Seismic Reliability Assessment of a Structure with Elasto-Plastic Hysteresis

提出了一种近似解析方法，用于求解具有双线性滞后的单自由度机械系统在调幅非白随机激励下的非平稳响应。通过引入附加状态变量和非线性函数来描述系统的滞后特性。利用截断高斯概率密度函数和几个δ函数组成的非高斯概率密度函数，导出了等效线性系统的等效线性系数和力矩方程。通过求解力矩方程，计算了均方响应和平均耗散滞能，并与相应的数字仿真结果进行了比较。为了研究滞回系统的随机振动，采用带质量的铅悬臂梁进行了实验。测量了两种随机激励（即白噪声和占主导频率的非白噪声）下平稳响应的功率谱和均方根值。假设双线性迟滞模型，采用矩方程方法进行了理论分析。理论与实验结果吻合较好。结果表明，即使在低输入电平的情况下，迟滞对能量耗散响应的影响仍然存在。研究了半充液圆柱槽内液面参数振动问题。水箱受到水平、垂直和俯仰激励。在晃动运动的响应分析中，考虑了液面振荡的非线性。应用伽辽金方法，导出了控制轴对称液体表面振荡的非线性和参数常微分方程，其中包括高阶径向模态。证实了垂直激励引起参数激励。此外，还注意到俯仰激励在俯仰轴不与圆柱罐对称轴相交时也会引起参数激励。利用模型水箱进行了实验。理论与实验结果吻合较好。提出了用随机过程表示结构在地震作用下的动力特性的随机反应谱方法，其中一个样本函数可以看作是记录的强震加速度谱。该方法包括用随机过程对记录的地震动进行建模和用矩方程法对单自由度系统进行均方根响应分析。随机响应谱是系统最大均方根响应与自然周期的关系图，并与常规响应谱进行了比较。少

An approximate analytical technique is developed for obtaining the nonstationary response of a single-degree-of-freedom mechanical system with bilinear hysteresis subjected to amplitude modulated nonwhite random excitations. The hysteretic behavior is described by introducing an additional state variable and nonlinear functions. The equivalent linear coefficients and also the moment equations of the equivalent linear systems are derived using a non-Gaussian probability density function which is composed of a truncatd Gaussian probability density function and a couple of delta functions. The mean square responses and the mean dissipated hysteretic energy are calculated by solving the moment equations and are compared with the corresponding digital simulation results.An experiment is conducted by using a lead cantilever beam with a mass in order to examine the random vibrations of a hysteretic system. Power spectra and root mean square values of the stationary responses to two types of r … More andom excitation, i.e., white noise, and nonwhite noise with a dominat frequency, are measured. A theoretical analysis is carried out by assuming a bilinear hysterersis model and using the moment equations approach. A fairly good agreement is found between the theoretical and experimental results. It is shown that the effect on the response of energy dissipation due to hysteresis is observed even in the case of low input level.Parametric vibration of the liquid surface in a partially filled circular cylindrical tank is investigated. The tank is subjected to horizontal, vertical and pitching excitations. Nonlinearity of the liquid surface oscillation is considered in the response analysis of the sloshing motion. The nonlinear and parametric ordinary differential equations, governing the axisymmetric liquid surface oscillation and including the higher order radial modes, are derived by applying Galerkin's method. It is confirmed that the vertical excitation causes the parametric excitation. In addition, it is noted that the pitching excitation also causes the parametric excitation when the pitching axis does not intersect the symmetrical axis of the circular cylindrical tank. An experiment was conducted using a model tank. Good agreement was found between the theoretical and experimental results.The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the rms response analysis of a single-degree-of freedom system by using the moment equations method. The stochastic respone spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum. Less