Theoretical and experimental modeling of beam-type flexural wave behaviours of orthogonally stiffened plates

Abstract

This paper deals with one-dimensional beam-type flexural wave behaviours of the orthogonally stiffened plate. A truncated model with one stringer and multiple stiffeners is experimentally investigated for free vibration behaviours of natural frequencies and beam-type mode shapes. Numerical simulations of the truncated model of the orthogonally stiffened plate and the beam models coupled with periodic resonators are performed to investigate the similarity of the free vibration behaviours of the experimental model and the theoretical model. Issues involved in the equivalent simplification such as the coupling form between the beam and the resonators, and the evaluation of the parameters of the theoretical model are addressed. The experimental results of the spectral responses of the forced vibrations are presented to verify the spectral location of the local resonant attenuation band indicated by the complex wavenumber spectrum curves of the flexural wave propagating through the equivalently simplified beam model coupled with periodic resonators. Results show that the beam model coupled with periodic resonators in series connection is generally qualified to show the local resonant attenuation phenomenon of the one-dimensional beam-type truncation model of the orthogonally stiffened plate. The local resonant attenuation bands are caused by the bending resonance of various orders of the stiffeners. For each of the local resonant attenuation bands, there are two resonant attenuation frequencies respectively corresponding to the translational and rotational coupling between the stringer and the stiffeners.