Abstract
<title>Abstract</title> <p>Structures suffer from vibrations and nonlinear energy sinks can be used to reduce the vibrations. The present work develops a transverse nonlinear vibration model for a vertical cantilever considering its self-weight and introduces a nonlinear energy sink to reduce the forced transverse vibration of the cantilever. Based on the linearized governing equation the natural frequencies and the mode shapes are determined. The effects of the self-weight of the natural frequencies and the modes shapes are examined. The steady-state response of the forced vertical cantilever with a nonlinear energy sink are analyzed by the Galerkin truncation and the harmonic balance method. The outcomes are numerically verified by the Runge-Kutta method. The investigation indicates that the effects of the self-weight on the frequencies and the modes are rather limited and the nonlinear energy sink reduces the forced vibration significantly.</p>