| As one of the most basic components in engineer, the study of beam's nonlinear vibration has an important theoretical significance and engineering practical value. Researches on beams dynamics have provided a reference for the research on structures such as panel and other complex structures. Meanwhile, as considered similar to the curing model of pipeline, the results of beams'research have certain significance for plumbing problems. In recent years, in addition to isotropic materials, the properties of a beam material in engineering are diversiform. Currently, most common studies are focused on the nonlinear dynamic behaviors of homogeneous beam, while the nonlinear dynamics of composite laminated structures are merely studied. In this dissertation, the nonlinear dynamics of a homogeneous simply supported slender beam is taken into consideration, which, is subjected to harmonic base excitation. Based on the homogeneous beams, the nonlinear dynamics of composite laminated beam is also studied. The main contents of this dissertation are given as below:Firstly, based on the multiple scales method, the primary resonance of the beam is analyzed, using modal superposition method and asymptotic expansion method, with the homogeneous simply supported slender beam as research object, which is subjected to transverse harmonic base excitation. The first-order and second-order approximation solutions of the nonlinear dynamic equation are obtained, and the differences between these two methods are compared. Based on the comparison, conclusion has been made that the asymptotic expansion method has significant advantages of reasonable expression and clearer calculation process.Secondly, the super-harmonic resonance and sub-harmonic resonance of the homogeneous simply supported slender beams are analyzed by using asymptotic expansion method. The result shows that the system will produce super-harmonic resonance on the third mode when it produces sub-harmonic resonance on the first mode. The first-order approximate solution of the steady-state responses is calculated, and the amplitude-frequency response curves of the system are obtained. Finally, according to Von-Karman type equations for geometric nonlinearity and Reddy's high-order shear deformation theory, the nonlinear governing partial differential equations of the motion are derived by using the Hamilton's principle, which are suitable for composite laminated beam subjected to the transverse excitations. The nonlinear dynamics behavior of the composite laminated beam subjected to transverse harmonic excitations is also analyzed in this dissertation. |
