A highly stable and accurate computational method for eigensolutions in structural dynamics

A new computational method for the linear eigensolution of structural dynamics is proposed. The eigenvalue problem is theoretically transformed into a specific initial value problem of an ordinary differential equation. Based on the physical meaning of the sign count of the dynamic stiffness matrix, a stability control device is designed and combined with the fourth-order Runge-Kutta method. The resulting method finds the eigenvalues and eigenvectors at the same time, with high accuracy and high stability. Numerical examples show that the proposed method still gives high accuracy solutions when there is a great difference in magnitude among the eigenvalues, and also when some eigenvalues are very close to each other.