ABSTRACT
The accuracy obtainable from the finite element method depends on being able to duplicate the vibration mode shapes. Using only one finite element between structural joints or corners gives good results for the first lowest mode because the static deflection curve is a good approximation to the lowest dynamic mode shape. For higher modes, several elements are necessary between structural joints. This chapter introduces the basic ideas of the finite element method and also discusses the development of the corresponding mass matrix to complete the equations of motion for the dynamic problem. In determining the stiffness matrix of the entire structure in terms of local elements, it is necessary first to match the displacements of the adjacent elements to ensure compatibility. When the generalized force is proportional to the displacement, it can be transferred to the left side of the equation of motion to combine with the stiffness matrix for the free vibration.
