Stability boundaries of a swinging spring with oscillating support

✍ Scribed by G. Ryland II; L. Meirovitch

• Book ID: 104153964
• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 750 KB
• Volume: 51
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(77)80051-5

✦ Synopsis

This paper is concerned with the motion of a flexible pendulum whose support oscillates harmonically along a vertical line. The motion is described by two simultaneous ordinary differential equations for the generalized co-ordinates: namely, the angular excursion of the pendulum and the axial elastic motion of the pendulum bob. For small angles, an explicit solution is possible for the elastic motion. As a result, the pendulum oscillations are governed by a form of Ince's equation. Periodic solutions of the equation are obtained by using a method employing Hill's determinants. A simple computational procedure is developed which permits the calculation of large symmetric tridiagonal determinants. This procedure is used to compute combinations of system parameters for which periodic solutions are possible. Then periodic solutions are used to produce stability diagrams in a three-dimensional parameter space, where the stability diagrams can be regarded as three-dimensional Strutt diagrams.