Research On Structural Dynamics Problems With Uncertain Parameters

The analysis of mechanical behavior of structure under dynamic loads is an indispensable link in the design and construction of large complex structures.Due to the limitation of people’s cognition and the complexity of engineering structure,the structure model is inevitably affected by a variety of uncertain factors,such as random loads-earthquakes and waves,as well as the uncertainty of the structure itself.Considering the research related to structural dynamics with uncertain factors has also become more and more important.In this paper,uncertain quantification of structural dynamics is the main research content,and the uncertain quantification of dynamic response and the uncertain model updating are studied.The main contents are as follows:First of all,a thorough literature survey is conducted on the research topic of this article,the research background and significance are introduced.The sources of uncertainty and the uncertainty quantification methods of structural dynamics systems are reviewed.Secondly,introduces the pseudo excitation method of stationary random vibration and the derivation process of response analytical sensitivity based on the pseudo excitation method.Taking a three-layer shear frame structure as an example,the response sensitivity based on the pseudo excitation method and differential sensitivity under random loads are calculated,and a comparison was made.Third,the modified perturbation method is used to quantify the uncertain response with uncertain parameter structure,and the Taylor second-order expansion is performed based on the response.Without relying on the form of the governing equation,the complicated derivation operation of the random matrix is avoided,and the derivation of response statistical characteristics is given.The calculation results of the modified perturbation method and the Monte Carlo method are compared and verified using a simple model,which shows the accuracy and efficiency of the modified perturbation method calculations,and the response of large complex structures is calculated using this method.Finally,a study on structural stochastic model updating was carried out,considering the influence of uncertainty,based on the structural response power spectrum obtained by the pseudo excitation method,and the structural parameters were identified based on the Bayesian theoretical framework model updating method.Numerical examples show that the proposed uncertain model updating method has a good recognition effect.