International Scholarly Research Notices / 2011 / Article / Tab 2

Research Article

Numerical Study of Characteristic Equations of Thermoelastic Waves Propagating in a Uniaxial Prestressed Isotropic Plate

Table 2

Collected data of the wave speeds under the natural state and two initial states with two uniaxial prestresses 0 . 0 2 𝑐 4 4 and 0 . 0 4 𝑐 4 4 applied in the 𝑋 1 -direction.

Wave speed (mm/ΞΌs)Longitudinal waveShear wave Corresponding differences of wave speed due to (3.5)–(3.7)LamΓ© mode

Natural state 𝑐 𝐿 0 = 4 . 5 9 0 𝑐 𝑆 0 = 2 . 1 0 6 β€”β€” 𝑐 L a m e 0 = 2 . 9 7 8

𝑐 [ 1 0 0 ] L 1 = 4 . 5 4 6 𝑐 [ 0 0 1 ] S 1 = 2 . 1 3 0 Ξ” 𝑐 [ 1 0 0 ] L 1 = βˆ’ 0 . 0 4 4 Ξ” 𝑐 [ 0 0 1 ] S 1 = 0 . 0 2 4 𝑐 L a m e 1 = 2 . 9 8 2
𝑐 [ 0 1 0 ] S 1 = 2 . 1 3 0 Ξ” 𝑐 [ 0 1 0 ] S 1 = 0 . 0 2 4 Ξ” 𝑐 L a m e 1 = 0 . 0 0 0 4
Prestress
𝑇 𝑖 1 1 = 0 . 0 2 𝑐 4 4
𝑐 [ 0 1 0 ] L 2 = 4 . 5 8 5 𝑐 [ 0 0 1 ] S 2 = 2 . 0 5 6 Ξ” 𝑐 [ 0 1 0 ] L 2 = βˆ’ 0 . 0 0 5 Ξ” 𝑐 [ 0 0 1 ] S 2 = βˆ’ 0 . 0 5 0 𝑐 L a m e 2 = 2 . 9 0 8
𝑐 [ 1 0 0 ] S 2 = 2 . 1 0 9 Ξ” 𝑐 [ 1 0 0 ] S 2 = 0 . 0 0 3 Ξ” 𝑐 L a m e 2 = βˆ’ 0 . 0 7 0 7
𝑐 [ 0 0 1 ] L 3 = 4 . 5 8 5 𝑐 [ 1 0 0 ] S 3 = 2 . 1 0 9 Ξ” 𝑐 [ 0 0 1 ] L 3 = βˆ’ 0 . 0 0 5 Ξ” 𝑐 [ 1 0 0 ] S 3 = 0 . 0 0 3
𝑐 [ 0 1 0 ] S 3 = 2 . 0 5 6 Ξ” 𝑐 [ 0 1 0 ] S 3 = βˆ’ 0 . 0 5 0

𝑐 [ 1 0 0 ] L 1 = 4 . 5 0 2 𝑐 [ 0 0 1 ] S 1 = 2 . 1 5 4 Ξ” 𝑐 [ 1 0 0 ] L 1 = βˆ’ 0 . 0 8 8 Ξ” 𝑐 [ 0 0 1 ] S 1 = 0 . 0 4 8 𝑐 L a m e 1 = 2 . 9 8 6
𝑐 [ 0 1 0 ] S 1 = 2 . 1 5 4 Ξ” 𝑐 [ 0 1 0 ] S 1 = 0 . 0 4 8 Ξ” 𝑐 L a m e 1 = 0 . 0 0 0 8
Prestress
𝑇 𝑖 1 1 = 0 . 0 4 𝑐 4 4
𝑐 [ 0 1 0 ] L 2 = 4 . 5 8 0 𝑐 [ 0 0 1 ] S 2 = 2 . 0 0 6 Ξ” 𝑐 [ 0 1 0 ] L 2 = βˆ’ 0 . 0 1 0 Ξ” 𝑐 [ 0 0 1 ] S 2 = βˆ’ 0 . 1 0 0 𝑐 L a m e 2 = 2 . 8 3 8
𝑐 [ 1 0 0 ] S 2 = 2 . 1 1 2 Ξ” 𝑐 [ 1 0 0 ] S 2 = 0 . 0 0 6 Ξ” 𝑐 L a m e 2 = βˆ’ 0 . 1 4 1 4
𝑐 [ 0 0 1 ] L 3 = 4 . 5 8 0 𝑐 [ 1 0 0 ] S 3 = 2 . 1 1 2 Ξ” 𝑐 [ 0 0 1 ] L 3 = βˆ’ 0 . 0 1 0 Ξ” 𝑐 [ 1 0 0 ] S 3 = 0 . 0 0 6
𝑐 [ 0 1 0 ] S 3 = 2 . 0 0 6 Ξ” 𝑐 [ 0 1 0 ] S 3 = βˆ’ 0 . 1 0 0

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