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.

Stress-Focusing Effect in a Uniformly Heated Solid Sphere

1991 ◽  
Vol 58 (1) ◽  
pp. 58-63 ◽  
Author(s):  
Toshiaki Hata
Keyword(s):  
Arrival Time ◽  
Solid Sphere ◽  
Stress Waves ◽  
Ray Theory ◽  
Reflected Waves ◽  
Focusing Effect ◽  
Inverse Transform ◽  
Ray Path ◽  
Very High ◽  
Constant Period

The ray theory is applied to the stress-focusing effects in a uniformly heated solid sphere. The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Laplace transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply-reflected waves. Inverse transform of each ray gives rise to the exact solution of the transient response up to the arrival time of the next ray. The numerical results reveal that stresses peak out periodically at a constant period and, unlike the case of cylinder, the radial stress at the center of the sphere is bounded.

scholarly journals Study on the Viscoelasticity Measurement of Materials Based on Surface Reflected Waves

Materials ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 1875 ◽  
Author(s):  
Jun-jie Chang ◽  
Yuan-yuan Li ◽  
Xue-feng Zeng ◽  
Hai-ying Zhong ◽  
Tao-lei Wan ◽  
...  
Keyword(s):  
Theoretical Study ◽  
Loss Modulus ◽  
Experimental System ◽  
Ultrasonic Waves ◽  
Reflection Method ◽  
Multiple Reflections ◽  
Reflected Waves ◽  
Surface Reflection ◽  
Overall Efficiency

The reflected waves received from ultrasonic waves propagating in materials contain information that constitutes the physical properties, material composition, defects, and degradation states. When measuring the dynamic viscoelasticity, the traditional bottom reflection method (BRM) cannot be used to measure the bottom irregular samples. In this paper, the storage modulus, loss modulus, and loss tangent are extracted by the surface reflection method (SRM) to evaluate the elastomer sample viscoelasticity. A theoretical study on the phase change caused by multiple reflections in the case of non-thin layer coupling is conducted. Based on this research, the experimental system is built. The results show that considering the thickness of the coupling layer can optimize the determination of viscoelasticity and reduce the error of the viscoelastic evaluation results of an elastomer with the traditional BRM. Finally, based on the principle of the SRM, the density of the elastomers is measured, and the feasibility and overall efficiency of this method are verified by experiments.

Reconsideration of the Stress-Focusing Effect in a Uniformly Heated Solid Cylinder

1994 ◽  
Vol 61 (3) ◽  
pp. 676-680 ◽  
Author(s):  
T. Hata
Keyword(s):  
Free Surface ◽  
Infinite Series ◽  
Stress Waves ◽  
Ray Theory ◽  
Solid Cylinder ◽  
Reflected Waves ◽  
Focusing Effect ◽  
Ray Path ◽  
Very High ◽  
Constant Period

The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the cylinder result in very high stresses at the center. Ho solved the problem by using Laplace transform on time and presented the solution as infinite series summations, which converge very slowly for certain combinations of time and the radius of a cylinder. However, adopting a concept of the ray theory, the solution of stress waves in the cylinder is sorted out into rays according to the ray path of multiply reflected waves. The results expressed in an infinite series reveal that stresses peak out periodically at a constant period and the order of singularity of the stresses in a cylinder is O(ρ−2).

Polarographic and spectrophotometric behaviour of some N-p-phenyl substituted benzamidines

1991 ◽  
Vol 56 (12) ◽  
pp. 2791-2799 ◽  
Author(s):  
Juan A. Squella ◽  
Luis J. Nuñez-Vergara ◽  
Hernan Rodríguez ◽  
Amelia Márquez ◽  
Jose M. Rodríguez-Mellado ◽  
...  
Keyword(s):  
Spectrophotometric Study ◽  
Absorption Bands ◽  
Electrochemical Parameters ◽  
Wide Ph Range ◽  
Group A ◽  
Substituent Constants ◽  
Ph Range ◽  
The Waves

Five N-p-phenyl substituted benzamidines were studied by DC and DP polarography in a wide pH range. Coulometric results show that the overall processes are four-electron reductions. Logarithmic analysis of the waves indicate that the process are irreversible. The influence of the pH on the polarographic parameters was also studied. A UV spectrophotometric study was performed in the pH range 2-13. In basic media some variations in the absorption bands were observed due to the dissociation of the amidine group. A determination of the pK values was made by deconvolution of the spectra. Correlations of both the electrochemical parameters and spectrophotometric pK values with the Hammett substituent constants were obtained.

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