Thermodynamics and Statistical Mechanics of Vibrations of Beams

摘要

The primary goal of this research is to investigate whether the laws ofstatistical mechanics can be applied to structural vibrations. To achieve a qualitative understanding of the situation, investigation has been pursued on issues: deviation from equipartition, energy thresholds, energy transfer from low to high frequency modes, energy transfer from high to low frequency modes, correlation radius and geometry of phase space. Issues on dissipative systems, high energy vibrations, and Planck Constant for structural beams have also been investigated. From this research, it is found that there exists a sequence of energy thresholds for beam vibrations. They characterize the energy levels which should be exceeded in order to get equipartition of kinetic energy over the beam particles. The maximum energy threshold corresponds to the transition to developed chaos. Computational simulations indicate that upper energy threshold decays at low number of degrees of freedom and seems to grow at large number of degrees of freedom. The work also leads to the development of thermodynamics of limit cycles which has been applied to Duffing's oscillator and cantilever beam.