This study investigates the effect of nonlinear inertia on the dynamic response of an asymmetric building equipped with Tuned Mass Dampers (TMDs). In the field of structural engineering, many researchers have developed models to study the behavior of nonlinear TMDs, but the effect of nonlinear inertia has not received as much attention for asymmetric buildings. To consider nonlinear inertia, the equations of motion are derived in a local rotary coordinates system. The displacements and rotations of the modeled building and TMDs are defined by five-degree-of-freedom (5-DOFs). The equations of motion are derived by using the Lagrangian method. Also in the proposed nonlinear model, the equations of motion are different from a conventional linear model. In order to compare the response of the proposed nonlinear model and a conventional linear model, numerical examples are presented and the response of the modeled buildings are derived under harmonic and earthquake excitations. It is shown that if the nonlinear inertia is considered, the response of the modeled structures changes and the conventional linear approach cannot adequately model the dynamic behavior of the asymmetric buildings which are equipped with TMDs.

中文翻译：

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惯性非线性对装有质量阻尼器的非对称建筑物动力响应的影响

这项研究调查了非线性惯性对装有调谐质量阻尼器（TMD）的不对称建筑物动力响应的影响。在结构工程领域，许多研究人员开发了模型来研究非线性TMD的行为，但是非线性惯性的影响并未引起非对称建筑物的广泛关注。为了考虑非线性惯性，在局部旋转坐标系中导出了运动方程。建模建筑物和TMD的位移和旋转由五自由度（5-DOF）定义。运动方程式是使用拉格朗日方法导出的。同样在所提出的非线性模型中，运动方程与常规线性模型不同。为了比较所提出的非线性模型和常规线性模型的响应，给出了数值示例，并在谐波和地震激励下得出了建模建筑物的响应。结果表明，如果考虑非线性惯性，则建模结构的响应会发生变化，并且传统的线性方法无法充分地模拟配备了TMD的非对称建筑物的动态行为。