Keywords: wave propagation, laminated composite beam, finite element method, dispersion, high frequency, wave finite element method.

During the launch phase, space launchers utilize pyrotechnic devices to separate fairing and payload. Shocks generated by device activation are characterized by high peak acceleration and broadband frequency spectrum [0-100 kHz], and could damage payload equipment. Consequently, wave propagation phenomena occurring at the vicinity of equipment must be accurately predicted before flights in order to make sure that they will not induce damage. Hence, research studies are conducted to improve the reliability of numerical simulations.

A significant number of research papers in the literature propose models in order to analyse wave propagation phenomena in beams. A state of the art review of these models can be found in the book written by Graff [1]. In this review, it is highlighted that the classical beam theories of Bernoulli-Euler and Timoshenko are insufficient to accurately predict wave propagation at high frequencies. To avoid this limitation, high-order theories are proposed by Gopalakrishnan [2]. Unfortunately, these theories cannot be predictive if the beam has a complex cross-section, because correction factors have to be calibrated.

Calculation of transient response is also a difficult aspect of the modelling of wave propagation in beams. Indeed, classical analytical methods are often limited to simple geometries. Then, numerical methods such as the finite element method coupled with time integration method are used. However, numerical dispersion and dissipation can be significant if the mesh is too coarse in the direction of propagation [3]. Nevertheless, some recent methods such as the wave finite element method (WFEM) [4] have been developed in order to overcome these limitations by combining the accuracy of analytical methods and the modelling flexibility of numerical methods. Although this method was employed successfully to predict steady state response, prediction of transient response has not attracted the same attention, not to mention the case of laminated composite beams at high frequencies.

In this paper, the efficiency of the WFEM to simulate wave propagation in laminated composite beam is studied. Numerical examples highlight that the WFEM is more efficient than the FEM to compute transient response and phase velocities at high frequencies.

1

K.F. Graff, "Wave motion in elastic solids", 2nd edition, Dover Publications, 1991.

2

S. Gopalakrishnan, A. Chakraborty, D.R. Mahpatra, "Spectral Finite Element Method - Wave Propagation, Diagnostics and Control in Anisotropic and Inhomogeneous Structures", Springer edition, 2007.

3

T. Belytschko, T.J.R. Hughes, "Computational methods for transient analysis", Amsterdam, North-Holland (Computational Methods in Mechanics, Volume 1), 1983.

4

J.-M. Mencik, M.N. Ichchou, "Wave finite elements in guided elastodynamics with internal fluid", International Journal of Solids and Structures, vol. 44(7-8), 2148-2167, 2006. doi:10.1016/j.ijsolstr.2006.06.048

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