FREE VIBRATION ANALYSIS OF NON-UNIFORM BEAMS WITH AN ARBITRARY NUMBER OF CRACKS AND CONCENTRATED MASSES

✍ Scribed by Q.S. LI

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 222 KB
• Volume: 252
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.4034

✦ Synopsis

An exact approach for free vibration analysis of a non-uniform beam with an arbitrary number of cracks and concentrated masses is proposed. A model of massless rotational spring is adopted to describe the local #exibility induced by cracks in the beam. Using the fundamental solutions and recurrence formulas developed in this paper, the mode shape function of vibration of a non-uniform beam with an arbitrary number of cracks and concentrated masses can be easily determined. The main advantage of the proposed method is that the eigenvalue equation of a non-uniform beam with any kind of two end supports, any "nite number of cracks and concentrated masses can be conveniently determined from a second order determinant. As a consequence, the decrease in the determinant order as compared with previously developed procedures leads to signi"cant savings in the computational e!ort and cost associated with dynamic analysis of non-uniform beams with cracks. Numerical examples are given to illustrate the proposed method and to study the e!ect of cracks on the natural frequencies and mode shapes of cracked beams.