含阻尼效应的黏弹性杆稳态响应的解析解

ANALYTICAL SOLUTIONS OF STEADY-STATE RESPONSES OF A VISCOELASTIC ROD WITH THE DAMPING EFFECT

  • 摘要: 基于格林函数法和叠加原理,给出了简谐激励下开尔文黏弹性杆稳态响应的解析解。运用拉普拉斯变换法得到了任意边界条件下黏弹性杆强迫振动的格林函数解。设计了一个统一方案,将杆的各种边界表示为矩阵形式,便于确定格林函数中的待定常数。算例表明,材料黏性阻尼和外部阻尼导致杆位移在空间和时间上不可分离。

     

    Abstract: In this paper, the analytical solutions of the steady-state responses of a viscoelastic rod in Kelvin’s model subjected to time-harmonic forces are derived based on Green’s function method and the superposition principle. Laplace transform method is employed to obtain Green’s function for the forced vibration of the viscoelastic rod with arbitrary boundary conditions. A unified strategy applied to various boundaries is proposed to determine unknown constants involved in the Green’s function. Computational results show that the dynamic deflection of the rod considering viscous damping of the material and external damping is not separable in time and space.

     

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