New benchmark free vibration solutions of passive constrained layer damping beams by the symplectic method

IF 2.2 3区 工程技术 Q2 MECHANICS Archive of Applied Mechanics Pub Date : 2024-10-09 DOI:10.1007/s00419-024-02693-4
Xinran Zheng, Chengsha Wei, Shizhao Ming, Wei Tang
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Abstract

In this paper, new analytic solutions for the free vibration analysis of passive constrained layer damping (PCLD) beams, which are widely used in engineering to suppress vibrations and noise, are shown based on the symplectic method. The Hamiltonian-based governing equations and the new boundary condition expressions of PCLD beams are established by the original vector and its dual vector obtained by variation of the quasi Lagrangian function. The explicit solutions are obtained in the symplectic space in a direct, rigorous way without any trail functions under various boundary conditions. To verify the accuracy of the present method, the frequency parameters and loss factors of PCLD beams are compared with the results available in the literature. Comprehensive results under various boundary conditions are also tabulated for further benchmark use.

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用交映法求解被动约束层阻尼梁的新基准自由振动解
被动约束层阻尼(PCLD)梁在工程中被广泛用于抑制振动和噪声,本文基于交映法,展示了对其自由振动分析的新解析解。通过准拉格朗日函数的原始矢量及其变化得到的对偶矢量,建立了 PCLD 梁的基于哈密顿的支配方程和新的边界条件表达式。在各种边界条件下,以直接、严谨的方式在交映空间中获得了显式解,而无需任何踪迹函数。为了验证本方法的准确性,将 PCLD 梁的频率参数和损耗因子与文献中的结果进行了比较。此外,还列出了各种边界条件下的综合结果,以便进一步作为基准使用。
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来源期刊
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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Rapid heating of FGM plates resting on elastic foundation Large deformation modeling of flexible piezoelectric materials Dynamic statistical damage constitutive model based on the Hoek–Brown criterion at high strain rates Correction to: Microstructure evolution and fluid transport in porous media: a formal asymptotic expansions approach New benchmark free vibration solutions of passive constrained layer damping beams by the symplectic method
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