NATURAL FREQUENCIES OF A NON-UNIFORM BEAM WITH MULTIPLE CRACKS VIA MODIFIED FOURIER SERIES

A new method is presented in this paper for computing the natural frequencies of a non-uniform beam with an arbitrary number of transverse open cracks. The essence of this new method lies in the use of a kind of modified Fourier series (MFS) which is specially developed for a beam with transverse open cracks. Unlike conventional Fourier series, modified Fourier series can approach a function with internal geometrical discontinuities. Based on the modified Fourier series, one can treat the cracked beam in the most usual way and thus reduce the problem to a simple one. The beam can be of non-uniform cross section and the number of cracks can be arbitrary. By using the present method, only standard linear eigenvalue equations, rather than non-linear algebraic equations, need to be solved. All the formulae are expressed in matrix form which renders the programming quite straightforward.