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Acceleration Wave Propagation in Inhomogeneous Heat-Conducting Rods

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An acceleration wave is a singular surface propagating through a material body across which the particle acceleration experiences a finite discontinuity, or jump, but the particle velocity and deformation gradient are continuous. Acceleration waves may propagate in 1-, 2-, or 3-dimensional material bodies. For purely elastic materials and for heat-conducting elastic materials, and for many other materials, it is possible to deduce an explicit expression for the squared speed of acceleration waves. It is also possible to deduce an explicit nonlinear equation (of Bernoulli type) for the growth of acceleration wave amplitude, for which exact solutions may be written down. Acceleration wave theory is of great interest in mechanics generally because it furnishes some of the few exact solutions that are available in nonlinear mechanics. Chen [1] has given a full account of most aspects of acceleration wave theory. Straughan [2, Chap. 4] also has given an excellent account of...

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  • DOI: 10.1007/978-94-007-2739-7_923
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References

  1. Chen PJ (1973) Growth and decay of waves in solids. In: Truesdell C (ed) Mechanics of Solids, vol III. Springer, Berlin, pp 203–402

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  2. Straughan B (2011) Heat waves. Springer, Berlin

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  3. Fu YB, Scott NH (1988) Acceleration wave propagation in an inhomogeneous heat-conducting elastic rod of slowly varying cross section. J Thermal Stress 11:127–140

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Correspondence to Nigel H. Scott .

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Scott, N.H. (2014). Acceleration Wave Propagation in Inhomogeneous Heat-Conducting Rods. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_923

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