Parametric resonances of convection belt system. (English) Zbl 1204.70017
The authors analyze the transverse vibrations of moving belts which are used in transmission gearing. The authors consider parametric resonances, effects of cross-area of the belts, detuning, viscoelastic parameters and transport speed. Equations of motion of the considered system are essentially nonlinear because of the nonlinear dependence of transverse displacements on the strains of the belt. To describe viscoelastic properties of the belt material, the authors choose the Kelvin viscoelastic model. This system can be considered like a continuous gyroscopic system with weakly nonlinear terms and with parameter excitation. To solve the governing equations, the authors employ the method of multiple scales. Stability analysis of steady-state solutions is performed by means of the linearized Lyapunov stability theory. Finally, the authors discuss the effects of averaged transport speed and the amplitude and frequency speed variation on the steady-state response.
Reviewer: Yuri N. Sankin (Ul’yanovsk)
MSC:
| 70K28 | Parametric resonances for nonlinear problems in mechanics |
| 70K20 | Stability for nonlinear problems in mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74D05 | Linear constitutive equations for materials with memory |
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