The stability of systems with distributed parameters and lumped forces

Abstract

The Lyapunov-function method is used to investigate the stability of systems with distributed parameters and lumped forces described by linear partial differential equations (for example, elastic structures with lumped masses, dampers, elastic aircraft with rigid control rudders, etc.). By introducing additional variables, the initial equations of high order are represented by a system of evolution equations and constraint equations, which are first-order partial differential equations. At the points where the lumped forces are applied, certain phase functions experience a discontinuity of the first kind and matching conditions are satisfied. A method for stability investigation is developed for these systems. The change to first-order equations helps to construct the Lyapunov functionals. As an example, the stability of torsional vibrations of an elastic aerofoil with a suspended engine is considered.