ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2002 · 73 citations · 0 references
Natural SciencesMechanical EngineeringDifferential EquationsMechanical Behavior Of MaterialsStructural DynamicsContinuum MechanicsDynamic Mechanical AnalysisElasticity TheoryTime-dependent DeformationViscoelastic BehaviorViscoelastic PropertiesDifferential Equation FormulationFractional Differential EquationsRod TheoryStandard Linear Solid ModelTime-dependent Compressive DeformationViscoelastic EffectsViscoelastic ModelingViscoelastic Rheology
We study dynamics of a viscoelastic rod with fractional derivative type of dissipation under time dependent loading. First the moment curvature relation for the rod from the generalized Zener model of a standard linear solid is derived. Then, we show that the dynamics of the problem is governed by a single linear differential equation with fractional derivative. The existence and uniqueness of solutions for this equation is studied in detail. The form of the solution for the case of periodic compressive force is also obtained.