INTERACTION OF NONLINEAR NORMAL MODES OF A CANTILEVER BEAM

In the current study, real normal mode manifold approach is used to determine the nonlinear normal modes of the cantilever beam governed by a cubic order geometric and inertial nonlinearity. The system of governing partial differential equations are discretized by expanding the beam displacement using a series of modes which are the Eigenfunctions satisfying the linear beam equation along with the boundary conditions for a cantilever beam. The nonlinear normal modes are then determined by rewriting the discretized system of equation as two first order system of equations in terms of displacement and velocity. The method of multiple scales is adapted as solution procedure to derive the two first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the interacting modes of a cantilevered beam. The numerical results show how energy imparted to the first mode get exchanged with other modes through the nonlinear interactions. The bar chart of the logarithmic of generalized coordinate is analyzed for the first ten modes. The nonlinear frequency response diagrams of the cantilever beam for the primary resonance are obtained. The stable and unstable portions of each frequencyresponse curves are then determined. The influences of excitation level and nonlinearity on the nonlinear frequency response curves have been inspected.