比例内共振下TMD与框架结构间的非线性动态P - delta相互作用

D. Afshar, M. Amin Afshar
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引用次数: 1

摘要

研究了轴向载荷对剪力框架与调谐质量阻尼器在谐波载荷和地震侧向载荷作用下动力相互作用的影响。考虑到非线性几何刚度由小型和大型TMD重力负载框架列,耦合的非线性运动微分方程TMD和框架。然后,研究了小、大TMD与车架的相互作用,并建立了运动方程。非线性P - δ效应耦合了TMD和框架响应。利用多尺度方法,导出了非线性微分方程的渐近解,并研究了二对一内共振的影响,即比例共振。通过绘制模态振幅响应随激励频率和振幅变化的图,研究了近内共振下系统的稳定性。在图中可以观察到跳跃和饱和现象。对结构与TMD的阻尼比、质量比、轴向载荷比等参数变化对结构与TMD响应幅值的影响进行了参数化研究。研究比较了tmd -结构相互作用的两种线性和非线性动力在谐波和地震激励下的时间和频率响应。
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Nonlinear dynamic P‐delta interaction between TMD and the frame structure under proportional internal resonances
The effect of axial loads on the dynamic interaction of a shear frame and tuned mass dampers (TMDs) is evaluated under harmonic and seismic lateral loads. Taking into account the nonlinear geometric stiffness created by the small and large TMD gravity load on the frame columns, the nonlinear differential equations of motion of coupled TMD and frame are derived. Then, the interaction between the small and large TMD and the frame is studied, and the equations of motion are investigated. Nonlinear P‐delta effects couple the TMD and frame responses. By using the method of multiple scales, the asymptotic solution of the nonlinear differential equations is derived, and the effect of two‐to‐one internal resonance, called proportional resonance, is examined. System stability under near‐internal resonance is investigated by plotting the modal amplitude responses vs. variations of excitation frequency and amplitude. The jump and saturation phenomena can be observed in the plots. A parametric study is conducted on the effect of variations of the quantities, e.g., damping ratios of the structure and TMD, the mass ratio, and the axial load ratio, on the response amplitude of the structure and TMD. The time and frequency responses of two linear and nonlinear dynamics for the TMD–structure interaction under harmonic and seismic excitation are also studied and compared.
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