Seismic Reliability Assessment of a Structure with Elasto-Plastic Hysteresis

提出了一种求解单自由度双线性滞回机械系统在调幅非白随机激励作用下的非平稳响应的近似解析方法。通过引入附加状态变量和非线性函数来描述结构的滞回行为。利用由一个高斯型概率密度函数和一对Delta函数组成的非高斯型概率密度函数，推导出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，计算了系统的均方响应和平均耗散滞回能量，并与相应的数值模拟结果进行了比较。两类r-…平稳响应的功率谱和均方根值测量了更多的随机激励，即白噪声和具有主导频率的非白噪声。采用双线性滞回模型，采用矩方程法进行了理论分析。理论计算结果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，迟滞效应对能量耗散响应也有影响。研究了部分充液圆柱形储罐液面的参数振动。坦克受到水平、垂直和俯仰激励。在晃动响应分析中考虑了液面振动的非线性。应用Galerkin方法，导出了含高阶径向振型的轴对称液面振动的非线性常微分方程组和参数常微分方程组。证实了参数激励是由垂直激励引起的。另外，当俯仰轴与圆柱形水舱对称轴不相交时，俯仰激振也会引起参数激振。利用模型水箱进行了实验研究。提出了用随机过程来预测结构在地震激励下的动力行为的随机反应谱方法，其样本函数之一可以看作是记录的强震加速度图。该方法包括用随机过程模拟记录的地面运动和用矩方程法分析单自由度系统的均方根响应。随机反应谱是最大均方根响应与系统固有周期的关系图，并与常规反应谱进行了比较。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