Closed form expressions of the system matrices

Closed form of Element Stiffness Matrix

Closed form of Element Mass Matrix

Closed form of Element Damping Matrix

It can be observed that the damping matrix D becomes unsymmetric, hence, the above equation of motion is solved as a general dynamic system, in terms of the state vector x. In order to transform above equation to the state space form, 2n dimensional state vector x and excitation vector X is introduced such that