A theoretical and experimental study of modal interactions in resonantly forced structures

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Tech


The influence of modal interactions on the response of harmonically excited flexible L-shaped metallic and composite structures has been investigated analytically and experimentally. Each metallic structure possesses a two-to-one internal resonance, while each composite structure possesses a three-to-one internal resonance and either a two-to-one or a one-to-·one internal resonance. For the metallic structures, a weakly nonlinear analysis is used to derive the autonomous system of equations which describe the evolution of the amplitudes and phases of the internally resonant modes. These equations are obtained for primary- and secondary-resonant excitations. The excitation frequency or amplitude is used as a control parameter and the resulting bifurcations (saddle-node, pitchfork, and Hopf bifurcations) are studied. Theoretical analyses for internally resonant systems are used to predict and explain the responses of the composite structures.