| Membranes are usually flexible and thus may exhibit a large deflection when subjected to out-of-plane loads,resulting in a strong geometric nonlinearity and further difficulty in solving the deflection problems of membrane analytically.Therefore,in the literature,there are few analytical solutions for thin film problems,and in most cases,numerical solutions are available.In some cases,however,analytical solutions are indispensable,especially when it is necessary to understand the effects of changes in parameters on variables.This study is the preliminary study of a prospective rainfall sensor,aiming at providing a theoretical basis for the anticipated research and development,that is,an analytical theory for the problem of large deflection of a peripherally-fixed circular membrane under the action of a given amount of liquid gravity.This problem involves the usually so-called fluid-structure coupling phenomenon,and its governing equations for this problem contain both differential operation and integral operation,resulting in serious difficulties in analytical study.In this study,the governing equations including differential operation and integral operation are solved successfully by using power series method,and the analytical solution for the problem of axisymmetric deflection of a circular membrane under a certain amount of liquid self-weight loading is finally given.The main research contents covered in this study are as follows:(1)The existing analytical theories of circular membrane problems are reviewed and summarized.(2)The theoretical basis of elastic mechanics involved in the process of analytical study is briefly introduced.(3)The fluid-membrane interaction is analyzed,and the coupling problem is simplified.(4)The governing equations of liquid-membrane coupling problem are established,and the governing equations contain differential operation and integral operation are solved by power series method.(5)The validity of analytical solution is analyzed,and a conducted numerical example shows that the analytical solution has good convergence.(6)An experimental research is carried out and the results show that the analytical solution obtained is reliable.(7)In order to facilitate the development of rain gauge and the subsequent theoretical research,the parameters are analyzed and the analytical solution is compared with the well-known Hencky solution used in existing researches and applications.This study shows that the power series method is an effective analytical method for solving differential-integral equations.And this dissertation provides a new analytical solution to circular membrane problems and a detailed analytical theory for the anticipated development of a new type of of rain gauge. |
