Steady-state responses of a viscoelastic plate with in plane variable speed motion under non-homogeneous boundary conditions

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (13) : 156-162.

ZHANG Dengbo1， CHEN Liqun1,2

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Abstract

Steady-state responses for lateral nonlinear 1∶2 principal parametric resonance of a viscoelastic plate with in plane 1∶3 internal resonance of translation were investigated under nonhomogeneous boundary conditions. A governing partial differential equation of motion and corresponding nonhomogeneous boundary conditions for the plate with in plane translation were established considering effects of viscoelasticity on boundary conditions. The multi-scale method was applied to establish the solvability conditions during the plate having sub-harmonic parametric resonance. The stability of the system’s frequency-amplitude responses was judged using Routh-Hurvitz criterion. Effects of in-plane translation speed disturbance amplitude and viscoelastic coefficient on the system’s steady-state responses were investigated. The system’s steady-state responses under homogeneous boundary conditions and non-homogeneous ones were compared. Finally, the differential quadrature method was introduced to verify approximate analytical results using the multi-scale method.

Key words

plate with in plane motion / sub-harmonic parametric resonance / 1∶3 internal resonance / multi-scale method / differential quadrature method

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ZHANG Dengbo1， CHEN Liqun1,2. Steady-state responses of a viscoelastic plate with in plane variable speed motion under non-homogeneous boundary conditions[J]. Journal of Vibration and Shock, 2020, 39(13): 156-162

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