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A high‐speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of the L(0,1) mode impinging on a traction‐free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high‐amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2% with the exception of the dispersion curve for the L(0,2) mode which deviates by 0.7%.

@article{zemanek_experimental_1972, title = {An {Experimental} and {Theoretical} {Investigation} of {Elastic} {Wave} {Propagation} in a {Cylinder}}, volume = {51}, issn = {0001-4966}, url = {http://scitation.aip.org/content/asa/journal/jasa/51/1B/10.1121/1.1912838}, doi = {10.1121/1.1912838}, abstract = {A high‐speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of the L(0,1) mode impinging on a traction‐free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high‐amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2\% with the exception of the dispersion curve for the L(0,2) mode which deviates by 0.7\%.}, number = {1B}, urldate = {2015-10-26TZ}, journal = {The Journal of the Acoustical Society of America}, author = {Zemanek, Joseph Jr}, month = jan, year = {1972}, keywords = {Elasticity, Elasticity theory, Reflection coefficient, Velocity measurement, elastic waves}, pages = {265--283} }

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