TY - JOUR
T1 - Dispersion relations of waves in a rod embedded in an elastic medium
AU - Parnes, R.
N1 - Funding Information:
t This work was supported by the National Science Foundation 78-15049 with Weidlinger Associates, New York, U.S.A. Z On leave at Laboratoire de MCcanique des S&des, Ecole Polytechnique,
PY - 1981/5/8
Y1 - 1981/5/8
N2 - The dispersion relations of waves propagating in a system consisting of an elastic rod of radius a embedded in a linear elastic medium are investigated, and phase speeds of waves of wavelength λ which propagate under steady state conditions are determined. The dispersive behaviour is found to be dependent on several non-dimensional parameters defined by the geometric ratio a λ, as well as on non-dimensional ratios of the rod-medium properties. It is shown that the resulting waves which can propagate under steady state conditions are surface waves which decay with the radial distance and which permit no radiation damping of energy. It is further shown that such waves can propagate freely only if the propagation speed of longitudinal waves in the corresponding free rod is less than that of shear waves propagating in the medium. Results are presented by means of dispersion curves and surfaces. From a study of the analytical results obtained, lower and upper bounds on the phase speeds are established.
AB - The dispersion relations of waves propagating in a system consisting of an elastic rod of radius a embedded in a linear elastic medium are investigated, and phase speeds of waves of wavelength λ which propagate under steady state conditions are determined. The dispersive behaviour is found to be dependent on several non-dimensional parameters defined by the geometric ratio a λ, as well as on non-dimensional ratios of the rod-medium properties. It is shown that the resulting waves which can propagate under steady state conditions are surface waves which decay with the radial distance and which permit no radiation damping of energy. It is further shown that such waves can propagate freely only if the propagation speed of longitudinal waves in the corresponding free rod is less than that of shear waves propagating in the medium. Results are presented by means of dispersion curves and surfaces. From a study of the analytical results obtained, lower and upper bounds on the phase speeds are established.
UR - http://www.scopus.com/inward/record.url?scp=0019875351&partnerID=8YFLogxK
U2 - 10.1016/0022-460X(81)90291-1
DO - 10.1016/0022-460X(81)90291-1
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AN - SCOPUS:0019875351
SN - 0022-460X
VL - 76
SP - 65
EP - 75
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 1
ER -