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- W4288078093 abstract "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." @default.
- W4288078093 created "2022-07-28" @default.
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- W4288078093 date "2022-11-01" @default.
- W4288078093 modified "2023-10-15" @default.
- W4288078093 title "Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries" @default.
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- W4288078093 doi "https://doi.org/10.1016/j.jsv.2022.117216" @default.
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