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Harmonic wave generation in nonlinear thermoelasticity. (English) Zbl 0899.73089
Summary: The basic equations that describe nonlinear thermoelastiv interactions in a continuous medium were derived under the simplifying monomode hypothesis to provide an effective basis for the investigation of nonlinear thermoelastic bulk wave propagation. The one-dimensional equations are solved for a semi-bounded region (half-space) subjectred to a prescribed harmonic displacement at its boundary. Two methods of solution are used: (i) The straightforward expansion in a small parameter for the near-field solution. The first two orders of approximation are obtained and briefly discussed. It appears, in particular, that the second order solution induces an alteration in the velocity of propagation of the fundamental mode due to thermal influence. (ii) The multiple scale technique for the far-field solution. Here, the characteristic cureves are investigated and the solution in the first approximation is obtained for points in the half-space not too far from the boundary. In particular, the formation of discontinuities is put in evidence. Comparison is established with the results obtained by the Poincaré expansion, thus establishing the limits of validity of the latter.
MSC:
74J10Bulk waves (solid mechanics)
74B20Nonlinear elasticity
80A20Heat and mass transfer, heat flow