Efficient, wide-band coupled structural-acoustic computations combining time and frequency domain finite elements/equivalent sources

Abstract

Time and frequency domain computations are complementary, and here, the overall goal is to combine them to generate wide-band solutions of coupled structural-acoustic problems. Modal frequency response computations are efficient for low frequencies but become inefficient as the number of basis functions required to represent the response grows large. Modal formulations are required for large problems because the coupled equation system becomes densely populated when acoustic pressure forces are included. In contrast, the equation system remains sparsely populated in time domain formulations when the time step size is chosen appropriately, allowing large problems to be solved efficiently in terms of nodal degrees-of-freedom. However, the analysis times depend linearly on the number of time steps and a large number are generally required to represent the ringing response of low frequency modes. Here, the number of time steps is limited by applying an exponential taper to the time domain solution and truncating the computations. This reduces leakage effects, but does not affect components of response that have damped out before it is applied. Examples are given to illustrate the computations and the tradeoff between number of basis functions in the modal frequency response computations and number of time steps in the transient analyses.Time and frequency domain computations are complementary, and here, the overall goal is to combine them to generate wide-band solutions of coupled structural-acoustic problems. Modal frequency response computations are efficient for low frequencies but become inefficient as the number of basis functions required to represent the response grows large. Modal formulations are required for large problems because the coupled equation system becomes densely populated when acoustic pressure forces are included. In contrast, the equation system remains sparsely populated in time domain formulations when the time step size is chosen appropriately, allowing large problems to be solved efficiently in terms of nodal degrees-of-freedom. However, the analysis times depend linearly on the number of time steps and a large number are generally required to represent the ringing response of low frequency modes. Here, the number of time steps is limited by applying an exponential taper to the time domain solution and truncat...