Abstract
Energy finite element analysis (EFEA) has been developed to compute the energy distribution of vibrating structures. The method adopts the energy density as the basic variable of differential equation. The energy density can be used to analyze the behavior of vibrating beams. Firstly, an EFEA equation is obtained from the classical displacement equation. In the applications of uniform and non-uniform beams, the EFEA results are compared with the analytical and FEA results. Secondly, a junction formulation solving the discontinuity problem of energy density at the junction of two beams with stepped thickness is proposed. The EFEA equation combined with junction formulation is used to solve the energy transmission problem of the coupling beams with stepped thickness and variable cross-section. The smoothed results of coupling beams are achieved, and the differences of energy density at the junctions are analyzed. The feasibility of the EFEA approach is validated by using several design examples under the various frequencies and structural damping loss factors.
Highlights
In mid-to-high frequency range, the prediction of complex structural response using traditional finite element analysis (FEA) approach is time-consuming and costs a plenty of resources because the wavelength decreases when the analysis frequency increases [1, 2]
The paper has focused on energy finite element analysis of vibrating beams with stepped thickness and variable cross-section in mid-to-high frequency range
An energy finite element formulation based on the energy variation and the far field assumption has been proposed for predicting the distribution of energy density of uniform beams
Summary
In mid-to-high frequency range, the prediction of complex structural response using traditional finite element analysis (FEA) approach is time-consuming and costs a plenty of resources because the wavelength decreases when the analysis frequency increases [1, 2] For this reason, statistical energy analysis (SEA) approach was proposed and widely applied to the industrial applications [3, 4]. Energy finite element analysis (EFEA) approach was recently proposed for the prediction of structural response in mid-to-high frequency range [7, 8]. The EFEA approach is extended to the coupled beams with stepped thickness and variable cross-section in mid-to-high frequency range It is less investigated on the published documents. The feasibility of the developed EFEA approach is validated by using several design examples under the various excitation frequencies and hysteresis damping loss factors
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