Structural Damage Identification Method Using Modal Approximate Sensitivity

In recent decades,the method of structural damage identification by using the change of structural vibration modal parameters has attracted wide attention in the engineering field.On the one hand,due to the limitation of test conditions and cost,it is often only possible to measure the low-order modal parameters of structural vibration,but it is difficult to obtain the high-order modal parameters of structural vibration in engineering practice.On the other hand,it is a difficult task to calculate high-order modes by finite element model for large structures due to the large number of degrees of freedom.Therefore,it is a very meaningful work to study the method of structural damage identification only using the low-order mode of structural vibration and avoiding the high-order mode in the calculation process to improve the calculation efficiency.In view of this,this paper mainly studies the method of structural damage identification based on the sensitivity analysis of low-order modes(fundamental frequency or the first two modes).In the calculation,approximate sensitivity is used to avoid high-order modes.The unified formula of approximate sensitivity of modal flexibility is derived,and the influence of approximate sensitivity on the calculation results of damage identification is discussed in detail.The main research contents include:This paper makes a detailed comparative study on the existing approximate calculation methods of mode sensitivity.Taking a truss structure as an example,the calculation results of three approximate calculation methods of mode sensitivity,namely,truncated mode method,iterative mode method and Neumann series expansion method,are compared in detail.The advantages of Neumann series expansion method in the calculation of approximate mode sensitivity are illustrated.According to the condition that some structures can only obtain the basic frequency mode,the structural damage identification equation based on the approximate sensitivity of the basic frequency mode is derived by using Neumann series expansion method,and the relevant methods of damage identification inversion calculation using only the basic frequency mode are studied.Taking a roof truss model as an example,the feasibility of the proposed method is verified.Based on the calculation formula of approximate sensitivity of mode,the existing flexibility sensitivity method is improved,and the unified calculation formula of approximate sensitivity of mode flexibility is derived.The formula can be used for the calculation of flexibility or approximate sensitivity of generalized flexibility of each order.Based on this,the structural damage identification equation based on approximate sensitivity of mode flexibility is established.Taking a corridor model as an example,it is verified that The validity of the proposed method.Finally,the shortcomings of the proposed method are analyzed and summarized,and the problems that need to be solved in the subsequent research work are explained.