Membranes often feature in dynamic structures. The design of such structures generally includes the evaluation of their dynamic characteristics, such as natural frequecies and mode shapes. The quasi-statics ad dyamic responses of thin rubber sheeting were investigated through non-contact experimental techniques. The rubber sheeting was modelled as a membrane structure and the material was assumed to be hyper-elastic, isotopic and incompressible. Two hyper-elastic material models were considered, namely the Mooney-Rivlin model and the Neo-Hookean model. The natural frequencies and mode shapes of the hyprt-elastic membrane were anatically and numerically calculated by assuming small linear vibrations and an equi-bi-axial stress state in the membrane. To validate the mathematical analyses, experimental modal analysis was performed where the vibration response was measured with a laser Doppler vibrometer. The analytical model, shows that the natural frequencies of the membrane depend on the initial stretch. Mathematical and experimental results agree well at the lower modes. However, measurement resolution is found to be a vital factor which limits the extraction of closely spaced modes due to difficulties with the accurate identification of nodal line in a purely experimental approach.

中文翻译：

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非接触实验方法表征超弹性膜的响应

膜通常以动态结构为特征。这种结构的设计通常包括对它们的动态特性（例如自然频率和振型）的评估。通过非接触实验技术研究了薄橡胶板的准静态动力响应。将该橡胶板建模为膜结构，并假设该材料是超弹性的，同位素的和不可压缩的。考虑了两个超弹性材料模型，即Mooney-Rivlin模型和Neo-Hookean模型。通过假设膜中存在较小的线性振动和等双轴应力状态，通过解析和数值方法计算了hyprt弹性膜的固有频率和振型。为了验证数学分析，进行实验模态分析，其中用激光多普勒振动计测量振动响应。分析模型表明，膜的固有频率取决于初始拉伸。在较低模式下，数学和实验结果吻合良好。然而，由于在纯粹的实验方法中难以准确识别节点线，因此测量分辨率是限制紧密间隔模式提取的重要因素。