Dynamics of two-dimensional composites of elastic and viscoelastic layers

Models of frequency response, acoustic transmission, and transient wave propagation are presented for a two-dimensional composite of elastic and viscoelastic layers, simply supported at the two boundaries. The three models adopt transfer matrices to relate state variables over the two faces of a layer. In the frequency domain, a viscoelastic constitutive law is derived by nonlinear fitting a Padé series to measured data of complex shear modulus. For an elastic material, the eigenproblem admits positive real eigenvalues and their negatives. For a viscoelastic material, it admits positive complex eigenvalues and their negative conjugates. The imaginary part of the eigenvalue acts as a velocity-dependent viscous damper. Modal analysis solving transient response utilizes the complex eigenquantities and the static-dynamic superposition method.