The Approximate Analysis of Nonlinear Behavior of Structure under Harmonic Loading
The Approximate Analysis of Nonlinear Behavior of Structure under Harmonic Loading
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发表时间：
2010
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通讯作者：
M. Bayat;M. Shahidi;A. Barari;G. Domairry
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作者：
M. Bayat;M. Shahidi;A. Barari;G. Domairry
在这项工作中，尝试对结构的非线性行为进行分析分析。尽管建筑结构的费用不断增加，但为了保持其线性行为，非线性是不可避免的，因此，非线性分析对该领域的科学家来说非常重要。非线性动力学研究强调了这样一个事实：现实世界中遇到的所有动态系统本质上都是非线性的，这意味着它们作为微分方程的描述包含非线性项。这种非线性以不同的方式出现，例如通过摩擦项、科里奥利和离心项、大幅度效应或其他结构非线性。非线性使得标准线性动力学不足以分析和理解非线性机械系统。由于结构面临侧向力和强烈地震，尤其是在断层附近，结构的一部分保持线性，但一部分结构表现出非线性；这是通过阻尼非线性振荡器来模拟的。本文对代表结构动态行为的带阻尼振子非线性方程进行了解析求解。最后将所得结果与数值结果进行比较，并以图表的形式展示出来；解析解与数值方法的解非常吻合。
In this work, attempt has been made to analyze the nonlinear behavior of structures analytically. Despite the increasing expenses of building structures, to maintain their linear behavior, nonlinearity has been inevitable and therefore, nonlinear analysis has been of great importance to the scientists in the field. Studying on nonlinear dynamics highlights the fact that essentially all dynamic systems encountered in the real world are nonlinear, meaning that their description as differential equations contains nonlinear terms. Such nonlinearities appear in different ways, such as through frictional terms, coriolis and centrifugal terms, large amplitude effects, or other structural nonlinearities. The nonlinearities make that standard linear dynamics not sufficient for the analysis and understanding of nonlinear mechanical systems. As structures confront lateral forces and intense earthquakes especially near fault regions, a part of the structure remains linear, but some part of it behaves nonlinearly; this is simulated by a damped nonlinear oscillator. In this paper, the nonlinear equation of oscillator with damping which is representative of the dynamic behavior of a structure has been solved analytically. In the end, the obtained results are compared with numerical ones and shown in graphs and in tables; analytical solutions are in good agreement with those of the numerical method.