag-to-span ratios and ratios of wave speeds. Amplitudes of unstable motions are obtained using the nonlinear cable theory.(2) Anti-symmetric response of a cable through bifurcation under in-plane symmetric time-varying load is analyzed. The in-plane nonlinear equations of motion of a cable under symmetric forcing are solved by a Galerkin method. The frequency range where the anti-symmetric responses occur is shown at first. Then, nonlinear symmetric response and the corresponding anti-symmetric response within the unstable region calculated by using the Runge-Kutta-Gill m … More ethod. Nonlinear coupling between symmetric and and anti-symmetric responses are observed in the particular sag-to-span ratios. Anti-symmetric responses in the present problem.(3) Dynamic unstable regions and amplitudes of the responses of a beam subjected to a sinusoidally time-varying axial force for various boundary conditions and loading conditions are examined. Conservative and follower forces are considered for the fixed-free beam. Dynamic unstable regions which are obtained by the small deflection theory are discussed at first and amplitudes of unstable motions are obtained by the nonlinear theory of beams caused by axial force due to deflection and nonlinear curvature of beams.(4) Dynamic stability problem of an annular sector plate subjected to in-plane dynamic moments at the radial edges is examined. The basic equation is reduced to a set of ordinary differential equations by applying a Galerkin method, and transformed into an eigen-value problem by using the harmonic balance method. The stability of the system can be directly determined from the sign of the real parts of the eigen-values.(5) The nonlinear dynamic instability of an annular sector plate subjected to equal and opposite time-varying moments is examined. The equation of motion describing a large deflection of the annular sector plate based upon Berger's approximate equation is analyzed by the Galerkin method. The resulting equations for time variables are integrated by using the Runge-Kutta-Gill method. Numerical results are presented for various boundary conditions, damping forces, and static moments.(6) Experimental results for anti-symmetric responses of the fixed-fixed beam subjected to symmetric forcing are presented and compared with theoretical results. Vertical and lateral vibrations of steel bridges under moving load are measured and discussed. Less