Design of low-frequency vibration isolators with high-static-low-dynamic characteristic via functionally graded beam systems

This paper presents a novel and simple approach to designing low-frequency vibration isolators via functionally graded beam systems. Without complex mechanisms and nonlinear devices, high-static stiffness and wide anti-resonance frequency bands can be achieved by optimizing material gradients and auxiliary masses. The discrete equation governing the bending and vibration of the beam system is established by employing Timoshenko’s theory and a Chebyshev spectral method. The dynamic characteristics, steady-state frequency response, and bending under static loads, are numerically calculated and used to evaluate its vibration isolation performance and support stiffness. The effects of the material gradient and auxiliary masses on the force transmissibility and static stiffness were investigated. It was found that adjusting the auxiliary masses can change the position of anti-resonance peaks, and tailoring axial material gradient can broaden the anti-resonance frequency bands. Exploiting these effects and describing the axial material distribution by the Chebyshev expansions, the constrained particle swarm optimization algorithm is adopted to design two low-frequency vibration isolators, in order to demonstrate the feasibility of using functionally graded materials to isolate low-frequency vibration and maintain structural stiffness. The results show that near the operating frequency, the transmissibility decays more than 93%, more importantly, the static stiffness is larger than 190 kN/m. This work shows a promising approach to vibration isolator design, i.e., tailoring functionally graded materials to precisely manipulate structural dynamic responses.