Impacts of PU Foam Stand-Off Layer on the Vibration Damping Performance of Stand-Off Free Layer Damping Cantilever Beams

Longqiang Liang,Yingjie Sang,Fandi Meng,Weibo Huang,Mingliang Ma,Peng Lyu

doi:10.1155/2020/8871562

Abstract

Stand-off free layer damping is a vibration reduction method based on the traditional free layer damping. In this paper, a stand-off free layer damping cantilever beam is prepared with the steel plate as the base layer, rigid polyurethane (PU) foam as the stand-off layer, and rubber as the damping layer, and the motion equation of the cantilever beam is derived. The dynamic mechanical properties of damping rubber and PU foam are tested and analyzed. Through hammering tests, we have studied the effect of the density and thickness of the PU foam layer on the amplitude-frequency curves, modal frequencies, and loss factors of the cantilever beams. The results show that the rubber damping material is a major font of energy dissipation of the cantilever beam, and PU foam acts mainly to expand the deformation of the damping layer and plays a role in energy consumption. By increasing the density and thickness of PU foam within a certain range, the vibration peaks of the first five modes of the cantilever beam decreases gradually, the loss factors rise, and the damping performance is improved. Meanwhile, increased density and thickness enhances the overall stiffness of the beam, making the modal frequencies get higher.

Highlights

Shock and Vibration damping model can achieve better vibration reduction performance without changing the natural frequency of the structure
Based on the modal superposition method and the Lagrange equation, the motion equation of the cantilever beam is derived. e dynamic mechanical properties of PU foam and rubber damping materials are tested and analyzed. rough hammering tests in which the damping layer remains constant, the influence of the density and thickness of PU foam on the vibration damping performance of the stand-off free layer damping cantilever beam is analyzed from the perspectives of the amplitude-frequency curve loss factor and modal frequency
The nonlinear vibration and damping of the cantilever beam are not considered. e following assumptions are made in analyzing the deformation of the stand-off free layer damping cantilever beam. (1) e overall structure produces small deflection deformation, and the resonance remain in the elastic region. (2) e shear deformation of each layer is not considered, and the moment of inertia of the structure is ignored. (3) ere is no relative slip between the layers, and the lateral displacement of the layers is equal. (4) e cantilever beam conforms to the plane assumption

Summary

Derivation of Motion Equation

Motion equation is a mathematical expression for describing the dynamic displacement of a structural system. ere are different ways to establish the motion equation of the vibration system. E following assumptions are made in analyzing the deformation of the stand-off free layer damping cantilever beam. E total potential energy of the cantilever beam includes deformation potential energy of the base layer, the stand-off layer, and the damping layer. En, the motion equation of the stand-off free layer damping cantilever beam is as follows: φ€. We make 􏼈q€(t)􏼉 􏼈q􏽥􏼉eiωt, and motion equation (19) of the stand-off free layer damping cantilever beam can be reduced to an eigenvalue equation:. A stand-off free layer damping cantilever beam model is established by means of experiment. 9 12 15 from 2.03% to 5.09%), which proves the validity of the motion equation

Experiment

Results and Discussion

Conclusions