Chapter 5 Waves in unbouded regions.pptVIP

One of the two dotted lines in the figure is the well-known Rayleigh surface wave, which can propagate over an elastic half-space and is not dispersive. The other dotted line is the well known Bleustein-Gulyaev surface wave which has only one displacement component u3 and can propagate over a piezoelectric half-space but does not have an elastic counterpart. These two surface waves are included as references. It is seen that for short waves with larger k, the frequencies of the extensional and flexural waves approach that of the Rayleigh surface wave. Similarly, for short waves, the frequencies of the face-shear wave approach that of the Bleustein-Gulyaev wave. * * : Love wave : B-G wave 7. Gap waves * 7.1 A Gap between Two Half-Spaces of Different Ceramics * * * * * * 7.2 A Gap between Two Half-Spaces of the Same Ceramic * 7.2.1 Symmetric Waves * 7.2.2 Anti-Symmetric Waves * 8. Waves on a circular cylindrical surface * * * * * * surface wave speed in (5.3-12) 9. Acoustic wave generation * * * * * Propagating waves in a plate Propagating waves in a piezoelectric plate The major surfaces of the plate are traction-free and are electroded. The electrodes are shorted Eigenvalue value problem The wave frequencies are normalized by the lowest thickness-shear frequency Dispersion relations of waves in an electroded ceramic plate poled along the x3 direction In the figure, the three branches passing the origin are the so-called low frequency branches. They represent the extensional, flexural, and face shear waves. The other six branches are high-frequency branches, which have finite intercepts with the (O axis. These intercepts are called cutoff frequencies, below which the corresponding waves cannot propagate. Cutoff frequencies are in fact the frequencies of pure thickness modes. The six high frequency branches shown represent three thickness-shear waves, one thickness-stretch wave, and two thickness-twist waves. * Boundary conditions reflected wave * * 2.2 Reflect