Vibration absorbers for flexible structures under random excitation: theory and experiments



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Texas Tech University


A large number of flexible mechanical stmctures such as aerospace and ocean stmctures 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 stmcture, which may cause the system to fail.

In this research, a flexible beam with a tip appendage, which consists of a masspendulum 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 and the vibration absorption characteristics of the pendulum are observed both theoretically and experimentally.

The equations of motion, in the form of integro-differential equations goveming 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 nondimensionalized, 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. The dependence of mean square responses on the frequency ratio is studied.

For the experimental investigation, time histories, mean square responses, autocorrelation, power spectral density, and probability 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 and vibration absorption characteristics of a continuous pendulum, a one-story building with a continuous pendulum system was also studied experimentally.

The outcome of this research reveals the scope and limitations of the beampendulum oscillator as a vibration-absorbing device in applications where random disturbance occurs.