Weight Effects on Vertical Transverse Vibration of a Beam with a Nonlinear Energy Sink

Reductions in the vibration of a continuum system via a nonlinear energy sink have been widely investigated. It is usually assumed that weight effects can be ignored if the vibration is measured from the static equilibrium configuration. The present investigation reveals the dynamic effects of weight on the vertical transverse vibrations of a Euler–Bernoulli beam coupled with a nonlinear energy sink. The governing equations considering and neglecting weights were derived. The equations were discretized with some numerical support. The discretized equations were analytically solved via the harmonic balance method. The harmonic balance solutions were compared with the numerical solution via the Runge–Kutta method. Finite element simulations were performed via ANSYS software (version number: 2.2.1). Free and forced vibrations, predicted by equations considering or neglecting the weights, were compared with the finite element solutions. For the forced vibrations, the amplitude–frequency responses determined by the harmonic balance method agree well with those calculated by the Runge–Kutta method. The free and forced vibration responses predicted by the equations considering the weights are closer to those computed by the finite element method than the responses predicted by the equation neglecting the weights. The assumption that weights can be balanced by static deflections leads to errors in the analysis of the vertical transverse vibrations of a Euler–Bernoulli beam with a nonlinear energy sink.