Journal of Guidance Control and Dynamics · 1991 · 762 citations · 12 references
EngineeringMechanical EngineeringStructural DisplacementsStructural EngineeringStabilityMechanicsRheologyNonlinear Vibration ControlStructural DynamicFractional DynamicStructural VibrationState EquationsRheological Constitutive EquationFractional-order SystemMechanical SystemsViscoelasticallydamped StructuresMaterial DampingStructural MechanicsVibration Control
The study develops fractional‑order state equations to predict and improve feedback control for reducing motion in viscoelastically damped structures. Damping materials are modeled with fractional‑order time derivatives of stress and strain, from which structural equations of motion are derived and used to formulate the fractional‑order state equations. The resulting models accurately capture broadband damping effects, reveal substantial differences between structural and state equations, and highlight additional advantages of the fractional‑order formulation. Nomenclature is provided.
Fractional order state equations are developed to predict the effects of feedback intended to reduce motion in damped structures. The mechanical properties of damping materials are modeled using fractional order time derivatives of stress and strain. These models accurately describe the broadband effects of material damping in the structure's equations of motion. The resulting structural equations of motion are used to derive the fractional order state equations. Substantial differences between the structural and state equations are seen to exist. The mathematical form of the state equations suggests the feedback of fractional order time derivatives of structural displacements to improve control system performance. Several other advantages of the fractional order state formulation are discussed. Nomenclature
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