On the vibrations of lumped parameter systems governed by differential-algebraic equations
In this paper, we consider the vibratory motions of lumped parameter systems wherein the components of the system cannot be described by constitutive expressions for the force in terms of appropriate kinematical quantities. Such physical systems reduce to a system of differential-algebraic equations, which invariably need to be solved numerically. To illustrate the issues with clarity, we consider a simple system in which the dashpot is assumed to contain a Bingham fluid for which one cannot describe the force in the dashpot as a function of the velocity. On the other hand, one can express the velocity as a function of the force.
differential-algebraic equations bingham fluid nonlinear vibrations dissipation stored energy coulomb friction nonlinear damping