Damped frequency response apparatus, systems, and methods

Apparatus, systems, and methods are disclosed to solve an equation associated with a structure of the form {−ω2MR+iωBR+[(1+iγ)KR+i(K4R)]}Y=FR, wherein ω is a time-harmonic excitation frequency, MR is a reduced form of a symmetric mass matrix M, BR is a reduced form of a viscous damping matrix B, γ is a scalar global structural damping coefficient, KR is a reduced form of a symmetric stiffness matrix K, K4R is a reduced form of a symmetric structural damping matrix K4 representing local departures from γ, FR is a reduced form of a matrix F, and Y is a matrix having a plurality of vectors corresponding to the plurality of load vectors acting on the structure and included in the matrix F.Board of Regents, University of Texas Syste