Nonlinear free vibration of stiffened plate with four edges clamped

One approach is presented to study the nonlinear freevibration characteristic of stiffened plates. The stiffened plate is dividedinto plate and stiffeners. The plate is considered to be geometricallynonlinear, and the stiffeners are taken as Euler beams. Assuming thedisplacement of the stiffened plate, Lagrange equation and modalsuperposition method are used to derive the dynamic equilibrium equations ofthe stiffened plate according to energy of the system. The single-moderesults are obtained through Elliptic function and the perturbation method,and the multimode results are obtained through incremental-iterativemethods. At last, a stiffened plate with four immovable clamped edges isstudied through both the present approach and FE software ANSYS. Theconvergence of solution is analyzed, and the relationship between nonlinearnatural frequency and its amplitude is discussed when the number ofstiffeners in the two direction is different. Some nonlinear vibrationcharacteristics of stiffened plate are obtained, which can providereferences for engineering design.