Modal Analysis for Localization Phenomena in a Structure with Two Pendulum Vibration Absorbers

Abstract

This paper theoretically investigates the localization phenomena in two pendulum vibration absorbers that are installed on a structure. It was previously reported that localization occurred in the two pendulum vibration absorbers. In order to clarify the mechanism of the appearance of localization, modal analysis is applied to examine localization from the viewpoint of vibrational modes. The equations of motion of the system are derived in the physical coordinates, and then they are transformed to the modal equations of motion. The frequency response curves for the primary harmonic vibrations are theoretically determined in both the physical and modal coordinates. It is shown that the modal equations form an autoparametric system because the first and third modes are directly excited by the external force, and the second mode is indirectly excited through the nonlinear coupling terms. Numerical results show that the two pendulum vibration absorbers can suppress the primary resonance peak, but two new peaks appear at the excitation frequency ranges lower and higher than the natural frequency of the structure. Localization occurs near the peak at the lower excitation frequency range where all modes appear simultaneously.