Abstract
It is shown that a general form of the bilinear functional in conjunction with classical concepts of thermodynamics leads to the results not admitted by the particular form commonly used in the literature. The conservation theorem for a wide class of continuous bodies is established. A generalized Lagrangian function for linear dissipative materials is introduced. Two specific examples: problem of elastodynamics and problem of thermoelasticity are selected in order to illustrate the proposed approach.
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