阻尼局部共振夹层梁的自由振动和受迫振动
Free and forced vibrations of damped locally-resonant sandwich beams
摘要：
本文研究了多自由度粘滞阻尼谐振器周期性分布于芯层矩阵中的局部共振夹层梁的动力学问题。采用等效单层梁模型，耦合质量弹簧阻尼器子系统代表的谐振器，两种解决方案的方法。第一种方法是直接积分法，可提供任意载荷下的精确频率响应。第二种是复模态分析方法，通过推导复模态的正交条件，获得精确的模态脉冲和频率响应函数。计算所有的特征值，而不遗漏任何人的挑战性的问题，解决了应用最近推出的轮廓积分算法的特征方程作为一个确切的频率响应矩阵的行列式，其大小是$4 \times 4$，无论谐振器的数量。数值算例验证了所提方法的正确性和鲁棒性。
英文摘要：
This paper addresses the dynamics of locally-resonant sandwich beams, where multi-degree-of-freedom viscously-damped resonators are periodically distributed within the core matrix. Using an equivalent single-layer Timoshenko beam model coupled with mass-spring-dashpot subsystems representing the resonators, two solution methods are presented. The first is a direct integration method providing the exact frequency response under arbitrary loads. The second is a complex modal analysis approach obtaining exact modal impulse and frequency response functions, upon deriving appropriate orthogonality conditions for the complex modes. The challenging issue of calculating all eigenvalues, without missing anyone, is solved applying a recently-introduced contour-integral algorithm to a characteristic equation built as determinant of an exact frequency-response matrix, whose size is $4 \times 4$ regardless of the number of resonators. Numerical applications prove exactness and robustness of the proposed solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
