Elastic wave propagation in bars of arbitrary cross section: A generalized Fourier expansion collocation method

2014 ◽  
Vol 136 (3) ◽  
pp. 985-992
Author(s):  
Jonathan C. Lesage ◽  
Jill V. Bond ◽  
Anthony N. Sinclair
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Collocation Method ◽  
Cross Section ◽  
Fourier Expansion ◽  
Arbitrary Cross Section ◽  
Elastic Wave Propagation

Elastic Wave Propagation in Rods of Arbitrary Cross Section

1965 ◽  
Vol 32 (2) ◽  
pp. 290-294 ◽  
Author(s):  
R. L. Rosenfeld ◽  
Julius Miklowitz
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Cross Section ◽  
Harmonic Wave ◽  
Applied Pressure ◽  
Arbitrary Cross Section ◽  
Elastic Wave Propagation ◽  
Long Distance ◽  
Shear Modes ◽  
Long Time

A study is made of the problem of transient elastic wave propagation when a load is applied to one end of an infinitely long rod of arbitrary cross section. Fourier and Laplace transforms aid in developing a general solution in the form of a sum over all modes of harmonic wave propagation and integrals over all wavelengths. An expansion at long wavelength reveals two types of modes of propagation which are called longitudinal and radial shear modes. For a suddenly applied pressure, the long-distance, long-time response is found to be an integral of the Airy integral.

Stress Wave Propagation in a Bar of Arbitrary Cross Section

1982 ◽  
Vol 49 (1) ◽  
pp. 157-164 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Fourier Expansion ◽  
Frequency Equation ◽  
Arbitrary Cross Section ◽  
Stress Wave Propagation ◽  
Flexural Waves ◽  
Elliptical Cross ◽  
Phase Velocities ◽  
Wave Numbers

In this paper a method for solving wave propagation problems of an infinite bar of arbitrary cross section has been presented. The frequency equation for finding phase velocites for longitudinal, torsional, and flexural waves have been obtained by making use of the Fourier expansion collocation method which has been developed by the author on the vibration and dynamic response problems of membranes and plates. As a numerical example, the phase velocities versus wave numbers are calculated for elliptical and truncated elliptical cross-section bars.

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