An Experimental Investigation of Multimode Responses in a Cantilever Beam

Abstract

An experimental investigation into the planar, multimode response of a cantilever metallic beam to a transverse harmonic excitation is presented. The cantilever beam was tested in both the horizontal and vertical directions. In the vertical configuration, the beam was excited near its fourth natural frequency and energy was transferred from the directly excited fourth mode to a low-frequency mode through both resonant and nonresonant modal interactions. In the latter case, the response contained contributions from the first and fourth modes, whereas in the former case, the response contained contributions from the fourth, second, and fifth modes. The mechanism responsible for the resonant interaction involving the three modes is a subcombination internal resonance of the additive type; that is, Ω ≈ ω4 ≈ 1/2(ω2 + ω5), where the ωi are the natural frequencies of the beam. This type of resonance occurs in systems with a dominant cubic nonlinearity. In the horizontal configuration, the beam was excited near its fourth and sixth natural frequencies. Again, energy was transferred to a low-frequency mode, but in this case only through a resonant interaction due to a subcombination internal resonance of the additive type. Power spectra, time series, and frequency- and amplitude-response curves were obtained for characterization of the dynamic multimode responses.