| A large number of flexible mechanical structures such as aerospace and ocean structures which are subjected to random excitation may be modeled as a flexible beam with a tip mass. Under certain conditions (high excitation amplitude, etc.), large deformation may sometimes be produced in the structure, which may cause the system to fail.; In this research, a flexible beam with a tip appendage, which consists of a mass-pendulum attached to its tip, is investigated under random excitation. The pendulum is used as an autoparametric vibration absorber. The energy transfer between the beam and the pendulum is observed both theoretically and experimentally.; The equations of motion, in the form of integro-differential equations governing the system dynamics, are obtained using D'Alembert's Principle. The Galerkin method is used to obtain the system ordinary differential equations. The equations are non-dimensionalized, and the acceleration coupling terms are eliminated to write the equations in Markov space. The moment closure schemes, in conjunction with stochastic averaging, are used to solve for the mean-square response of the beam and the pendulum. For the experimental investigation, mean square response, autocorrelation function, and power spectral density functions of the system parameters are observed and presented to reveal the energy exchange between the beam and the pendulum. To observe the autoparametric interaction in another mechanical system, an experiment of one-story building with a continuous pendulum was also studied.; The outcome of this research reveals the scope and limitations of the beam-pendulum oscillator as a vibration-absorbing device in applications where random disturbance occurs. |
