Keywords: energy flow analysis, energy finite element method, spectral element method, energy spectral element method, high frequency, plate, joint.

The finite element method (FEM) and the boundary element method (BEM) have an inherent characteristic that produces too large models at high frequencies. Then a vast amount of research activity was completed for high frequency dynamics and one of the most commonly used techniques is statistical energy analysis (SEA). In SEA, the structure is divided into a set of subsystems that interact through energy exchange. However, the spatial variation of the response in each subsystem cannot be obtained as it provides one energy level for each subsystem.

In this work, three other methods are used to explore the energy density and energy flow in plate-like structures and their coupling at high frequency. All of them provide information on the spatial average energy distribution within the various subsystems. The energy flow analysis (EFA) is an analytical energy formulation which uses the proportionality relationship between energy flow (intensity) and energy density, and an energy balance on a differential control volume [1].

One alternative solution is to solve EFA equations with standard finite element approximations, which is called energy finite element method (EFEM). The spectral element method (SEM) is the analytical solution of wave equations in the frequency domain tailored as a finite element method [2]. The energy spectral element method (ESEM) is a new approach to solve the analytical energy equation of EFA using the same concepts of SEM [3].

In this paper these three methods are used to predict vibration response of plates at high frequencies. Simulated cases using flexural waves for a simple plate and coplanar coupled plates are analyzed and compared with the solutions obtained using the EFEM, the SEM and the ESEM.

1

O.M. Bouthier, R.J. Bernhard, "Simple models of the energetic of transversely vibrating plates", Journal of Sound and Vibration, 182, 149-166, 1995. doi:10.1006/jsvi.1995.0187

2

J.F. Doyle, "Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms", second ed., Springer, New York, USA, 1997.

3

E.R.O. Santos, J.R.F. Arruda, J.M.C. Dos Santos, "Modeling of coupled structural systems by an energy spectral element method", Journal of Sound and Vibration, (in press, available on-line), 2008. doi:10.1016/j.jsv.2008.02.039

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