Patent ID: 7188039
Filing Date: 2007-03-06
Classification: G06F

Abstract:
1. A method of solving a first equation associated with a structure, the first equation being of the form {−ω 2 M R +iωB R +[(1+iγ)K R +i(K 4R )]}Y=F R , wherein ω is a time-harmonic excitation frequency, wherein M R is a reduced form of a symmetric mass matrix M, wherein B R is a reduced form of a viscous damping matrix B, wherein γ is a scalar global structural damping coefficient, wherein K R is a reduced form of a symmetric stiffness matrix K, wherein K 4R is a reduced form of a symmetric structural damping matrix K 4 representing local departures from γ, and wherein F R is a reduced form of a matrix F including a plurality of load vectors acting on the structure, the method comprising: factoring the reduced matrix M defining an intermediate matrix C=(1+iγ)L computing a plurality of eigenvalues and eigenvectors for a second equation CΦ computing a matrix P=Φ solving a third equation of the form (D(ω)+PQ(ω)R)Z=Φ forming a product Y=L communicating an approximation of a vibration-induced displacement of the structure, including at least a portion of a product comprising the matrix Φ multiplied by the product Y, to a user interface.