Sensitivity analysis and modification of structural dynamic characteristics using second order approximation

This paper presents a formulation in the form of an inverse eigen value problem for modification of vibration behavior of structures. The proposed method which is based on the second order approximation in Taylor expansion is expressed in terms of variables relating to stiffness or mass matrix parameters in a finite element formulation. An initial sensitivity analysis identifies the regions within the structure where the modifications would yield the required changes in the structures dynamic characteristics. An algorithm is developed which allows efficient modification of structural dynamics characteristics without iterations. These modifications are conducted locally so that only elemental stiffness and matrices are affected. The algorithm is applied to four case studies and it is found that large modification of natural frequencies of up to 10% can be realized with an induced error of less than 5% for truss structures, and less than 3% for plane problems.