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

✍ Scribed by D.Y. ZHENG; S.C. FAN

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 345 KB
• Volume: 242
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3360

✦ Synopsis

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 modi"ed Fourier series (MFS) which is specially developed for a beam with transverse open cracks. Unlike conventional Fourier series, modi"ed Fourier series can approach a function with internal geometrical discontinuities. Based on the modi"ed 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.