A correction method for dynamic analysis of linear continuous systems

A method to improve the dynamic response analysis of continuous classically damped linear system is proposed. As in fact usually, following a classical approach, a reduced number of eigenfunctions are accounted for and the response is evaluated by integrating the uncoupled differential equations of motion in modal space, neglecting the contribution of high frequency modes (truncation procedure). Here, starting from the given system, it is proposed to set up two differential equations governing the motion of two new continuous systems: the first one contains only the first m non-zero eigenvalues of the given system and the second one contains the remainder non-zero ∞ − m eigenvalues. By summing up the response of the two aforementioned systems it is proven that the global response is recovered. Then, the response of the first system is evaluated by classical dynamic methods (Duhamell integral or step-by-step integration procedures), while the particular solution of the second one is obtained in series form that is shown to converge quickly.