Modal analysis of a non-rotating cantilever beam using finite element method

In this paper finite element method is used to carry out structural dynamic analysis of non-rotating modes of a Cantilever beam. Strain and kinetic energy expressions are derived step by step. Finite element model of the non-rotating cantilever beam is formulated and then analyzed to produce modal response model of the beam. The 2-D beam or beam element is developed with the aid of the first theorem of Castigliano. The use of Castigliano's first theorem is for the distinct purpose of introducing the concept of minimum potential energy without resort to the higher mathematic principles of the calculus of variations. The displacement function is discretized to obtain the stiffness matrix and mass matrix for a beam element. The mass matrix, stiffness matrix and force vector are combine to obtain the finite element equations of motion for a beam element. The beam is divided into ten beam element and the summation of the mass matrix and stiffness matrix of each beam element gives the assembled mass matrix and stiffness matrix. Modal analysis of the beam element is carried out to obtain the natural frequencies and mode shapes of the beam element. The results of the finite element model of the non-rotating cantilever beam are validated with the results of NISA 11 packet program.