Alternative Admissible Functions for Natural Frequencies and Modeshapes of a Beam with Lumped Attachments

In this paper, the use of a combination of trigonometric and low order polynomials as admissible functions to be used with the method of assumed modes is investigated for the calculation of the natural frequencies and modeshapes of a beam with lumped attachments. Since the admissible functions do not satisfy the boundary conditions, penalty terms are used to replace the constraints of the boundary conditions of the beam, with virtual stiffness elements of appropriate values representing the boundary conditions. By comparison with previously obtained results, the proposed method using the assumed modes approach with admissible functions and penalty terms is evaluated for accuracy and computational effectiveness. It is shown that the proposed method is accurate and shows no ill-conditioning for the problem of an Euler-Bernoulli beam with lumped attached elements.