Research Of Structural Dynamic Modification Method Based On Frequency Response Functions

Structural dynamics modification technology is an economical and effective means to improve and enhance the dynamic characteristics of mechanical structures.It is widely used in aerospace,marine and automotive,civil bridges,weapons industry,machinery and other industries.The problems involved in structural dynamic modification can be divided into two categories: "forward problems" and "inverse problems".The former mainly evaluate the changes of dynamic characteristics(such as natural frequency and mode,etc.)of the structure due to the partial modification of original structure,which can be described as a reanalysis problem.The latter mainly studies how to modify an existing structure in order to achieve the expected dynamic characteristics.Analysis of structural dynamics modification problem can be mainly based on three kinds of models: The first is space state model composed of mass matrix,stiffness matrix and damping matrix.The second is modal model,which is composed of modal frequencies and modal vectors.The third is frequency response functions(FRFs)model,which is composed of the frequency response function of the vibrating system.Based on FRFs model,this paper has studied the “forward problem” and “inverse problem” of related structural dynamic modification,discussed the sensitivity of dynamic characteristics to structural parameters as well.The main contents are as follows:(1)Aiming at the “forward problem” of structural dynamics modification,a reanalysis method based on FRFs is proposed.This method is based on ShermanMorrison-Woodbury formula to establish the relationship between the FRFs of original structure,modifying parameters and the FRFs of modified structural,three sets of numerical examples have verified the feasibility of this method.This method can be applied to multi-point and complex modification means(such as adding mass,stiffness,damping and spring-mass substructures simultaneously).(2)Aiming at the “inverse problem” of structural dynamics modification,a method of shifting natural frequency based on FRFs is proposed.This method is based on the established relationship between FRFs of modified structure and FRFs of original structure,using the characteristic that amplitude is at the maximum at the natural frequency to calculate the size of modify parameter.In the numerical experiment,comparing with the internationally well-known modified method,and the results verified the effectiveness and superiority of this method.This method is suitable for the situation where the number of target natural frequencies does not exceed the number of modifying parameter variables,and an analytical solution in the mathematical sense can be obtained.(3)Aiming at the “inverse problem” of structural dynamics modification,a method for assignment of natural frequencies and mode shapes based on FRFs is proposed.This method takes the desired natural frequencies and mode shapes as the target,and takes the physical property range of the modified variable as the constraint condition to establish an optimization model.Genetic algorithm is used to solve this model to obtain the optimal modification amount.The advantage of this method is that different modification means can be selected according to actual engineering conditions,and multiple sets of target frequencies and mode shapes can be assigned simultaneously.(4)In order to determine the suitable modification means,the sensitivity of dynamic characteristics to structural parameters is studied.This chapter analyzes the first-order and second-order sensitivity formulas of each natural frequency to structural parameters(mass of stiffness)based on modal model,and numerical examples are used to verified.The sensitivity analysis results can provide a certain basis for the selection of the modification means in the modification method of the structural dynamics “inverse problem” proposed above.