Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11817
Title: Toroidal vibrations of anisotropic spheres with spherical isotropy
Authors: Chau, KT 
Issue Date: 1998
Publisher: American Society of Mechanical Engineers
Source: Journal of applied mechanics, 1998, v. 65, no. 1, p. 59-65 How to cite?
Journal: Journal of applied mechanics 
Abstract: This paper derives the exact frequency equation for the toroidal mode of vibrations for a spherically isotropic elastic sphere. The vibrations of spherically isotropic solids are solved by introducing two wave potentials (Φ and Ψ) such that the general solutions for free vibrations can be classified into two independent modes of vibrations, namely the "toroidal" and "spheroidal" modes. Both of these vibration modes can be written in terms of spherical harmonics of degree n. The frequency equation for the toroidal modes is obtained analytically, and it depends on both n and β [= (Cn - C12)/(2C44)], where C11, C12, and C44 have the usual meaning of moduli and are defined in Eqs. (2) - (3); and, as expected, Lamb's (1882) classical frequency equation is recovered as the isotropic limit. Numerical results show that the normalized frequency ωa/Cs increases with both n and β, where ω is the circular frequency of vibration, a the radius of the sphere, and C, is the shear wave speed on the spherical surfaces. The natural frequencies for spheres of transversely isotropic minerals and crystals, with β ranging from 0.3719 to 1.8897, are also tabulated. However, two coupled differential equations are obtained for the spheroidal modes, which remain to be solved.
URI: http://hdl.handle.net/10397/11817
ISSN: 0021-8936
EISSN: 1528-9036
DOI: 10.1115/1.2789046
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

16
Last Week
0
Last month
0
Citations as of Aug 17, 2017

WEB OF SCIENCETM
Citations

9
Last Week
0
Last month
0
Citations as of Aug 4, 2017

Page view(s)

30
Last Week
4
Last month
Checked on Aug 21, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.