On generalized fractional vibration equation. (English) Zbl 1373.74025
Summary: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley-Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.
MSC:
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 34K37 | Functional-differential equations with fractional derivatives |
Keywords:
vibration; fractional dynamics; fractional viscoelastic systems; fractional differential equationReferences:
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