Analytical and experimental investigations of an autoparametric beam structure

This paper discusses theoretical and experimental investigations of vibrations of an autoparametric system composed of two beams with rectangular cross sections. Different flexibilities in the two orthogonal directions are the specific features of the structure. Differential equations of motion and associated boundary conditions, up to third-order approximation, are derived by application of the Hamilton principle of least action. Experimental response of the system, tuned for the 1:4 internal resonance condition, are performed for random and harmonic excitations. The most important vibration modes are extracted from a real mechanical system. It is shown that certain modes in the stiff and flexible directions of both beams may interact, and, intuitively unexpected out-of-plane motion may appear. Preliminary numerical calculations, based on the mathematical model, are also presented.