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Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements. (English) Zbl 1126.74019

Summary: This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler-Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74J99 Waves in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74S25 Spectral and related methods applied to problems in solid mechanics
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