Flexural Vibration of a Viscoelastic Sandwich Beam in its Plane of Lamination

Abstract

Abstract When a laminated sandwich beam consisting of alternating elastic and viscoelastic layers bends in the plane normal to its plane of lamination, the relatively compliant viscoelastic layers are sheared between the adjoining elastic layers and energy is dissipated. This mechanism, known as constrained-layer or shear damping, is a proven method for damping flexural vibration, but only in the plane normal to the plane of lamination. For vibration parallel to the plane of lamination, the elastic layers need not deflect together, and the viscoelastic layers are sheared when adjoining elastic layers undergo different deflections. This mechanism of damping is discussed herein. In this paper, we study the vibration of a symmetrically laminated five-layer sandwich beam in its plane of lamination. Taking the viscoelastic material to have frequency-independent hysteretic damping, we derive a boundary-value problem governing steady harmonic motion of the sandwich beam and then obtain its discretized counterpart. For the particular case of a beam with simply supported elastic layers, we obtain the resonant frequencies and loss factors of the composite beam, and study their dependence on geometric and material properties.