13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- (GPa) ratio (kg m-3) (℃-1) Facing 70(1 0.001i) + 0.3 2700 2.3E 5− Core 7(1 0.001i) + 0.3 1000 1.8E 5− Table 2. Comparisons of the natural frequencies With temperature load of 50℃ Modes Numerical (Hz) Analytical (Hz) Error (%) (1,1) 245.56 255.44 4.02 (2,1) 645.10 659.75 2.27 (1,2) 955.35 963.44 0.85 (3,1) 1290.6 1304.5 1.07 (2,2) 1318.9 1346.7 2.11 (3,2) 1928.3 1970.6 2.19 (1,3) 2079.4 2079.7 0.02 (4,1) 2166.4 2174.8 0.39 Numerical dynamic responses, used to test the analytical solutions, are obtained using VA one. FEM is utilized to acquire the velocity response, caught at (0.1m, 0.1m), while BEM (boundary element method) is used to get sound pressure level, caught at (0.1m, 0.1m, 3m). a. Velocity b. Sound Pressure Level Figure 3. Comparisons of dynamic responses 50 C 30 0 T φ θ Δ = ° = ° = ° From Fig. 3, one can find out that the trends of the response are of the same. There are both three evident peaks on each curve. So far, it could be believable that the present analytical solution is correct based on the above mutual validation. 4. Discussion 4.1. Different thermal loads Thermal load can change the intrinsic property and influence the dynamic characteristics of the
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