SOME CHARACTERISTICS OF FREQUENCY-DEPENDENT STRUCTURAL MATRICES

The traditional finite element method applied to dynamic problems employs shape functions which are based on a static displacement assumption. The more exact approach uses frequency-dependent shape functions and frequency-dependent mass and stiffness matrices. These matrices are usually constructed as a series expansion in powers of the frequency of vibration. A formula is presented which relates the higher ordered terms in the mass matrix expansion to those in the stiffness matrix expansion. An additional result gives expressions for the mass and stiffness matrices in terms of the values of the shape function at the boundary of the element. The results presented hold for models based on shape functions derived as solutions to differential equations which are the Euler equations for the particular variational principle used to define the mass and stiffness matrices. © 1990.