Finite amplitute oscillations in curvilinearly aeolotropic elastic sylinders

Author:
R. R. Huilgol

Journal:
Quart. Appl. Math. **25** (1967), 293-298

DOI:
https://doi.org/10.1090/qam/99895

MathSciNet review:
QAM99895

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References | Additional Information

**[1]**J. L. Ericksen and R. S. Rivlin,*Large elastic deformation of homogenous anisotropic materials*, J. Rational Mech. Anal.**3**, 281-301 (1954) MR**0063232****[2]**A. E. Green and J. E. Adkins,*Large elastic deformations and Nonlinear continuum mechanics*, Clarendon Press, Oxford, 1960 MR**0269158****[3]**R. R. Huilgol,*A finite deformation possible in transversely isotropic materials*, to be published in ZAMP**[4]**M. Singh and A. C. Pipkin,*Note on Ericksen's problem*, Zeit. Angew Math. Phys.**16**, 706-709 (1965)**[5]**R. R. Huilgol,*Certain dynamics problems in finite deformations of transversely isotropic elastic materials*, to be published**[6]**J. K. Knowles,*Large amplitude oscillations of a tube of incompressible elastic materials*, Quart. Appl. Math.**18**, 71-77 (1960) MR**0112336****[7]**J. K. Knowles,*On a class of oscillations in the finite-deformation theory of elasticity*, J. Appl. Mech.**29**, 283-286 (1961) MR**0137346****[8]**Guo Zhong-Heng and R. Solecki,*Free and forced finite-amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material*, Arch. Mech. Stos.**15**, 427-433 (1963) MR**0163494****[9]**J. K. Knowles and M. T. Jakub,*Finite dynamic deformations of an incompressible elastic medium containing a spherical cavity*, Arch. Rational Mech. Anal.**18**, 367-378 (1965) MR**0174206****[10]**C.-C. Wang,*On the radial oscillations of a spherical thin shell in the finite elasticity theory*, Quart. Appl. Math.**23**, 270-274 (1965) MR**0187477****[11]**C. Truesdell,*Solutio generalis et accurata problemaium quamplurimorum de motu corporum elasticorum incompribilium in deformationibus valde magnis*, Arch. Rational Mech. Anal.**11**, 106-113 (1962); Addendum, ibid,**12**, 427-428 (1963) MR**0145725****[12]**C. Truesdell and W. Noll,*The nonlinear field theories of mechanics*, Encyclopaedia of Physics, Ed. S. Flügge, Vol. III/3, Springer-Verlag, Berlin, 1965, Sees. 61-62 MR**1215940****[13]**C. Truesdell,*The mechanical foundations of elasticity and fluid dynamics*, J. Rational Mech. Anal.**1**, 125-300 (1952) MR**0046838****[14]**M. Baker and J. L. Ericksen,*Inequalities restricting the form of the stress-deformations relations for isotropic elastic solids and Reiner-Rivlin fluids*, J. Wash. Acad. Sci.**44**, 33-35 (1954) MR**0063235****[15]**R. S. Rivlin and D. W. Saunders,*Large elastic deformation of isotropic materials*. VII,*Experiments of the deformation of rubber*, Phil. Trans. Roy. Soc. London (**A**)**243**, 251-288 (1951)**[16]**W. S. Blackburn,*Second-order effects in the torsion and bending of transversely isotropic incompressible elastic beams*, Quart. J. Mech. Appl. Math.**11**, 142-158 (1958) MR**0093132**

Additional Information

DOI:
https://doi.org/10.1090/qam/99895

Article copyright:
© Copyright 1967
American Mathematical Society