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Title |
Vibration Analysis of Multi Cracked Nonuniform Nanobeam by using Differential Transformation Method
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Authors |
신영재(Young-Jae Shin) ; 박성현(Sung-Hyun Park) ; 김진홍(Jin-Hong Kim) ; 유영찬(Yeong-Chan Yoo) |
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DOI |
http://dx.doi.org/10.11112/jksmi.2016.20.5.093 |
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Keywords |
Differential transformation method ; Nonlocal elasticity theory ; Nonlocal effect ; Vibration analysis ; Nanobeam |
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Abstract |
In this study, the governing equations of motion for multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium were derived. DTM(differential transformation method) was applied to vibration analysis of multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium. The non-dimensional natural frequencies of this nanobeam were obtained for eoe, crack stiffness and elastic medium stiffness with various boundary conditions. The results obtained by this method was compared with previous works and showed the close agreement between two methods. The important conclusions obtained by this study are as follows : 1. As the length of nanobeam is shorter, the effect of scale coefficient is greater. 2. The locations of crack change non-dimensional natural frequency, In the case of fixed-fixed ends, the non-dimensional natural frequency is the biggest in the first crack location of 0.6L of nanobeam length, and the smallest in both ends. In the case of fixed-free ends, the closer the location of first crack go tho the free end, the bigger the non-dimensional natural frequency. 3. As the stiffness of crack is greater, the non-dimensional natural frequency is smaller, And the effect of crack stiffness is similar on both fixed-free ends and fixed-fixed ends. 4. The bigger the stiffness of elastic medium, the greater the non - dimensional natural frequency.
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