一般线性粘弹性阻尼器耗能结构瞬态响应的非正交振型叠加精确解

EXACT NON-ORTHOGONAL MODAL SUPERPOSITION SOLUTIONS OF TRANSIENT RESPONSE OF MDOF DISSIPATION STRUCTURES WITH GENERAL LINEAR VISCOELASTIC DAMPERS

对一般线性粘弹性阻尼器(含线性橡胶隔震支座)耗能结构的非正交振型叠加精确解法进行了系统研究。首先采用最一般的线性粘弹性阻尼器的积分型精确分析模型,用微分积分方程组实现一般粘弹性阻尼器耗能结构的时域非扩阶精确建模;然后采用传递矩阵法,直接在耗能结构原始空间上获得了一般线性粘弹性耗能变频结构在任意激励和非零初始条件下位移与速度时域瞬态响应的非正交振型叠加精确解;通过与3种典型结构的对比分析,验证了该精确解的正确性、简易性和普适性。该非扩阶精确解具有明确的物理意义,可视为现有比例粘滞阻尼定常结构的经典正交振型叠加精确解在一般线性粘弹性阻尼耗能变频结构的推广,能从本质上精确揭示耗能结构的振动机理,即尽管耗能结构的振型不具有正交性,但耗能结构响应仍然可精确分解为各振型响应的线性组合。此振动机理将为建立耗能结构精确的振型分解反应谱法提供分析路径,同时可将现有用于一般粘滞阻尼定常结构的参数识别、动力修改、最优控制及优化设计等方法推广到一般粘弹性阻尼变频非定常结构。

The exact non-orthogonal modal superposition solutions of transient response of MDOF dissipation structures with general linear viscoelastic dampers including elastomeric isolators are studied systematically. By using the general integral models of viscoelastic dampers, which are the most general exact models of linear viscoelastic dampers, the exact dynamic integral-differential response equations in original structural space for MDOF dissipation structures with general linear viscoelastic dampers are established. Then, by using transfer matrix method, the exact non-orthogonal modal superposition solutions in original structural space for displacement and velocity transient response of MDOF dissipation structures with general linear viscoelastic dampers due to arbitrary exterior forcing loadings and initial conditions are obtained. It is verified that these exact solutions are correct, general, simple, direct, and provide better physical insights through solutions in comparison with three kinds of more general typical dissipation structures. These exact solutions in original structural space are similar to the classical modal superposition results for proportionally damped structures usually obtained using the mode-orthogonality relationships, and can exactly discover the vibration characteristics of viscoelastic dissipation structures, namely： though the dissipation structural modes are not orthogonal, the dynamic equations can not be decoupled by using structural modes, the structural transient response can be exactly expressed in terms of a superposition of individual modal response. Therefore, by using above characteristics, it may be possible to extend the existing modal superposition response spectrum method, structural identification, model updating, optimization, and control algorithms available for viscously damped structures to general viscoelastically damped structures.