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Investigation of Solenoidal Condition for Solving Wave Propagation Problems by Lamé's Decomposition

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In this paper, the application of Lamé's decomposition with solenoidal condition is studied on solving wave propagation problems in elastic cylinders and plates, and several existing analytic approaches are also remarked. For wave propagation problems in cylinders, it is demonstrated that the solenoidal condition for Lamé's decomposition can be generalized to a more general constraint condition, and the existing approaches are found to be the special cases of Lamé's decomposition under the general constraint condition. This result illuminates the reason why the different approaches have the equivalent frequency equations. For wave propagation problems in plates, the analysis using solenoidal condition leads to the same results as that given by existing analytic approach. Especially, through comparison, the fact is concluded that only solenoidal condition for Lamé's decomposition is complete when the analysis for displacement components is considered.

Affiliations: 1: LTCS and Department of Mechanics & Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, P.R. China; 2: Department of Mechanical Systems Engineering, Aichi University of Technology Gamagori-city, Aichi Prefecture 443-0047, Japan

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