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Simple formulas for the natural frequencies of non-uniform cables and beams

Lenci, S. ; Clementi, F. ; Mazzilli, C.E.N.

International journal of mechanical sciences, 2013-12, Vol.77, p.155-163 [Periódico revisado por pares]

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Título:
Simple formulas for the natural frequencies of non-uniform cables and beams
Autor: Lenci, S. ; Clementi, F. ; Mazzilli, C.E.N.
Assuntos: Error estimation ; Free vibrations ; Non-uniform beams ; Non-uniform cables ; Poincaré–Lindstedt method
É parte de: International journal of mechanical sciences, 2013-12, Vol.77, p.155-163
Descrição: The asymptotic development method is used to obtain approximate analytical expressions for the natural frequencies of non-uniform cables and beams. By manipulating the first-order terms, we obtain the mechanical properties (mass, stiffness, etc.) of the equivalent uniform cables and beams having the same (up to the first order) frequencies of the non-uniform one. The second order terms provide an error estimation for the previous expressions. Some examples are reported to illustrate the effectiveness and simplicity of the proposed formulas. •The problem of free vibration of non-uniform cables and beam is addressed by asymptotic developments method.•A solution exact up to the first order is obtained.•The mechanical properties of the equivalent uniform beams and cable are obtained.•Simple formulas for the frequencies are obtained for arbitrarily shaped beams and cables.•An error estimation is proposed.
Editor: Elsevier Ltd
Idioma: Inglês

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