Natural Frequencies Modification Of Structures With Spillover Suppression

Structural dynamic modification(SDM)is an effective method of solving vibration problem in engineering applications,including removing inherent frequency from frequency of excitation,changing node positions on the mode of vibration and to reduce amplitude of vibration.For past several decades,research of SDM has achieved many results.This paper gives a new research technique for natural frequencies modification.The structural dynamic characteristics,which usually refer to its modal properties-natural frequencies and mode shapes,are determined by its mass,stiffness and damping distributions.Structural dynamic modification is a procedure aimed at identifying the changes required in a structural system to modify its dynamic characteristics,in other words,the mass and stiffness matrices are modified to obtain a desired frequencies and mode shapes.Two different problems are usually considered for SDM-the direct problem and the inverse problem.The direct problem is the forward problem for the prediction of the new modal properties of a dynamic system subjected to structural modification.The inverse problem deals with the determination of the most appropriate modifying project and value to obtain the desired dynamic behaviors in the framework of a given set of possible modifications.Considering the inverse problem of structural dynamic modification,a method for updating mass and stiffness matrices without spillover is discussed through changing of physical parameter in an undamped structure,which is also called as “no spill-over” property in changing of nature frequency.The work details in this paper includes: 1.A necessary and sufficient condition for(35)M and(35)K to jointly satisfy to prevent spill-over is presented;2.Introducing a factor of spill-over restrain into the objective function,a discussion has been taken comparing numerical results between before introducing and after.Numerical examples show that,using the presented updating method,the updated model achieves the result that modifying some eigenpairs accurately with dropping the changing maximum of other eigenpairs from 1.32% to 0.06%.