| The circular arches were used extensively in many fields, such as mechanical engineering, vehicle engineering, air craft.etc. In practical engineering applications, the presence of the cracks easily lead to accidents and accident cost,even Heavy Casualties. So, it is of great significance to analysis free vibration of damaged circular arches, and provide a method combined the qualitative analysis and the quantitative analysis for the cracks of circular arches. The present paper proposes a novel method based on dynamic stiffness method, to addresses the evaluation of the planar natural frequencies of Timoshenko circular arches with multiple cracks. The dynamic stiffness matrices of the arch with multiple cracks, order 6, is derived in a recursive manner, according to the number of cracks. This method is used to compute the natural frequencies of damaged circular arches, to any desired accuracy.1、Study on free vibration of circular arches in plane and out-of- plane. The governing equations of motion of circular arches are given. The dynamic stiffness matrices, order 6, is derived. The Wittrick-Williams algorithm is used to compute the natural frequencies and modal, to any desired accuracy. There are some analysis of influence of material and shape of circular arches on the natural frequencies and modal.2、Study on free vibration of damaged circular arches in plane. The governing equations of motion of damaged circular arches are given. The dynamic stiffness matrices of the arch with multiple cracks, order 6, is derived in a recursive manner, according to the number of cracks. A variation of the Wittrick-Williams algorithm is used to compute the natural frequencies, to any desired accuracy. There are some analysis of influence of boundary conditions, crack strength, crack position, the number of crack on the natural frequencies and modal.3、Study on crack identification, based on the change of the natural frequencies and modal. The natural frequencies and modal are compared, in different condition. Feasible analysis of rack identification based on the change of the natural frequencies and modal, also is introduced. A method of rack identification based on the differences of curvature modal and the differences of modal, is presented.4、The results of modal tests verify the correctness of the analysis results of free vibration of damaged circular arches in plane, and the method of rack identification based on the differences of curvature modal and the differences of modal, is presented.Finally, the algorithm presented in this paper is written by MATLAB. Some examples are applied to verify the results of these algorithm. |
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