Nonlinear-eigenvalue problem for heat conduction in a one-dimensional coupled-thermoelastic layered composite (Q1091839)

The dynamic treatment of a one-dimensional transient coupled- thermoelastic problem of heat conduction is made for a layered plate which is exposed to a uniform sudden heating or cooling. The basic equations are transformed into a system of matrix equations, and the problem is formulated as a nonlinear eigenvalue problem of a polynomial matrix. Numerical computations are made for a plate of the sandwich structure. The real-valued eigenvalues and the complex-valued eigenvalues are given, corresponding to the thermal and mechanical modes of behaviour of the plate, respectively. The variation of those eigenvalues with the thermoelastic coupling coefficient is examined.