The Elastic Cylindrical Shell Under Radial Impulse

Abstract

In the motion of an elastic cylindrical shell following impulsive pressure, marked deviations from linear theory may occur through interaction of circumferential membrane force with flexural curvature. Energy is transferred to flexural modes of rather high order. The resulting flexural stress is significantly higher than that given by linear theory.

Intermittent transformation between radial breathing and flexural vibration modes in a single-walled carbon nanotube

“…In future studies, the model is presented for plane-strain rings, which, however, can be applied to plane-stress rings when E/(1Kn 2 ) is replaced by E, where E and n are Young's modulus and Poisson's ratio, respectively. Goodier & McIvor (1964) and McIvor (1966) predicted the transformation between an initial RBM and a flexural bending mode in an elastic cylindrical shell. It was shown that the coupled dynamic equations between the radial and tangential displacements can be simplified into a typical Mathieu differential equation.…”

“…The underlined third-order term in equation (2.5), which was not considered by Goodier & McIvor (1964) and McIvor (1966), is required to obtain governing equations for 2 and j to the third order. Following the same procedure as Goodier & McIvor (1964), we obtain the following differential equations of 2 and j, which govern the dynamic motion of the plane-strain ring:…”

“…The RBM couples with the flexural bending modes intermittently when the system parameters are in the instable region of the Mathieu stability diagram. Based on the method proposed in Goodier & McIvor (1964) and McIvor (1966), we add more nonlinear terms in the dynamic equations to obtain coupled equations that contain the fourth-order terms to avoid the divergence of the solution.…”

“…Detailed numerical investigations of these nonlinear differential equations will be presented in a separate paper. The series expansion method (Goodier & McIvor 1964;McIvor 1966) is employed in this study.…”

Love Wave Propagation in Electro-Magneto Non-Homogeneous Elastic Media

“…The elastic cylindrical shell under radial impulse was studied by Mcivor [1]. Cinelli [2] has investigated dynamic vibrations and stresses in elastic cylinders and spheres.…”