Nonlinear vibration isolation of a viscoelastic beam

In this paper, the transmissibility of a viscoelastic beam supported by vertical springs is defined by proposing a new vertical elastic support boundary. By contrasting with the viscoelastic beam with rigid vertical supports and the rigid rod with vertical elastic support ends, the necessity of the transmissibility of an elastic structure with vertical elastic supports is proved. In order to approximately solve the steady-state responses of the nonlinear transverse vibration of the viscoelastic beam under periodic excitation, the harmonic balance method in conjunction with the pseudo arc-length method is adopted. The numerical results are calculated to confirm the approximate analytic results. The comparison between the rigid rod and the elastic beam shows that neglecting the bending vibration of the structures will underestimate the frequency range in which the elastic support produces an effective vibration isolation. On the other hand, the comparison between the rigid support and the spring support demonstrates that ignoring the elasticity of the support ends will create a false understanding of the force transmission of elastic structures. In general, this paper presents the necessity of studying the force transmission of elastic structures with elastic supports. Moreover, this paper will become the beginning of the study of the vibration isolation of the elastic structure.