Summary
This paper considers the problem of transient wave propagation in Cosserat shells of variable thickness, the inhomogeneous material of which is linearly elastic and isotropic. We do not say that the shells are isotropic because varying thickness causes behaviour characteristic of anisotropy despite the material's being isotropic. The methods of rays and of singular wave curves are combined to find and integrate the transport equations governing growth-decay behaviour of the six possible wave modes. Conditions on material parameters, thickness variation, and wave geometry are obtained for various different uncouplings of the wave modes. Some special cases of propagation conditions and of decay equations are worked out in detail.
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Bonadies, M., Tonon, M. L.: Sulla legge di evoluzione di onde d'urto nella teoria lineare delle volte elastiche. Rend. Sem. Mat. Univers. Politecn. Torino39, 153–164 (1981).
Molina, C., Pastrone, F.: Wave propagation in lineary elastic shells. Meccanica22, 92–96 (1987).
Cohen, H., Thomas, R. S. D.: Transient waves in inhomogeneous anisotropic elastic shells. Acta Mechanica77, 47–67 (1989).
Cohen, H., Thomas, R. S. D.: Transient waves in inhomogeneous anisotropic elastic plates. Acta Mechanica58, 41–57 (1986).
Naghdi, P. M.: The theory of shells and plates. Encyclopedia of Physics (Flügge, S., chief ed.), Vol. VI a/2, Mech. of Solids II (Truesdell, C., vol. ed.), pp. 425–607, Berlin-Heidelberg-New York: Springer 1972.
Green, A. E., Naghdi, P. M., Wenner, M. L.: Linear theory of Cosserat surface and elastic plates of variable thickness. Proc. Camb. Phil. Soc.69, 227–254 (1971).
Cohen, H., Wang, C.-C.: On compatibility conditions for singular surfaces. Arch. Rat. Mech. Anal.80, 205–261 (1982).
Cohen, H., Thomas, R. S. D.: Decay of transient waves in inhomogeneous anisotropic elastic shells. In: Continuum mechanics and its applications (Graham, G. A. C., Malik, S. K., eds.), pp. 267–276, New York: Hemisphere Publishing Corporation 1989.
Cohen, H., Thomas, R. S. D.: Transient waves in inhomogeneous isotropic elastic plates. Acta Mechanica53, 141–161 (1984).
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Cohen, H., Thomas, R.S.D. Transient waves in inhomogeneous elastic shells of variable thickness. Acta Mechanica 83, 177–186 (1990). https://doi.org/10.1007/BF01172979
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DOI: https://doi.org/10.1007/BF01172979