(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory. By applying energy principle, a novel high dimensional nonlinear dynamic system of the rotating cantilever twisted plate is derived for the first time. The use of variable mode functions by polynomial functions according to the twist angles and geometric of the plate makes it more accurate to describe the dynamic system than that using the classic cantilever beam functions and the free-free beam functions. The comparison researches are carried out between the present results and other literatures to validate present model, formulation and computer process. Equations of motion describing the transient high dimensional nonlinear dynamic response are reduced to a four degree of freedom dynamic system which expressed by out-plane displacement. The effects of twisted angle, stagger angle, rotation speed, load intensity and viscous damping on nonlinear dynamic transient responses of the twisted plate have been investigated. It's important to note that although the homogeneous and isotropic material is applied here, it might be helpful for laminated composite, functionally graded material as long as the equivalent material parameters are obtained.