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Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

机译：基于设计频谱的非线性系统的有效线性阻尼和刚度系数

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摘要

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum.
机译：提出了一种随机方法，用于获得非线性系统对通过设计地震谱指定的激励的峰值响应的可靠估计。这是通过有效的方式实现的，而无需借助控制非线性运动方程的数值积分。首先，采用数值方案来推导在随机意义上与给定设计频谱兼容的功率谱。然后将此功率谱视为激励谱，以通过统计线性化方案确定与等效线性系统（ELS）相对应的有效阻尼系数和刚度系数。此外，将获得的系数与（线性）设计频谱结合使用以估计原始非线性系统的峰值响应。考虑具有分段线性刚度非线性系统以及双线性滞后系统的情况。地震烈度由欧洲抗震规范（EC8）规定的弹性设计范围规定。进行了与一组非平稳EC8设计频谱兼容加速度图有关的蒙特卡洛模拟，以确认非线性系统的平均峰值响应在统计线性化方法所提供的已知精度水平内与ELS的合理比较。以这种方式，所提出的方法产生了ELS，该ELS可以代替原始的非线性系统，从而在根据设计谱指定​​的强烈地震激励下，在结构的抗震设计的初始阶段进行有效的计算分析。

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