The principle of virtual work and the third order wave for continua with second order constitutive equations

A generalized form of the principle of virtual work where the virtual work is a time integral of virtual power is obtained. The corresponding Euler–Lagrange equation includes the divergence of the Lie derivative of stress. The equation of motion on the stress rate field is one of the results of this paper. A generalization of the acoustic tensor is obtained for a third-order wave. The generalized acoustic tensor seems the most important result of this paper. It can also be found by investigating an acceleration wave