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Free and forced vibrations of damped locally-resonant sandwich beams
European Journal of Mechanics - A/Solids ( IF 4.1 ) Pub Date : 2020-12-13 , DOI: 10.1016/j.euromechsol.2020.104188
Andrea Francesco Russillo , Giuseppe Failla , Fernando Fraternali

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. On adopting an established model in the literature, which consists of an equivalent single-layer Timoshenko beam coupled with mass-spring-dashpot subsystems representing the resonators, novel and exact analytical expressions are presented for the frequency response and modal response under arbitrary loads. Specifically, the frequency response is built by a direct integration method, while the modal impulse and frequency response functions are derived by a complex modal analysis approach, upon introducing orthogonality conditions pertinent to the complex modes. The expressions obtained for frequency response and modal response hold for any number of resonators and degrees of freedom within the resonators, any number of loads and positions of the loads relative to the resonators. In the proposed complex modal analysis approach, the challenging issue of calculating all complex eigenvalues, without missing anyone, is solved applying a recently-introduced contour-integral algorithm to an exact dynamic stiffness matrix that, here, is built with size depending only on the number of degrees of freedom at the beam ends, regardless of the number of resonators and degrees of freedom within the resonators. Numerical applications prove exactness and robustness of the proposed framework.



中文翻译:

局部共振夹层梁的自由振动和强迫振动

本文讨论了局部共振夹层梁的动力学问题,在这种动力学中,多自由度粘滞阻尼共振器周期性地分布在核心矩阵内。在采用已建立的模型中,该模型由等效的单层Timoshenko梁和代表谐振器的质量弹簧阻尼器子系统组成,给出了任意载荷下的频率响应和模态响应的新颖且精确的解析表达式。具体来说,频率响应是通过直接积分方法构建的,而模态脉冲和频率响应函数是在引入与复模有关的正交性条件时通过复模态分析方法导出的。对于频率响应和模态响应获得的表达式适用于任意数量的谐振器和谐振器内的自由度,任意数量的负载以及负载相对于谐振器的位置。在提出的复杂模态分析方法中,将所有复杂特征值计算而又不失任何人的挑战性问题,是通过将最近引入的轮廓积分算法应用于精确的动态刚度矩阵解决的,在这里,刚度矩阵的大小仅取决于不管谐振器的数量和谐振器内的自由度如何,光束末端的自由度的数量都是多少。数值应用证明了所提出框架的准确性和鲁棒性。在提出的复杂模态分析方法中,将所有复杂特征值计算而又不失任何人的挑战性问题,是通过将最近引入的轮廓积分算法应用于精确的动态刚度矩阵解决的,在这里,刚度矩阵的大小仅取决于不管谐振器的数量和谐振器内的自由度如何,光束末端的自由度的数量都是多少。数值应用证明了所提出框架的准确性和鲁棒性。在提出的复杂模态分析方法中,将所有复杂特征值计算而又不失任何人的挑战性问题,是通过将最近引入的轮廓积分算法应用于精确的动态刚度矩阵解决的,在这里,刚度矩阵的大小仅取决于不管谐振器的数量和谐振器内的自由度如何,光束末端的自由度的数量都是多少。数值应用证明了所提出框架的准确性和鲁棒性。不管谐振器的数量和谐振器内的自由度如何。数值应用证明了所提出框架的准确性和鲁棒性。不管谐振器的数量和谐振器内的自由度如何。数值应用证明了所提出框架的准确性和鲁棒性。

更新日期:2020-12-22
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