Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

Abstract

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

Crack identification in multiple cracked beams made of functionally graded material by using stationary wavelet transform of mode shapes

“…Surace and Ruotolo [20] stated that presence of a crack in a cantilever beam can be detected by the wavelet coefficient distribution computed from the time history response measured at free end. Liew and Wang [21] demonstrated that single crack in a simply supported beam can be localized from spatial wavelet transform of free vibration response measured along the beam length at a given time moment. This study was then continued by Wang and Deng [22] for the case of impulse response of beam and plate with different boundary conditions.…”

“…As the FEM is formulated on the base of frequency independent polynomial shape function, it could not be used to capture all necessary high frequencies and mode shapes of interest. An alternative approach called DSM fulfilled the gap of FEM by using frequency-dependent shape functions that are c 2019 Vietnam Academy of Science and Technology found as exact solution of vibration problem in the frequency domain [17][18][19][20][21]. Although exact solutions of the vibration problem are not easily constructed for complete structures, but they, if were available, enable to study exact response of the beam in arbitrary frequency range.…”

Exact receptance function and receptance curvature of a clamped-clamped continuous cracked beam

“…Substituting Eqs. (15) to (20) into Eqs. 7and 8the exact receptance and curvature receptance of the simply supported beam will be obtained.…”

“…Caddemi and Calio [13,14] presented the exact closed-form solution for the mode shapes of the Euler-Bernoulli beam with multiple open cracks. Lien et al [15] presented a mode shape analysis of multiple cracked functionally graded beamlike structures by using dynamic stiffness method for crack detection purpose. One of authors of this paper applied 3D finite elements to investigate the change in mode shapes at the crack positions [16].…”

Xác định vị trí vết nứt trong dầm fgm bằng phân tích wavelet dừng các dạng dao động riêng

“…Do đó, vấn đề xác định vết nứt trong kết cấu FGM là thực sự cần thiết và đã thu hút sự chú ý của nhiều nhà nghiên cứu trong và ngoài nước. Hầu hết các nghiên cứu hiện nay về xác định vị trí vết nứt trong kết cấu đều sử dụng phương pháp thí nghiệm không phá hủy dựa trên các đặc trưng động lực như là tần số, dạng dao động riêng, hàm phản ứng tần số,... Các đặc trưng động lực học của dầm FGM có vết nứt được xác định bằng các phương pháp giải tích [1][2][3][4][5][6], phương pháp bán giải tích Galerkin [7], phương pháp phần tử hữu hạn (FEM) [8][9][10], và phương pháp độ cứng động lực (DSM) [11][12][13][14].…”