Nonlinear oscillations of a fully submerged buoyant pendulum under gravity waves

The hydrodynamic interaction between a fully submerged buoyant pendulum and a surface gravity wave is investigated experimentally and analytically in this piece of work. In theoretical font, a nonlinear equation governs the transverse motion of the pendulum, attached to the bottom of a water wave tank, in the water. The method of multiple scales is

employed to the equation of motion to derive modulation and frequency response equations. Eigen values of the Jacobian equations related to first-order modulation equations are

assessed to examine the stability of the stationary solution. This analysis is extended to illustrate the response of the buoyant pendulum and the stability of the stationary points.

Further in the experimental study, Particle Image Velocimetry (PIV) and high-speed imaging are utilized to explore the properties of the pendulum oscillation induced by the gravity

waves in a water channel. The time-series data of the angular displacement of the pendulum from its mean position is obtained using image analysis in MATLAB. The resulting

frequency spectra not only confirm the primary resonance but also reveal a subharmonic response. These experimental findings are rigorously validated both numerically and

analytically. Additionally, the instantaneous velocity field using PIV is measured in order to visually represent the hydrodynamic interaction between the system responses.