Abstract
An efficient formula for determining the matrix of frequency response functions is derived for the linear system of ordinary differential equations of structural dynamics having constant coefficients. The eigenvalues and eigenvectors of the system associated with the known mass, stiffness and damping matrices are used to accomplish this without recourse to the inversion of complex matrices at each excitation frequency. The result may be applied to single or multi-point excitation techniques and the matrices need not be symmetric. The eigenvalues are assumed to occur in complex conjugate pairs with non-positive real parts and the Jordan canonical form of the system matrix is presumed to be diagonal. Expressions are given for the sensitivity of the response and an example of an eight storey building is used to demonstrate the computational efficiency of the formula.
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