Dynamic analysis for nonlinear vibration of prestressed orthotropic membranes with viscous damping. (English) Zbl 1359.74254
Summary: This paper is concerned with the nonlinear damped vibration of prestressed orthotropic membrane structures. The Krylov-Bogolubov-Mitropolsky (KBM) perturbation method is employed for solving the governing equations of large amplitude nonlinear vibration of rectangular orthotropic membranes with viscous damping. Presented herein are asymptotic analytical solutions for the frequency and displacement function of large amplitude nonlinear damped vibration of rectangular orthotropic membranes with four edges simply supported or fixed. Through the computational example, we compared and analyzed the frequency results. Meanwhile, the vibration mode of the membrane and the displacement and time curve of each feature point on the membrane surface were analyzed. The results obtained herein provide a simple and convenient approach to calculate the frequency and lateral displacement of large amplitude nonlinear vibration of rectangular orthotropic membranes with low viscous damping. In addition, the results provide some computational basis for the vibration control and dynamic design of membrane structures.
MSC:
| 74K15 | Membranes |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 74B20 | Nonlinear elasticity |
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