Modal Approach for Forced Vibration of Beams with a Breathing Crack
(0) This paper presents a method for the vibration of a beam with a breathing crack under harmonic excitation.The infinitely thin crack is characterised by a parameter αc that takes into account the shape and the depth of the crack.The closed-and open-crack states are both modelled by a modal approach: two sets of equations of motion cast in the modal coordinates of their individual mode shapes.The state change (from closed to open or vice versa) involves the calculation of the modal coordinates associated with the new state from the modal coordinates of the previous state.By imposing the continuity of displacement and velocity the beam at the instant of the state change,the matrix that transforms the modal coordinates from one state to the other is determined and proved to be the Modal Scale Factor matrix.This analytical approach takes advantage of exact nature and mathematical convenience of beam modes and is time-efficient.Forced vibration at various values of crack parameter αc is determined.It is found that as αc decreases (crack length increases) the vibration becomes increasingly erratic and finally chaotic.
cracked beam breathing crack vibration modal approach modal scale phase portrait
Luis Baeza Huajiang Ouyang
Dpto.de Ingenieria Mecanica,Universidad Politecnica de Valencia,Valencia,Spain Department of Engineering,University of Liverpool,Liverpool L69 3GH,U.K.
国际会议
The 8th International Conference on Damage Assessment of Structures(DAMAS 2009)(第八届结构损伤评价国际学术会议)
北京
英文
39-46
2009-08-03（万方平台首次上网日期，不代表论文的发表时间）