Free Vibration Analysis of Elliptic Plate by Conformal Mapping Method

Abstract

Thin plate structure is very common in various engineering fields. So, it is very important to analyze its vibration characteristics in order to avoid the fatigue damage. Though the rectangular or circular plates are popular because of the low cost of their manufacturing, occasionally due to the stress imbalance which results from eccentric mass during manufacturing them, circular plates may become elliptic plates. In the view of above facts, it is also necessary to study the vibration of elliptic plates. However, the traditional approaches, such as Rayleigh-Ritz method and Mathieu function, have their own limitation so that they will be very awkward. Therefore, this article has brought up a new approach to the study of the vibration of thin plate, which is called conformal mapping method. This method could map a complicated curve plate (like elliptic plate) into a circular plate. Then the theory of free vibration of circular plates in complicated boundary conditions will be used to calculate the analytical solution of natural frequencies (accurate solution) and the corresponding modal vibration modes. This method is universal for any thin plates which have complicated curve shapes so that it will widen the horizon of the study of vibration of plates in practice and break through the limitation of above traditional methods.