scholarly journals Determination of transient responses of a thick-walled transversely isotropic spherical shell by the ray theory.

1986 ◽  
Vol 52 (473) ◽  
pp. 35-41
Author(s):  
Toshiaki HATA
Keyword(s):  
Spherical Shell ◽  
Transversely Isotropic ◽  
Ray Theory ◽  
Transient Responses ◽  
Transversely Isotropic Spherical Shell ◽  
Isotropic Spherical Shell

Determination of Transient Responses of a Thick-Walled Spherical Shell by the Ray Theory

1978 ◽  
Vol 45 (1) ◽  
pp. 114-122 ◽  
Author(s):  
Yih-Hsing Pao ◽  
Ahmet N. Ceranoglu
Keyword(s):  
Spherical Shell ◽  
Arrival Time ◽  
Applied Pressure ◽  
Ray Theory ◽  
Multiple Reflections ◽  
Transient Responses ◽  
Reflected Waves ◽  
Ray Path ◽  
The Waves

The dynamic response of a thick-walled elastic spherical shell subject to radially symmetric loadings is studied by applying the theory of rays. The Fourier transformed solution of the waves in the shell is sorted out into rays by following the ray-path of the multiply reflected waves at both surfaces. Inverse transform of each ray, which is obtainable in closed form, gives rise to the exact solution of the transient response up to the arrival time of the next ray. Numerical results are shown for internally applied pressure with a step or a square-time function. The radial stresses are found to be critically large in tension due to multiple reflections at both surfaces of a thick shell.

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