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Frequency analysis of cracked functionally graded cantilever beam

In this paper, a functionally graded cantilever beam with an open crack is investigated on the base of Timoshenko beam theory; power law of functionally graded material (FGM) and taking into account actual position of neutral axis instead of the central one. The open and edge crack is modeled by coupled translational and rotational springs stiffness of which is calculated by the formulas conducted accordingly to fracture mechanics. | Journal of Science and Technology 55 (2) (2017) 229-243 DOI: 10.15625/0866-708X/55/2/8292 FREQUENCY ANALYSIS OF CRACKED FUNCTIONALLY GRADED CANTILEVER BEAM Nguyen Ngoc Huyen1, Nguyen Tien Khiem2, * 1 2 ThuyLoi University, 175 Tay Son, Dong Da, Hanoi Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi * Email: ntkhiem@imech.ac.vn; khiemvch@gmail.com Received: 3 May 2016; Accepted for publication: 1 November 2016 ABSTRACT In this paper, a functionally graded cantilever beam with an open crack is investigated on the base of Timoshenko beam theory; power law of functionally graded material (FGM) and taking into account actual position of neutral axis instead of the central one. The open and edge crack is modeled by coupled translational and rotational springs stiffness of which is calculated by the formulas conducted accordingly to fracture mechanics. Using the frequency equation obtained in the framework of the theory natural frequencies of the beam are examined along the crack parameters and material properties. This analysis demonstrates that sensitivity of natural frequencies of FGM beam to crack is strongly dependent on the material constants of FGM. Keywords: FGM, Timoshenko beam; cracked beam, modal analysis; 1. INTRODUCTION Due to advantage properties compared to the laminate composites the functionally graded material (FGM) has been intensively studied recently and got wide application in the high-tech industries. An overview of the problems for manufacturing, modelling and testing FGM was given in [1]. Numerous methods such as the Finite Element Method (FEM) [2]; Spectral Element Method (SEM) [3]; Dynamic Stiffness Method (DSM) [4] or Rayleigh-Ritz method [5] have been developed for analysis of structures made of FGM. Nevertheless, the analytical methods are still the most accurate and efficient for dynamic analysis of functionally graded beam-like structures [6-9]. While the most of the aforementioned studies .