Dynamic response of pre-stressed orthotropic circular membrane under impact load

Abstract

In this paper, the governing equations of motion of pre-stressed orthotropic circular membrane under impact load are derived in polar coordinates based on the principle of virtual displacement and solved by the Krylov–Bogoliubov–Mitropolsky perturbation method. The analytical solutions of the displacement, speed, acceleration and frequency of circular membrane with fixed edges are obtained. Then the dynamic response of membrane is experimentally studied by using a new pneumatic experimental system. A comparison between the experimental and theoretical results validates the theoretical model and the vibration principles of membrane under different conditions. The results also indicate the relationship between dynamic response of membrane and various parameters related to radius, elastic modulus, pretention force, and load. This study provides a theoretical model to calculate the dynamic response of pre-stressed orthotropic circular membrane under impact load. In addition, a new pneumatic experimental system to study the dynamic response of pre-stressed membrane is developed as well.

Keywords

Dynamic response circular membrane perturbation method orthotropic concentrated impact load

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References

Alekseev

(1951) Elastic annular membranes with a stiff centre under the concentrated force. Engineering Corpus 10(1): 71–80. [In Russian.].

Babu

Sudhagar

Rajamohan

(2016) Dynamic characterization of thickness tapered laminated composite plates. Journal of Vibration and Control 22(16): 3555–3575.

Beck

Grabmüller

(1992) Wrinkle-free solutions of circular membrane problems. Zeitschrift für Angewandte Mathematik und Physik 43(3): 481–504.

Chen

Zheng

(2003) Large deformation of circular membrane under the concentrated force. Applied Mathematics and Mechanics 24: 28–31.

Chen

Wang

(1981) The symmetrical deformation of circular membrane under the action of uniformly distributed loads in its central portion. Applied Mathmatics and Mechanics 2(6): 653–668.

Coman

Bassom

(2012) On the wrinking of a pre-stressed annular thin film in tension. Journal of the Mechanics and Physics of Solids 60(8): 1601–1617.

Dai

Yan

Yang

(2013) Nonlinear dynamic analysis for FGM circular plates. Journal of Mechanics 29(2): 287–296.

Hailesilassie

Partl

(2013) Adhesive blister propagation under an orthotropic bituminouswaterproofing membrane. Construction and Building Materials 48(11): 1171–1178.

Hao

Yan

(2006) Exact solution of large deformation basic equations of circular membrane under central force. Applied Mathematics and Mechanics 27(10): 1333–1337.

10.

Chen

Sun

Zheng

(2012) Large-deflection axisymmetric deformation of circular clamped plates with different moduli in tension and compression. International Journal of Mechanical Sciences 62: 103–110.

11.

Hencky (1915) Über den sapnnungszustand in Kreisrunden platten mit verschwindende verschwindender Biegungssteifigkeit [Over the stress condition in circular plates with vanishing vanishing bending stiffness]. Zeitchrift für Mathematikund Physik 63: 311–317. [In German.].

12.

Jin

(2008) Large deflection of circular membrane under concentrated force. Applied Mathematics and Mechanics 29(7): 889–896.

13.

Kao

Perrone

(1971) Large deflections of axisymmetric circular membranes. International Journal of Solids and Structures 7(12): 1601–1612.

14.

(1956) On the large deflection of elastic circular membrane with initial tension under uniformly distributed load. Acta Physica Sinica 12(4): 319–338.

15.

Liu

Zheng

Yang

(2014) Nonlinear damped vibration of pre-stressed orthotropic membrane sturctue under impact loading. International Journal of Structure Stability and Dynamics 14(1): 133–146.

16.

Micallef

Fallah

Curtis

et al. (2015) On the dynamic plastic response of steel membranes subjected to localised blast loading. International Journal of Impact Engineering 89(1): 25–37.

17.

Pavlin

Perrone

(1978) Finite difference energy techniques for arbitrary meshes applied to linear Plate problems. International Journal for Numerical Methods in Engineering 14(5): 647–664.

18.

Ribeiro

(2016) Linear modes of vibration of cylindrical shells in composite laminates reinforced by curvilinear fibres. Journal of Vibration and Control 22(20): 4141–4158.

19.

Sherbourne

Lennox

(1966) Elastic large deflections of annular membranes. Journal of the Engineering Mechanics Division 92(2): 75–99.

20.

Weinitschke

Erlangen

(1987) On finite displacements of circular elastic membranes. Mathematical Methods in the Applied Sciences 9(1): 76–98.

21.

Zheng

Guo

Song

et al. (2014) Nonlinear free vibration analysis of axisymmetric polar orthotropic circular membranes under the fixed boundary condition. Mathematical Problems in Engineering 2014(3): 1–8.

22.

Zheng

Liu

Gong

et al. (2013) A new method – ejection method for nondestructive online monitoring of the pretension of building membrane structure. Structural Control and Health Monitoring 20(4): 445–464.

23.

Zou

Chen

Wang

(1985) Power series solution for large deflection problem of pretension circular plate. Journal of Chongqing University 6(3): 38–52.