Optimum Mass Matrices for Short Wave Pulse Propagation Finite Element Models - Barauskas, R. (Nonlinear Analysis: Modelling and Control, 2003)
The matrices of a substructure ensuring minimum modal errors of the whole structure are obtained by using optimization approach. The mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of closeto-exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible. The goal is achieved by formulating the minimization problem for the penaltytype target function representing the cumulative relative modal error of the joined domain and by applying the gradient descent minimization method. After the optimum matrices of a component domain are obtained, they can be used in any structure as higher-order elements or super-elements. The “combined” mass matrices can be treated as a special case of the presented approach. The performance of the obtained dynamic models is demonstrated by solving short wave pulse propagation problems by using a only few nodal points per pulse length.
Keywords: modal synthesis; modal error; wave propagation