STRUCTURAL MODAL MULTIFURCATION WITH INTERNATIONAL RESONANCE .1. DETERMINISTIC APPROACH

The bifurcation and multifurcation in multimode interaction of nonline ar continuous structural systems is investigated. Under harmonic excit ation the nonstationary response of multimode interaction is considere d in the neighborhood of fourth-order internal resonance condition. Th e response dynamic characteristics are examined via three different ap proaches. These are the multiple scales method, numerical simulation, and experimental testing. The model considered is a clamped-clamped be am with initial static axial load. Under certain values of the static load the first three normal modes are nonlinearly coupled and this cou pling results in a fourth order internal resonance. The method of mult iple time scales yields nonstationary response in the neighborhood of internal resonance. Within a small range of internal detuning paramete r the third mode, which is externally excited, is found to transfer en ergy to the first two modes. Outside this region, the response is gove rned by a unimodal response of the third mode which follows the Duffin g oscillator characteristics. The bifurcation diagram which represents the boundaries that separate unimodal and mixed mode responses is obt ained in terms of the excitation level, damping ratios, and internal r esonance detuning parameter. The domains of attraction of the two resp onse regimes are also obtained. The numerical simulation of the origin al equations of motion suggested the occurrence of complex response ch aracteristics for certain values of damping ratios and excitation ampl itude. Both numerical integration and experimental results reveal the occurrence of multifurcation as reflected by multi-maxima of the respo nse probability density curves.