Non-linear vibrations of a simply supported rectangular plate carrying a centric mass

Abstract

Abstract Vibration is something that surrounds us in all areas, from everyday life to advanced industries. Among them, plates are found anywhere, so it has taken a fair share of study and analysis. Often, plates hold one or many point masses which completely changes their vibration frequencies and mode shapes. So, the main objective of this work is to analyze the effect of an added centric mass on the vibration Characteristics of simply supported rectangular plates and in both the linear and non-linear vibration regimes. The theoretical formulation adopted is based on Hamilton’s principle and spectral analysis. The expressions for the kinetic, linear and non-linear strain energies are derived taking into account the effect of the added mass on the kinetic energy and the effect of the membrane forces induced by the non-linearity on the strain energy. The generated equation has been solved numerically via an iterative procedure permitting to obtain the amplitude dependent frequencies and mode shapes. The results presented in this article are expected to be useful, both quantitatively and qualitatively, for a better understanding of the vibration of plates with an added mass.