Abstract

In aerospace industry, the computations of liquid-propelled launchers vibrations are based on linear elastic tanks coupled with an inviscid, incompressible fluid with free surface. In this specific case, the fluctuation of pressure on the free surface is supposed to be zero (i.e. the sloshing effects are neglected). Those vibrations are usually called hydroelastic vibrations. The discretized finite element dynamic problem is commonly expressed only in terms of displacements considering an added mass matrix, which represents the kinetic energy of the moving liquid expressed in terms of normal displacement interface. Those computations can be performed for various fluid level configurations, but no prestressing from geometrical nonlinearity is usually considered [1]. In the present study, the evaluation of the prestressed state influence on the coupled fluid structure vibrations is estimated numerically. This prestressing is supposed to be due to a gas or liquid pressurization, acting on the internal surface of the tank, inducing relatively large static displacement compared to the tank thickness. In reference [2], we have evaluated efficiently and accurately the nonlinear displacements for various filling rate with the use of an original level-set approach. We present here the hydroelastic vibrations around each known prestressed state corresponding to different level of liquid with the use of the added mass matrix. Using the open-source computing finite element platform FEniCS [3], numerical results are in very good agreements with experimental studies from the literature [4]. Comparisons with and without prestressing illustrates the contribution of the efect. To overcome an expensive added mass matrix computation, an appropriate reduced order model obtained by projection on prestressed dry modes is also proposed and show very encouraging results.

Abstract

In this study, the complex band structures of geometrically nonlinear periodic frame structures are calculated by using the Spectral Element Method (SEM). For this purpose, the spectral element matrix for a geometrically nonlinear beam element is derived. By solving the inverse eigenvalue problem for computing the complex dispersion curves k() instead of the conventional eigenvalue problem for calculating the real dispersion curves (k), the complex wave vector can be obtained, whose imaginary parts describes the evanescent behavior of the Bloch waves. Subsequently, the geometrically nonlinear effects on the evanescent behavior of the Bloch waves are investigated by evaluating the dispersion curves and the transmission spectra.