Nonlinear dynamic analysis of an elastic beam isolator sliding on frictional supports

The dynamic behavior of an elastic beam free to slide on two frictional supports is studied under sinusoidal and random excitations. The beam force–deflection relationship, originally expressed in terms of elliptic functions, is approximated by a polynomial fit of eleventh order. The friction force is modeled in terms of the sliding velocity and the end slope angle. Under sinusoidal excitation, the equation of motion of the system is solved numerically and the solution is utilized to estimate the system transmissibility. It is found that when the excitation frequency is increased beyond resonance, the friction at the sliding supports improves the transmissibility. The dependence of the response on initial conditions establishes the basins of attraction for different values of friction coefficient and excitation parameters. The dependence of the safety integrity factor on excitation amplitude level and friction coefficient reveals that the friction extends the stable region. Under random excitation, the system response statistics are estimated from Monte Carlo simulation results for different values of friction coefficient and excitation power spectral density level. The friction is found to result in a significant reduction of the system response mean square.