Study On The Uncertainty Problem In Nonlinear Vibration Analysis Of Lamination

In order to isolate or reduce the vibration of the product/component, as well as for conveniently assembling and disassembling, pre-tightening contacted cushion structures are usually applied in engineering. In some special condition. the destabilizing phenomena such as rotational slip between layers or separation of contact surface, may take place in these structures. In respect that the slip mechanisms are not comprehensive understand, and the nonlinear factors are complex in the structures. systematically experimental researches are difficult to carry out. Therefore, it is significant in engineering for the stopping rotation design and experimental study to investigate the dynamic behavior and the slip mechanisms of these structures. In addition, there are also plenty of uncertainty problem during the dynamic response analysis. Though the uncertainty often impact the response just a little influence in most cases, the cumulative effect of it may have great or unpredictable influence on the response. Therefore, study on description and transmission of the uncertainty with quantitative method, instead of increasing the safety coefficient, finer result and more reasonable structure design based on it will be obtained.In the first part of this thesis, based on the sample data, the methodology for interval-bound estimation is improved with small samples and lacking information in engineering, which provides theoretical basis for the quantitative study on the propagation of uncertainty afterwards. With huge samples, the present method of interval-bound estimation is much accurate and reliable. However, epistemic uncertainty may be generated with small samples, which will decrease the accuracy and reliability of the estimation results. Employing two-stage estimation method, the present interval-bound estimation method is improved. Moreover, the improved method is verified by numerical experiments.In the second part of this thesis, the pre-tightening contacted cushion structures are divided into two subsystems, i.e., the non-slip subsystem and the rotational slip subsystem. Furthermore, its dynamics responses are studied by deterministic method. The pre-tightening contacted cushion is simplified as a center-circle-plane structure. With considering the relatively rotary vibration and rotary slip DOFs, the criterion for slip is defined as the total momentum to overcome the friction between layers under the description of eccentric factor and simple harmonic motivation. The dimensionless governing equations for vibration are constructed based on the Hamilton’s principle. The equations are solved through numerical methods to obtain the dynamic responses of these two subsystems, which acquires comprehensive understanding of the slip mechanism.In the third part of this thesis, the influences of parametric and initial-value uncertainties on system responding are analyzed based on the deterministic analysis. Moreover, the transmission of the uncertainty is quantitatively solved by interval analysis. During the analysis of the uncertainty in engineering application, in combination of the improved method in the first part of this thesis, the influences of the parametric and initial-value uncertainties on the response and slip of the system are obtained with small samples. In general, the work of this part provides comprehensive understanding of the slip mechanism, and it is helpful for the robust decision of slip-forbade design to the eccentric pre-tightened cushion structure.