Lambda matrix flexibility
Abstract
To represent an harmonically vibrating continuous system having an infinite number of degrees of freedom by means of mathematical models of a finite number of coordinates, the relation between the excitation force vector and response displacement vector (the dynamic stiffness matrix [ D(λ)]) is inevitably frequency dependent. It is often required to compute the dynamic flexibility matrix [ Z(λ)], which is the inversion of [ D(λ)]. A new method is presented here to express [ Z(λ)] in terms of the eigensolutions of [ D(λ)]. It is similar to the classical format except that [ D(λ)] is no longer required to be expressible as a matrix polynomial in λ with constant coefficient matrices. In contrast to the state variables, which tend to increase the order of the matrices, only physical coordinates are concerned. [ D(λ)] may be nonsymmetric and defective.
 Publication:

Journal of Sound Vibration
 Pub Date:
 August 1991
 DOI:
 10.1016/0022460X(91)90482Y
 Bibcode:
 1991JSV...148..521L