Introduction

Due to the small weight and large flexibility, membrane structures are prone to vibration under external excitation. Furthermore, it may affect the normal function of membrane structures.

Objectives

In view of the limitation of traditional perturbation method and small deflection theory in solving strongly nonlinear vibration problem of membranes. an improved multi-scale method is proposed in this paper to investigate the characteristics of strongly nonlinear vibration of membrane.

Methods

Firstly, based on the large deflection theory of membrane and the improved multi-scale method, the strongly nonlinear damped vibration control equation of membrane with consideration of geometrical non-linearity is solved. Then, the analytical expressions of the frequency and displacement functions of the strongly nonlinear vibration of membranes are obtained, which are compared with the numerical results. Furthermore, the vibration characteristics of the membrane under the initial displacement are explained together with the experimental results.

Results and Conclusion

The results show that the improved multi-scale method is more suitable for solving the strongly nonlinear vibration of membranes than the traditional perturbation method, since the accuracy is higher. Therefore, such a discovery exhibit exposes a more accurate theoretical method for the vibration control and design of membranes.

中文翻译：

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初始位移下正交各向异性膜的强非线性阻尼振动：理论与实验

介绍

由于重量轻和柔性大，膜结构在外部激励下易于振动。此外，它可能影响膜结构的正常功能。

目标

鉴于传统的摄动方法和小挠度理论在解决膜的强非线性振动问题方面的局限性。为了研究膜的强非线性振动特性，提出了一种改进的多尺度方法。

方法

首先，基于膜的大挠度理论和改进的多尺度方法，求解了考虑几何非线性的膜的强非线性阻尼振动控制方程。然后，获得了膜的强非线性振动的频率和位移函数的解析表达式，并将其与数值结果进行了比较。此外，还说明了膜片在初始位移下的振动特性以及实验结果。

结果与结论

结果表明，与传统的摄动法相比，改进的多尺度法更适合于解决膜的强非线性振动，因为其精度更高。因此，这种发现展​​示了用于膜的振动控制和设计的更准确的理论方法。