Frequency Response of a Combined Structure Using a Modified Finite Element Method

A modified finite element method is proposed to analyze the frequency response of an arbitrarily supported linear structure carrying various lumped attachments. This is accomplished by updating the finite element mass and stiffness matrices of the linear structure without any lumped attachments using its exact natural frequencies and mode shapes, so that the eigensolutions of the updated linear structure coincide with the exact eigendata. Once the updated matrices for the linear structure are found, the finite element assembling technique is then exploited to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices. After assembling the global mass and stiffness matrices, the frequency response of the combined system can be easily obtained. Numerical experiments show that, using only a few finite elements, the proposed scheme returns natural frequencies and frequency responses that are nearly identical to those obtained by using a finite element model with a very fine mesh. The new method is easy to apply and efficient to use, and it can be extended to determine the frequency response of any combined linear structure over any specified range of excitation frequencies.