Fig. 1. Form function of the solid spheres for two materials.两种材料实心球形态函数幅频特性曲线
Fig. 2. Dispersion curves of the solid PMMA sphere: (a) Real-imaginary of eigenvalue; (b) normalized phase velocity.实心PMMA球频散曲线 (a)特征值实部-虚部; (b)归一化相速度
Fig. 3. Ray diagram for subsonic Rayleigh waves propagating around the sphere.亚音速Rayleigh波传播路径
Fig. 4. (a) Normalized dispersion curve of subsonic Rayleigh waves (black dotted line) and curves of 2ka/(2p + 1) (blue line); (b) pure elastic resonance.
(a)亚音速Rayleigh波归一化相速度(黑色点划线)和曲线2ka/(2p + 1)(蓝色线); (b)纯弹性共振
Fig. 5. Sensitivity of resonance-frequency: (a) fref = 4.15 kHz; (b) fref = 16.05 kHz.
PMMA球两个典型共振峰频率敏感度 (a) fref = 4.15 kHz; (b) fref = 16.05 kHz
Fig. 6. Sensitivity of resonance-amplitude: (a) fref = 4.15 kHz; (b) fref = 16.05 kHz
PMMA球两个典型共振峰幅度敏感度 (a) fref = 4.15 kHz; (b) fref = 16.05 kHz
Fig. 7. Sensitivity of resonance frequency to attenuation: (a) fref = 4.15 kHz; (b) fref = 16.05 kHz.
共振频率对衰减系数敏感度 (a) fref = 4.15 kHz; (b) fref = 16.05 kHz
Fig. 8. Flow chart of material parameters inversion.材料声学参数反演技术流程图
Fig. 9. Cost function of resonance frequency: (a)
; (b)
频率代价函数 (a)
; (b)
Fig. 10. Relative errors of the transverse wave velocity and the longitudinal wave velocity.剪切波和纵波声速相对误差
Fig. 11. Cost function of resonance amplitude: (a)
; (b)
.
幅度代价函数 (a)
; (b)
Fig. 12. Relative errors of the longitudinal wave attenuation coefficient and the transverse wave attenuation coefficient.纵波和剪切波衰减系数相对误差
Fig. 13. Arrangement of experimental system.实验布放及测量仪器
Fig. 14. Time-domain signal: (a) Echoes; (b) incident pressure.时域信号 (a)回波; (b)入射波
Fig. 15. Flow chart of obtaining form function.获取形态函数流程图
Fig. 16. Cost function: (a) Resonance frequency; (b) resonance amplitude.代价函数 (a)共振峰频率; (b)共振峰幅度
Fig. 17. Comparison between experimental and theoretical calculation.实验结果和理论计算对比
材料 | 密度/kg·m–3 | 纵波波速/m·s–1 | 剪切波波速/m·s–1 | 纵波衰减系数
${\alpha _{\rm{d}}}$![]() ![]() | 剪切波衰减系数
${\alpha _{\rm{s}}}$![]() ![]() | PMMA | 1190 | 2690 | 1340 | 0.0034 | 0.0053 | 钢 | 7700 | 5950 | 3240 | | | 水 | 1000 | 1500 | | | |
|
Table 1. Material parameters used in the calculations.
共振峰频率
${f_{{\rm{m}}j}}$![]() /kHz
| | 共振峰幅度
${A_{{\rm{m}}j}}$![]() ![]() | ${f_{{\rm{m}}1}}$![]() ![]() | 7.654 | | ${A_{{\rm{m}}1}}$![]() ![]() | 3.1556 | ${f_{{\rm{m}}2}}$![]() ![]() | 9.605 | ${A_{{\rm{m}}2}}$![]() ![]() | 3.1378 | ${f_{{\rm{m}}3}}$![]() ![]() | 11.48 | ${A_{{\rm{m}}3}}$![]() ![]() | 2.6025 | ${f_{{\rm{m}}4}}$![]() ![]() | 14.894 | ${A_{{\rm{m}}4}}$![]() ![]() | 2.5969 |
|
Table 2. Resonance frequency and amplitude obtained in experiment.
实验获取共振峰频率和幅度