A theoretical and experimental study of modal interactions in metallic and laminated composite plates

Abstract

This dissertation focuses on nonlinear modal interactions in plates. Our first investigation involved the activation of a two-to-one internal resonance in the response of a metallic cantilever plate. Although the plate was excited around the frequency of its second bending mode, its response contained a contribution from its first torsional mode. The frequency ratio between the bending and torsional modes was nearly two-to-one.

Next, we investigated the energy transfer from high-frequency to low-frequency modes in a cantilever graphite-epoxy composite plate (90/30/ — 30/ — 30/30/90)_s. The plate was excited around the natural frequency of its seventh (third torsional) mode. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by an amplitude and phase modulation of the seventh mode.

We studied combination resonances in the responses of cantilever composite plates with the layups (90/30/ — 30/ — 30/30/90)_s and (—75/75/75/ — 75/75/ — 75)_s to harmonic base excitations. We activated the combination resonance f_e≈ ω₂ + ω₇ in the (90/30/ — 30/ — 30/30/90)_s plate, where the w; are the natural frequencies of the plate and f<sub>e<sub> is the excitation frequency. In the (—75/75/75/ — 75/75/ — 75)_s plate, we activated the external combination resonance f<sub>e<sub>≈ 1/2(ω₂+ω₅) and the combination internal resonance f_e≈1/2(ω₂+ω₁₃) ≈ ω₈.

We carried out an experimental-modal analysis (EMA) of a nonclassically supported plate with and without a constrained-layer damping (CLD) patch attached on its upper left-hand side surface. The natural frequencies and mode shapes were used to ascertain the effect of the CLD patch.