Vibration isolation performance of a beam clamped with torsional quasi-zero-stiffness isolator

Elastic beam structures connected by hinges are a common basic component of many mechanical systems. In this study, the nonlinear transverse vibration of a beam with one end free and the other end simply supported with a torsion spring is investigated. A torsional quasi-zero-stiffness vibration isolator is employed at the fixed end of the beam for isolating the vibration excitation from the base. Using Hamilton’s principle, the differential equation of motion for the transverse vibration of the beam is obtained, and the natural characteristics of the beam are determined. The dynamic equation of the system is derived by using Galerkin truncation method and the harmonic balance method is adopted to obtain the nonlinear vibration response. Compared with the vibration transmissibility of the beam supported by the equivalent linear torsion spring, the quasi-zero-stiffness vibration isolation system shows superior vibration isolation performance. It is found that the beam fixed with a torsional quasi-zero-stiffness isolator can reduce the first resonant frequency and provide a wide effective isolation range at low frequency, which is rarely affected by the strong nonlinearity. The results would provide an innovative method of introducing the torsional quasi-zero-stiffness isolator into the passive vibration control of continuum system.