Model reduction in nonlinear structures

Model reduction is the method that approximates high order systems by lower order ones in mathematical models. Reduction method is efficient and accurate ways to represent and to simulate the responses of nonlinear structures. The motivation for this work arises in the problem of modeling, analysis, and simulation of very complex structures that may be composed of dozens or hundreds of individual components and that may need the order of millions of degree of freedom to capture necessary geometric detail in a finite element model. The reduction methods (LBR and CMS based reduction) are based on the linear transformation and use the physical coordinates rather than modal coordinates so these reduction methods are easy to apply on the complex nonlinear problems. This dissertation is to study several methods of reduced order modeling for structural systems. The objective of the reduced order methods is to provide a significant reduction in the number of degrees of freedom while retaining essential information from the original model.

For the free vibration the numerical integration are perform on the system having various nonlinearities. The reduced order model accurately represents the responses of the original model and very reliable on strong nonlinear damping and weak to moderate nonlinear static effects. For the forced vibration harmonic excitation the reduced model retains nonlinear characteristics in the frequency-response curve such as jump phenomena, backbone curve, and superharmonic resonance. For the variable frequency excitation, both the reduced and original system have good agreement in amplitude and frequency in the steady-state responses. In the random frequency response, the reduced model is in good agreement with the original model in frequency spectrum analysis even though the time responses of the reduced mode with strong nonlinear effect have deteriorated from the responses of the original model.

Based on the numerical results of the reduction method, it can be summarized that the reduced model captures the system response of the full model with good accuracy and linear based model reduction and a modified CMS reduction method are very promising to use in various nonlinear structural problems.