{"title":"New benchmark free vibration solutions of passive constrained layer damping beams by the symplectic method","authors":"Xinran Zheng, Chengsha Wei, Shizhao Ming, Wei Tang","doi":"10.1007/s00419-024-02693-4","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-024-02693-4","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
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.
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.