Abstract：One approach is presented to investigate the nonlinear free vibration characteristic of a stiffened plate. The stiffened plate is divided into a plate and stiffeners. The plate is considered to be geometrically nonlinear, and the stiffeners are taken as Euler beams. The strain and kinetic energy equations of both the plate and stiffeners are formulated, which are expressed by tensors. Substituting the strain and kinetic energy equations into Lagrange equation, a series of nonlinear differential equations with respect to in-plane and out-plane generalized coordinates are obtained. The multimode solution can be obtained by incremental-iterative method. The exact single-mode solution can be given in terms of the elliptic function. At last, a stiffened plate with four immovable simply supported edges is studied. Selecting the first four modes, the relationship between nonlinear natural frequency and its amplitude is discussed with the number of stiffeners in the two directions varying. Besides, the internal resonance is studied. Some nonlinear vibration characteristics of the stiffened plate are obtained, which are useful for engineering design.
马牛静;王荣辉;李平杰. 四边简支加劲板的几何非线性自由振动及内共振[J]. , 2012, 31(24): 60-64.
MA Niujing;WANG Ronghui;LI Pingjie. Geometrically nonlinear free vibration and internal resonance of a stiffened plate with four edges simply supported. , 2012, 31(24): 60-64.
2012, Vol. 31 
