Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science - Tập 238 Số 8 - Trang 3373-3390 - 2024
Trần Văn Liên1, Tran Binh Dinh1, Thang Nguyen1
1Hanoi University of Civil Engineering, Hanoi, Vietnam

Tóm tắt

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams with arbitrary boundary conditions based on the Nonlocal Elasticity Theory (NET) and the Timoshenko beam theory are presented. The NET considering the size effect of nanostructures is applied. FGM properties vary nonlinearly along the height of the beam. A crack model using two springs with stiffness depending on the crack depth is applied. The proposed solutions are provided explicitly as functions of integration constants determined from the standard boundary conditions. Frequency equations, that established in the form of the determinant of the matrix 3 × 3 order for arbitrary boundary conditions, are applied to analyse free vibration. Expressions for the mode shapes are given explicitly. The effects of geometry, material, nonlocal and crack parameters on the free vibration of the multiple cracked nanobeam are then analysed in detail.

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Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Tập 238 Số 8

3373-3390

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