The Linear Theory of Thermoelasticity: Course Held at the by Ian N. Sneddon (auth.)
By Ian N. Sneddon (auth.)
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Additional resources for The Linear Theory of Thermoelasticity: Course Held at the Department of Mechanics of Solids July 1972
E. 2:24) Vi = Vp • The veloci- ty Vp is called the velocity of Zongi tudina Z elastic waves. 35) We now turn our attention to the quasi-thermal mode~ but before doing so look at the form of waves of assigned length. 2 Plane Harmonic Elastic Waves 54 9 ... z -~ :2 , ')(,3 =- i ~2.. 2 with the quasi-elastic mode and with the quasi-thermal mode. 40) These equations show the same properties of modification and coupling observed above for thermo-elastic waves of constant frequency. Like the purely thermal distance, the quasi-thermal mode is a standing wave.
1 av. L .!.. r d)'t' + + 1 a2"t' -. J!. sin e D"t' + r 2 sin 8 as as a. in8· au. a. u" cots + T + -r- Ue Fig. 8 Curvilinear Coordinates 38 2 1 () t. ) () d e+ co t e () Ue - -- r G e + --:-- -\sln8d ee i " - - - --d'.. 16) If the stress and temperature fields are symmetric about the axis so that u. E.... r2 d + _1_ Jl(sin Sd e) _ dee + ()I"" + dX r 2. D r " ,. e+ rsin9 () ( . as ) cots l = d a u,. at 2. 25) If we substitute these expressions in the equation of motion Dd"l" 1( () r + -r 2«1 r..
16(1 + 'X. 21 ) It should be noted that i f X. 22) values of q 00 for four metals are included in Table 1 above. 23) of the Debye spectrum, which is the upper limit of the range of frequencies which can be attained in an elastic solid; here Vp denotes the velocity of longitudinal elastic waves and M is the mass of a constituent atom of the solid. 01. This implies that the upper limit of attainable frequencies in a solid is imposed by the thermoelastic damping and not by the atomic structure. 2 Plane Hannonic Elastic Waves 49 quencies attainable in a coherent pulse are in practice very much smaller than ttI* • In practical applications of the theory we therefore have 'X.