DYNAMIC STABILITY OF A PENDULUM UNDER PARAMETRIC EXCITATION.
Abstract
As background for the dynamic stability of structures, a pendulum undergoing parametric excitation is examined in detail. Theoretically, transient and steady state solutions were developed here for both linear and nonlinear theory. The linear theory showed the presence of various instability regions, and of 'beats' and 'waviness' in the response. The nonlinear theory showed the presence of various steady state limit cycles including some little known subharmonic resonances at 1/3, 1/4, 1/5 of the forcing frequency. The effects of initial amplitudes and phasing were determined by state plane diagrams and by analog computer simulation. Experimentally, the pendulum was excited and both transient and steady state records were obtained. Good agreement was obtained with the linear theory at small amplitudes and with the nonlinear theory at large amplitudes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1968
- Accession Number
- AD0682957
Entities
People
- Chandramohan K. Chhatpar
- John Dugundji
Organizations
- Massachusetts Institute of Technology