Primary and parametric resonance of a pendulum under combined base excitations: Experiments and simulations

This paper presents both new experimental and numerical investigations for large nonlinear oscillations of a pendulum subject to a combined base excitation. The equation of motion is developed and solved using combined numerical integration and arc-length continuation scheme. The numerical analysis fully preserves the nonlinearity of the system, avoiding any simplifications through Taylor series expansion. The nonlinear frequency response to unidirectional base excitation is initially determined. Subsequently, a thorough analysis of the nonlinear primary and parametric resonance induced by the interaction of coupled horizontal and vertical base excitation is undertaken. An experimental setup has been developed for testing the system’s response to both unidirectional and combined base excitations. A number of experiments have been undertaken to corroborate the numerical findings, which have been determined to be in significant agreement.