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Mechanical oscillators described by a system of differential-algebraic equations

Dalibor Pražák, Kumbakonam R. Rajagopal (2012)

Applications of Mathematics

The classical framework for studying the equations governing the motion of lumped parameter systems presumes one can provide expressions for the forces in terms of kinematical quantities for the individual constituents. This is not possible for a very large class of problems where one can only provide implicit relations between the forces and the kinematical quantities. In certain special cases, one can provide non-invertible expressions for a kinematical quantity in terms of the force, which then...

Mechanical oscillators with dampers defined by implicit constitutive relations

Dalibor Pražák, Kumbakonam R. Rajagopal (2016)

Commentationes Mathematicae Universitatis Carolinae

We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples...

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