Development of isoparametric, degenerate constrained layer element for plate and shell structures

An isoparametric, degenerate element for constrained layer damping treatments is presented. The element is valid for either plate or shell structures. The element is an 18-node degenerate element with nine nodes located on the base shell (or plate) structure and nine nodes on the constraining layer. Each node has five degrees of freedom; translations in x,y, and z and bending rotations alpha and beta about the midsurface where the node is located. The displacement field of the viscoelastic layer is interpolated linearly from the nodal displacements; therefore, the viscoelastic layer allows both shear and normal deformations. The base shell (or plate) structure and the constraining layer can be linearly elastic or piezoelectric for passive or active applications. The viscoelastic layer is assumed to be linearly viscoelastic. The equation of motion is derived through use of the principle of virtual work. For thin plate structures, numerical results show that the isoparametric element can predict natural frequencies, loss factors, and mechanical impedances that are as accurate as NASTRAN with substantially fewer elements. For thin shell structures, locking and spurious modes need to be resolved to yield reasonable results.