NATURAL FREQUENCY CHANGES OF A CRACKED TIMOSHENKO BEAM BY MODIFIED FOURIER SERIES

A new method is presented in this paper for computing the natural frequencies of a Timoshenko 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 developed particularly for a Timoshenko beam having an arbitrary number of transverse open cracks. Unlike the conventional Fourier series, the modified Fourier series can approach a function with internal geometrical discontinuities. Based on the modified Fourier series, one can treat the cracked Timoshenko beam in the usual way and thus reduces the problem to a simple one. 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 that renders the task of computer coding quite straightforward.