Evaluation of cantilever plates in the spinning situation: time histories and modal characteristics

A study on the dynamics of cantilever orthotropic plates under spinning conditions is presented in this article. The governing equations of motions are containing the centrifugal and Coriolis effects. Two approximation methods, the extended Galerkin method, and extended Kantorovich method, are utilized for the investigation of the mathematical model. The verification of the obtained results is conducted by comparing two methods that show good agreement. This investigation is concentrated on the time histories and the natural frequencies of the system. First, using time responses, the effects of different types and numbers of admissible functions used in the approximate solution are discussed. Next, the results are obtained to explore the impact of dimensionless parameters like material, hub radius ratio, stagger angle, etc. on the modal characteristics of the spinning structures. The results of the simulations exhibit the importance of the proper choice of both type and number for trial functions. Furthermore, the selection of orthogonal functions can be vital to guarantee the convergence speed of an approximate solution. Further discussion on the modal characteristic reveals that in different stiffness ratios of the plate, the centrifugal stiffening rate caused by spinning motion is affected by rotational speed. Moreover, this stiffening rate is depended on setting angle and hub radius ratio. Finally, the last part of the paper is devoted to the forced response analysis of the rotating plate.