Numerical and experimental investigation of coupled beam and pendulum oscillator

A large number of aerospace structures and large flexible mechanical structures may be modeled as a large flexible beam with a tip-mass. Sometimes, under certain conditions (high excitation amplitude, etc.), large deformation may be produced in the structure. In the field of design, the developments have led to the use of lightweight and high strength materials in these structures. Hence, modern structures are lighter, more flexible, and provide much lower energy dissipation, leading to an intense vibration response.

A vibrating (oscillating) system has a maximum response amplitude at the resonance conditions; as a result, the system should work before or beyond the resonance case. Otherwise, it has a maximum response amplitude, which may cause the system to fail.

In this research, a flexible beam with an appendage, which consists of a mass-pendulum attached to its tip, is investigated. Such an appendage can be located anywhere along the beam. However, in this research, only a tip appendage is considered. The pendulum which is considered as an auto-parametric vibration absorber.

The equations of the motion of a system are obtained using D'Alembert's principle. The partial differential equations are reduced to a set of ordinary differential equations using the Galerkin method. The equations are nonlinear since the analysis is based on large deflection and also coupling exists between the beam and the pendulum.

Numerical simulations are performed in order to obtain frequency response curves of the beam and the pendulum. The simulations are performed for different damping coefficients, both beam and pendulum, around primary resonance and under different forcing amplitudes.

Experiments are conducted for two different lengths of the beam. The longer beam is used for uninverted pendulum motion, and the shorter beam for the inverted pendulum motion. Four different pendulums are considered for the uninverted pendulum case, and one pendulum for the inverted pendulum case.

The results show that an energy exchange between the beam and pendulum, and also chaotic motion, is observed for some parameters of the beam and pendulum. Hence, the pendulum may be considered as a suitable auto-parametric vibration absorber.