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Free Vibration Analysis of Functionally Graded Timoshenko Beams with Variable Section
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    Abstract:

    Based on the concept of physical neutral surface, the governing differential equations of free vibration of an axial-loaded functionally graded material (FGM) beam with the material properties varying along the beam height are derived by using Hamilton principle, and then the power series solutions of the differential equations are obtained. Then, the frequency equation is obtained based on the general boundary conditions expressed by elastic constraints. The effects of the parameters such as the length-height ratio, the gradient index, the axial force, and the section variation coefficient on the natural vibration characteristics of functionally graded beams are analyzed. The results show that the shear deformation affects not only the flexural vibration but also the axial vibration.

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  • Received:
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  • Online: May 31,2021
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