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

Table 1

Material properties of the copper foil under the natural state and two initial states with two uniaxial prestresses 0.02𝑐₄₄ and 0.04𝑐₄₄ applied in the 𝑋₁-direction.

	Natural state	Prestress 𝑇^𝑖11=0.02𝑐44	Prestress 𝑇^𝑖11=0.04𝑐44
Thickness; (mm)	ℎ=0.1	ℎ=0.1	ℎ=0.1
Mass density; (mg/mm^3)	𝜌0=8.93	𝜌𝑖=8.913	𝜌𝑖=8.895
Elastic constants; (mg/mm⋅μs^2)	𝑐11=188.1; 𝑐12=108.9; 𝑐44=39.6; 𝑐^111=−1894 𝑐^112=−754; 𝑐^123=56 𝑐^144=−401; 𝑐^155=−287 𝑐^456=57	𝑐11=183.377; 𝑐22=𝑐33=187.343; 𝑐23=111.926; 𝑐12=𝑐13=106.094; 𝑐44=37.704; 𝑐55=𝑐66=39.636	𝑐11=178.655; 𝑐22=𝑐33=186.587; 𝑐23=114.952; 𝑐12=𝑐13=103.288; 𝑐44=35.807; 𝑐55=𝑐66=39.671
Temperature; (k°K)	Θ0=0.300	Θ𝑖=0.300	Θ𝑖=0.300
Thermal constant; (mg/mm⋅𝜇s^2⋅k°K^2)	𝛼=(𝜌0𝐶E)/Θ0=11.129	𝛼=11.107	𝛼=11.085
Thermoelastic coupling coeff. (mg/mm⋅𝜇s^2⋅k°K)	𝜆=(𝑐11+2𝑐12)𝛾=6.697	𝜆1=6.782; 𝜆2=𝜆3=6.648	𝜆1=6.867; 𝜆2=𝜆3=6.599
Thermal conductivity (mg/mm⋅𝜇s^2⋅k°K)	𝐤=0.398×10^−3	𝐤1=0.403×10^−3; 𝐤2=𝐤3=0.395×10^−3	𝐤1=0.408×10^−3; 𝐤2=𝐤3=0.392×10^−3

𝐶_E=3.74 is the heat capacity (mg/𝜇s²⋅k°K), and 𝛾=0.0165 is the thermal expansion coefficient (1/k°K).