The Dynamic Analysis Of The Nonlinear Beam

With the rapid development of science and technology, the structure becomes more and more light and tender, and it gives the structure design higher requirement.Beam is a kind of important structure element, and the nonlinearity in beam and structure is neglected in traditional design, which will lead to essential error in analysis and design, especially in long-time history dynamical behavior. The serious error in analysis will lead to disaster. The impact of geometric nonlinearity on the beam analysis and design will be considered in this article.The structure should have good static and dynamic characteristics in order to make equipment and products can work safely and reliably. Nonlinear Euler beam dynamic model and the nonlinear Timoshenko beam dynamic model are established in this thesis. By the comparison of dynamic response between linear beam and nonlinear beam, which conclude nonlinear term response has an important influence on the beam. The dynamic characteristics of the nonlinear beam is analyzed emphatically. The stress and strain of the nonlinear beam is solved by using the finite element method. The dynamic analysis is analyzed at the same time, the main research contents and conclusions are as follows:Firstly, geometric nonlinear characteristics of the beam is considered, under the condition of ignoring shear deformation, Euler beam model is established by using Hamilton’s principle of minimum potential energy principle. Under the condition of the influence of beam’s shear deformation. Timoshenko beam model is established.Finally, all system equations are solved and analyzed.Secondly, the nonlinear responses of main resonance, the subharmonic and ultraharmonic vibration of Euler beam beam are solved by the method of multiple scales under the condition of considering geometric nonlinear characteristics of the beam. Compared with the results of linear, resonance response amplitude system is larger.Thirdly, the stability and bifurcation behavior of beam is discussed under theparametric excitation, the stability condition of nonlinear beam is analyzed. The dynamics equations of Euler beam are obtained, the conditions that satisfying parameter exciting is solved, at the same time, response characteristics of the nonlinear beam under the action of parametric excitation are analyzed..Finally, based on the Hamilton energy principle of the TL formation, the effect of geometric nonlinear is considered, the nonlinear model of beam is established by using finite element method. At the same time, by means of Newmark-β, response and stress maximum of the dynamic beam is concluded.