Predicting anti-resonance frequencies using a novel eigenvalue formulation

Herein, we present a novel method for searching anti-resonance frequencies, using an eigenvalue analysis that does not need to search every dip of amplitude in the frequency response function. The eigenvalue equation is derived by utilizing the fact that the solutions of a forced vibration equation are equal to zero at anti-resonance frequencies.

The characteristics of the eigenvalue problem are analyzed with a one-dimensional (1D) bar example, and as engineering applications, four numerical examples are presented to demonstrate the computational efficiency and robustness of the proposed method.