Theoretical Study Of Structural Damping Ratio Identification Based On Improved Half-power Bandwidth Method

With the development of structural health monitoring technology,the comprehensiveness and accuracy of modal parameter identification are becoming more and more important.As one of structural modal parameters(frequency,mode shape,damping ratio),the accuracy of parameter identification is often limited.Considering that the half-power bandwidth method is widely used in the field of damping ratio identification and easy to calculate,but the identification accuracy is difficult to achieve the desired results,this paper studies the shortcomings of half-power bandwidth in damping ratio identification.(1)This paper summarizes the mechanism of damping generation in structures and the existing numerical models of damping,and confirms that the existing mature theories choose the viscous damping model.The advantages and disadvantages of damping ratio identification methods in viscous damping model are summarized.(2)In this paper,the theoretical derivation error of the classical half-power bandwidth method is analyzed,and the identification error of the half-power bandwidth method under the influence of excitation and noise in the single-degree-of-freedom system is analyzed.The results show that the half-power bandwidth method is suitable for the data of small damping structures and low noise pollution.Unless the excitation is an impulse,the half-power bandwidth method requires the excitation and response to be known and the damping ratio to be solved by the frequency response function.(3)In view of the theoretical error caused by the application of half-power bandwidth in the multi-degree-of-freedom system,a two-degree-of-freedom system is selected in this paper.The results show that the half-power bandwidth method has an irreducible error when solving the damping ratio of the two-degree-of-freedom system,especially for the identification results of the first modal damping ratio.For the identification error of the second order modal damping ratio,it decreases with the increase of the modal frequency ratio.However,the frequency ratio needs to be greater than 10 in order to obtain sufficient accuracy(the error is less than 1%),but it is difficult to have such a structure in practice.(4)In this paper,an approximate form considering the modal coupling is given by analyzing the influencing factors of the modal coupling between two free systems.By approximating the influencing factors of the modal coupling,the formula for the estimation error of the damping ratio of each order mode when the classical half-power bandwidth method is applied to the two-degree-of-freedom system is derived.Based on the error influence formula,this paper presents a formula for solving the damping ratio of the two-order half-power bandwidth method,which can achieve satisfactory accuracy in solving the damping ratio of the two-degree-of-freedom system,and greatly improves the identification error of the damping ratio of the classical half-power bandwidth method in the two-degree-of-freedom system.(5)In order to satisfy the requirement that the actual engineering structures belong to the multi-degree-of-freedom system,the proposed two-order half-power bandwidth method is extended in this paper,so that it can be applied to the solution of the damping ratio of multi-degree-of-freedom system.Through the damping ratio identification results of the5-DOF example model,it can be seen that the multi-order half-power bandwidth method developed from the two-order half-power bandwidth method in this paper has a very high accuracy in the damping ratio identification of the multi-DOF system compared with the classical half-power bandwidth method.The multi-order half-power bandwidth method can be used to identify the damping ratio for the multi-degree of freedom system.