Large amplitude vibration of buckled beams and rectangular plates

Abstract

The writer wishes to thank Edgar Thompson and Lloyd LeBlanc for their assistance in making the detailed spectral absorption coefficient calculations referred to in this note.

Non-linear vibration of Euler-Bernoulli beams

“…He pointed out the natural frequencies of buckled beams depend on the amplitude of vibration. Eisley [11,12] used a single-mode discretization to investigate the forced vibrations of buckled beams and plates. He considered both simply supported and clamped-clamped boundary conditions.…”

“…He considered both simply supported and clamped-clamped boundary conditions. For a clamped-clamped buckled beam, Eisley [11,12] used the first buckling mode in the discretization procedure. He obtained similar forms of the governing equations for simply supported and clamped-clamped buckled beams.…”

Entrainment of Micromechanical Limit Cycle Oscillators in the Presence of Frequency Instability

“…Beams may also be driven inertially through the piezoshaker. displacement curve, and amplitude-softening in postbuckled beams [57] due to symmetry breaking. The following discussion and the data presented here are for 35 μm long singly and doubly supported beams.…”

“…However, for a beam in the buckled state, the symmetry is broken due to the presence of the (unstable) unbuckled state and other (stable) buckled state to one side of the configuration. This produces a quadratic stiffness [57], αx 2 , which is always softening in addition to the cubic stiffness [60], [61], and produces even harmonics in the motion for large amplitude. Competition/collaboration between quadratic softening and cubic hardening/softening yields an equivalent…”

Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method

“…Using the Galerkin's method, Shin and Blotter [8] presented the solutions to free undamped large amplitude vibrations of plated on elastic foundations. Eisley [9] considered a large amplitude vibration of buckled beam and rectangular plates. The problem of two and three dimensional plates undergoing limit-cycle oscillations was investigated by Dowell [10].…”