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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 non-orthogonal mode superposition exact solution of dissipative structures of general linear viscoelastic dampers (including linear rubber bearings) is systematically studied. First of all, using the most accurate linear viscoelastic damped integral precise analytical model, the differential integral equations are used to realize the time-domain non-diffuse accurate modeling of the viscoelastic dampers energy dissipation structure. Then, using the transfer matrix method, In the original space of the structure, the non-orthogonal vibration model superposition exact solution of the transient response of the displacement and velocity in the general linear viscoelastic energy-dissipated frequency-varying structure under any excitation and non-zero initial conditions is obtained. By comparing with the three typical structures The correctness, simplicity and universality of the exact solution are verified and verified. The non-extended exact solution has a definite physical meaning and can be regarded as the classical orthomorphic superposition exact solution of the existing proportional viscous damping constant structure in the general linear viscoelastic damping energy dissipation frequency conversion structure can be essentially accurate The vibration mechanism of dissipative structures is revealed. Although the modes of dissipative structures do not have orthogonality, the dissipative structures can still be decomposed into the linear combinations of the responses of the modes. The vibration mechanism will provide an analysis path for the establishment of an accurate vibration mode decomposition response spectroscopy method for energy dissipation structures. At the same time, the existing methods for parameter identification, dynamic modification, optimal control and optimization design of the conventional viscous damping steady structures can be extended to General viscoelastic damping variable frequency unsteady structure.