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Analytical modeling of viscoelastic dampers for structural and vibration control. (English) Zbl 1090.74636

Summary: Different approaches to the mathematical modeling of viscoelastic dampers are addressed, and their theoretical basis and performance are compared. The standard mechanical model (SMM) comprising linear springs and dashpots is shown to accurately describe the broad-band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law. The SMM renders a Prony series expression for the modulus and compliance functions in the time domain, and the remarkable mathematical efficiency associated with exponential basis functions of Prony series greatly facilitates model calibration and interconversion. While cumbersome, nonlinear regression is usually required for other models, and a simple collocation or least-squares method can be used to fit the SMM to available experimental data. The model allows viscoelastic material functions to be readily determined either directly from experimental data or through interconversion from a function established in another domain. Numerical examples two common viscoelastic dampers demonstrate the advantages of the SMM over fractional derivative and power-law models. Detailed computational procedures for fitting and interconversion are discussed and illustrated. Published experimental data for a viscoelastic liquid damper and for a viscoelastic solid damper are used in the examples.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74D05 Linear constitutive equations for materials with memory
74H45 Vibrations in dynamical problems in solid mechanics
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