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

采用分析和试验相结合的方法，对斜拉索、桥梁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)研究了轴向周期性力作用下扁平垂拉索的动力稳定性。的调查。用伽辽金法求解了索的运动方程。首先给出了不同垂跨比和波速比的不稳定区域。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索的分岔不对称响应。用伽辽金法求解了索在对称受力作用下的平面内非线性运动方程。首先给出了发生反对称响应的频率范围。然后，采用Runge-Kutta-Gill m…More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。在特定的垂跨比下，观察到对称和反对称响应之间的非线性耦合。本问题中的反对称响应。(3)研究了在不同边界条件和荷载条件下，梁在正弦时变轴力作用下的动力不稳定区域和响应幅值。考虑了自由固定梁的保守力和随动力。首先讨论了由小挠度理论得到的动力不稳定区域，并由挠度和梁的非线性曲率引起的轴向力非线性理论得到了梁的不稳定运动幅值。(4)研究了环形扇形板径向边缘面内动力力矩作用下的动力稳定性问题。利用伽辽金方法将基本方程化为一组常微分方程，利用调和平衡方法将其转化为一个本征值问题。系统的稳定性可由特征值实部的符号直接确定。(5)研究了在等时变力矩和相反时变力矩作用下环形扇形板的非线性动力失稳问题。在Berger近似方程的基础上，用伽辽金方法分析了描述环形扇形板大挠度的运动方程。用龙格-库塔-吉尔法对得到的时间变量方程进行积分。给出了各种边界条件、阻尼力和静力矩的数值结果。(6)给出了固定-固定梁在对称受力下的反对称响应的实验结果，并与理论结果进行了比较。对钢桥在移动荷载作用下的竖向振动和横向振动进行了测量和讨论。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