Derivatives of dynamic stiffness matrices

The dynamic stiffness matrices have been widely used to give a better approximation of the model, both in linear and non-linear analysis. The derivatives of the dynamic stiffness matrices are required frequently in a number of numerical procedures, such as inverse iterations and Newton-Rapson iterations. It is well known that the mass matrix is equal to the first derivative of the dynamic stiffness matrix with respect to the minus of the square of the vibration frequency. In this paper, the above statement is generalized for general system parameters. It can be used to show that the geometric matrix is equal to the first derivative of the dynamic stiffness matrix with respect to the axial force.