Nonlinear dynamic buckling of multi-DOF structural dissipative systems under impact loading

The nonlinear dynamic buckling characteristics of multi-degree-of-freedom (MDOF), dissipative systems under impact loading are investigated. A fully plastic impact due to a striking body falling freely from a given height is postulated. The initial velocities of the system immediately after impact are determined analytically by applying the law of impulse momentum. The resulting response is governed by autonomous highly nonlinear ordinary differential equations (O.D.E.) which can be integrated only numerically. Instead, a qualitative analysis based on energy criteria is performed which allows to readily establish approximate dynamic buckling loads, very good for structural design purposes, as well as lower and upper bound dynamic buckling estimates for step loading and impact loading with given initial momentum. The efficiency and reliability of the proposed method is comprehensively demonstrated through numerous examples of two- and three-degree-of-freedom models.