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

✍ Scribed by D.Y. ZHENG; S.C. FAN

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 434 KB
• Volume: 246
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.3632

✦ Synopsis

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 modi"ed 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 modi"ed Fourier series can approach a function with internal geometrical discontinuities. Based on the modi"ed 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.