Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries

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Data

2022-11-10

Autores

Nunes, Afonso Willian [UNESP]
Silva, Samuel da [UNESP]
Ruiz, Adrián

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Editor

Elsevier

Resumo

A Lie symmetry method-based approach is proposed for systematically computing general solutions in closed-form for the mode shape equation of non-uniform and unconventional vibrating rods. The mode shape equation is modeled by the elementary rod theory, addressing polynomial, exponential, trigonometric, and hyperbolic cross-section variations. The method provides algorithmic order-reduction steps for solving the investigated mode shape equation, producing a first-order Riccati equation whose integration reveals the aimed solutions for the problem. Illustrative examples are presented, including original solutions in closed-form as well as solutions previously obtained in the literature by other approaches. Mode shapes from general solutions with appropriate rod boundary conditions are also considered for different examples.

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Palavras-chave

General solutions, Non-uniform rods, Mode shapes, Elementary rod theory, Lie symmetries

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