Modal Analysis Using Implicit Boundary Finite Element Methods

Modal analysis is widely used for linear dynamic analysis of structures. The finite element method is used to numerically compute stiffness and mass matrices and the corresponding eigenvalue problem is solved to determine the natural frequencies and mode shapes of vibration. Implicit boundary method was developed to use equations of the boundary to apply boundary conditions and loads so that a background mesh can be used for analysis. A background mesh is easier to generate because the elements do not have to conform to the given geometry and therefore uniform regular shaped elements can be used. In this paper, we show that this approach is suitable for modal analysis and modal superposition techniques as well. Furthermore, the implicit boundary method also allows higher order elements that use B-spline approximations. Several test examples are studied for verification.