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Transient analysis of transversely functionally graded Timoshenko beam (TFGTB) in conjunction with finite element method

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Khafaji S. O. W. , Al-Shujairi M. A. , Aubad M. J.

Archive of Mechanical Engineering

2020

tom LXVII, nr 3

299--321

In this work, transient and free vibration analyses are illustrated for a functionally graded Timoshenko beam (FGM) using finite element method. The governing equilibrium equations and boundary conditions (B-Cs) are derived according to the principle of Hamilton. The materials constituents of the FG beam that vary smoothly along the thickness of the beam (along beam thickness) are evaluated using the rule of mixture method. Power law index, slenderness ratio, modulus of elasticity ratio, and boundary conditions effect of the cantilever and simply supported beams on the dynamic response of the beam are studied. Moreover, the influence of mass distribution and continuous stiffness of the FGM beam are deeply investigated. Comparisons between the current free vibration results (fundamental frequency) and other available studies are performed to check the formulation of the current mathematical model. Good results have been obtained. A significant effect is noticed in the transient response of both simply supported and cantilever beams at the smaller values of the power index and the modulus elasticity ratio.

Analyzing frequency response analysis experimentally for bone healing detection: examining the potential of vibrational evaluations

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Kadhim A. J. , Aubad M. J. , Al-Juboori A. M.

Diagnostyka

2024

tom Vol. 25, No. 3

art. no. 2024315

Assessment of bone healing is essential for efficient orthopedic treatment. This work investigates the feasibility of assessing frequency response experimentally for bone healing detection, with a particular emphasis on the use of vibrational assessments. Detailed experimental studies were carried out to determine the ability of frequency response analysis to assess bone healing. Mechanical excitation was delivered to cracked bone samples at various frequencies, and the vibrational responses of the displacement and accelerations were measured. The experimental setting includes testing five samples, to cover a wide range of possibilities. The obtained vibrational, such phase, magnitude, and coherence, were examined to find common patterns and changes linked with the healing process. The results showed that frequency response analysis has the potential to identify bone healing, as unique vibrational responses were seen in healed samples under cyclic load for different turns (0, 1000, 2000, 3000, and 4000). The findings demonstrate the sensitivity of vibrational evaluations in capturing the mechanical properties and healing condition of bone tissue. Furthermore, the presence of cracks impacts both structural integrity and natural frequency. Natural frequency decreases as the number of cycles increases. The highest frequency reduction occurred at the first mode shape and maximum cycle number, indicating considerable fracture behaviour changes. Natural frequency can be used to assess bone health; higher stiffness and frequency are associated with smaller crack size.