Abstract

Periodic steady state solutions are generated from the nonlinear differential equation of an Euler-Bernoulli beam rod, constant speed crank, slider crank mechanism. The system is approximated by a single ordinary differential equation. To facilitate Harmonic Balance, the response and difficult nonlinear and linear portions of the ODE are expanded into two separate Fourier Series. Harmonic Balance/Fast Fourier Transform method is utilized to determine the harmonic content of each Fourier Series and generate periodic solutions which compared favorably with Runge-Kutta numerical integration. Stability of periodic solutions was examined using the monodromy matrix method. Nondimensional amplitude versus nondimensional crank speed was plotted to examine the effect on dynamic response of external force, piston mass, and crank length. Jump and period doubling bifurcations and regions of amplified response were found.

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