Transverse wave motion in constrained mechanical systems
Abstract
The effect of the finite rotation on the propagation of impact-induced transverse waves in the passive system is examined. The partial differential equations of motion of kinematically driven rotating beams are obtained using the principle of virtual work in dynamics. This system is classified as a passive system which does not normally respond in the case of zero initial conditions. This system, however, is ideally suited for examining the effect of the finite rotation on the propagation of impact-induced transverse waves. The jump discontinuity in the system parameters as the result of impact is predicted using the algebraic generalized impulse momentum equations that involve the coefficient of restitution. The dispersion relationship is defined and used to demonstrate the effect of the angular velocity and the flexural rigidity of the beam on the phase and the group velocities of the dispersive transverse waves. The analysis presented shows that as the angular velocity increases the phase velocities of the transverse waves decreases and in general, the finite rotation has more significant effect on the phase velocity of the low frequency waves as compared to the high frequency waves. As the result of the finite rotation, the phase velocities of the transverse waves is significantly different from the phase velocities predicted using the classical beam theory of nonrotating beams. A finite element computational procedure for the analysis of impact-induced transverse waves in articulated mechanical and structural systems is also developed. In order to establish the accuracy of the numerical procedure developed, the solution obtained using the finite element method is compared with the solution obtained using the partial differential equation and the method of the separation of variables. Numerical results show that there is a good agreement between the finite element and the eigenfunction solutions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- January 1992
- Bibcode:
- 1992PhDT........53H
- Keywords:
-
- Angular Velocity;
- Momentum Theory;
- Phase Velocity;
- Transverse Waves;
- Wave Propagation;
- Dispersing;
- Eigenvectors;
- Equations Of Motion;
- Finite Element Method;
- Group Velocity;
- High Frequencies;
- Low Frequencies;
- Partial Differential Equations;
- Rotation;
- Structural Mechanics