设置连接阻尼器的相邻结构随机地震动响应的简明封闭解

Concise closed-form solution for the random ground vibration response of two adjacent structures with connected dampers

针对两相邻结构间设置连接阻尼器对结构的减震影响问题,研究了基于Kanai-Tajimi谱地震动激励下的Kelvin型粘弹性阻尼器与相邻结构形成的组合体系的随机地震动系列响应(绝对位移及层间位移)的简明封闭解。首先,利用Kelvin型粘弹性阻尼器本构关系及Kanai-Tajimi谱的滤波方程,将组合体系基于复杂地震动激励精确转化为基于简明白噪声激励的运动方程;其次,利用复模态法获得了组合结构相对于地面的绝对位移、层间位移等系列响应方差及0阶~2阶谱矩的统一简明封闭解。最后,通过算例及与虚拟激励法进行对比,证明本文方法的正确性和简明性;通过与未设置阻尼装置结构体系的动力响应对比,说明了阻尼装置对相邻结构具有良好的减震效果,但局部楼层的层间位移及层间剪力会有所增加。

Aiming at the influence of connecting dampers between two adjacent structures on the vibration reduction of structures,the concise closed-from solutions of random motion series response(absolute displacement and storey displacement)of the composite system formed by Kelvin viscoelastic dampers and adjacent structures under Kanai-Tajimi spectral ground motion excitation are studied.Firstly,using the constitutive relationship of a Kelvin viscoelastic damper and the filtering equation of Kanai-Tajimi spectrum,the complex ground motion excitation of the composite system is accurately transformed into the equation of motion under a simple noise excitation;Secondly,using the complex mode method,the unified concise closed-form solutions of a series of response variances and 0-2 order spectral moments of the composite structure relative to the ground are obtained.Finally,an example is given and compared with the virtual excitation method to show the correctness and simplicity of the method in this paper.Compared with the dynamic response of the structural system without the damping device,the damping device has a good vibration reduction effect on adjacent structures,but the inter-storey displacement and inter-storey shear force will increase in local floors.