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

Abstract 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.

[1]  Shijian Zhu,et al.  Application of chaos method to line spectra reduction , 2005 .

[2]  Dmitry V. Balandin,et al.  Limiting performance analysis of impact isolation systems for injury prevention , 2001 .

[3]  Raymond H. Plaut,et al.  Nonlinear Oscillations of a Buckled Mechanism used as a Vibration Isolator , 2005 .

[4]  G. Marsaglia,et al.  The Ziggurat Method for Generating Random Variables , 2000 .

[5]  G. Losurdo,et al.  Measurement of the VIRGO superattenuator performance for seismic noise suppression , 2001 .

[6]  Ruggero M. Stanga,et al.  An inverted pendulum preisolator stage for the VIRGO suspension system , 1999 .

[7]  R. A. Ibrahim,et al.  Nonlinear Dynamics of a Sliding Beam on Two Supports and its Efficacy as a Non-Traditional Isolator , 2006 .

[8]  A. K. Mallik,et al.  Performance of Non-linear Vibration Isolators Under Harmonic Excitation , 1994 .

[9]  Alexander Veprik,et al.  UNIVERSAL BUMPERED VIBRATION ISOLATOR FOR SEVERE ENVIRONMENT , 1998 .

[10]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[11]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[12]  A. M. Ulanov,et al.  DESCRIPTION OF AN ARBITRARY MULTI-AXIAL LOADING PROCESS FOR NON-LINEAR VIBRATION ISOLATORS , 1997 .

[13]  D. Blair,et al.  Mathematical analysis of an Euler spring vibration isolator , 2002 .

[14]  Kenneth A. Strain,et al.  GEO 600 triple pendulum suspension system: Seismic isolation and control , 2000 .

[15]  Sayed M. Metwalli.  Optimum Nonlinear Suspension Systems , 1986 .

[16]  P. M. Alabuzhev,et al.  Vibration protecting and measuring systems with quasi-zero stiffness , 1989 .

[17]  D. Blair,et al.  High performance vibration isolation using springs in Euler column buckling mode , 2002 .

[18]  David Blair,et al.  Low Resonant Frequency Cantilever Spring Vibration Isolator for Gravitational Wave Detectors , 1994 .

[19]  T. Derby,et al.  INFLUENCE OF DAMPING IN VIBRATION ISOLATION , 1971 .

[20]  R. Plaut,et al.  Analysis of buckled and pre-bent fixed-end columns used as vibration isolators , 2005 .

[21]  C.-M. Lee,et al.  Prediction of non-chaotic motion of the elastic system with small stiffness , 2004 .

[22]  T. E. Shoup.  Shock and vibration isolation using a nonlinear elastic suspension , 1971 .

[23]  David Blair,et al.  Behaviour of a vibration isolator suitable for use in cryogenic or vacuum environments , 1991 .

[24]  Masaki Ando,et al.  Vacuum-compatible vibration isolation stack for an interferometric gravitational wave detector TAMA300 , 2002 .

[25]  Brian F. Feeny,et al.  Autocorrelation on symbol dynamics for a chaotic dry-friction oscillator , 1989 .

[26]  T E Shoup,et al.  An adjustable spring rate suspension system , 1977 .

[27]  Ryutaro Takahashi,et al.  Improvement of the vibration isolation system for TAMA300 , 2002 .

[28]  M. Hundal.  Response of a base excited system with Coulomb and viscous friction , 1979 .

[29]  C.-M. Lee,et al.  Alternative Vibration Protecting Systems for Men-Operators of Transport Machines: Modern Level and Prospects , 2002 .