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A new approach for free vibration analysis of axially functionally graded beams
  • Kumar Singh
Kumar Singh

Corresponding Author:[email protected]

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Abstract

=0.8cmFree vibration of axially functionally graded beams is analyzed. A novel and simple approach is presented to solve natural frequencies of free vibration of beams with arbitrarily axial nonhomogeneity. For various end restraints including simply supported, clamped, and free ends, we transform the governing equation with varying coefficients to Fredholm integral equations. The natural frequencies can be determined by requiring that the resulting Fredholm integral equation has a nontrivial solution. Our method has fast convergence and obtained numerical results have high accuracy. The effectiveness of the method is confirmed by comparing our numerical results with the exact ones available for homogeneous and nonhomogeneous cantilever beams with certain specified polynomial gradients. Moreover, the fundamental frequencies of a graded beam combined of aluminum and zirconia as two constituent phases under typical end supports are evaluated for axially varying material properties. The present results are of benefit to optimum design of nonhomogeneous beam structures.

Keywords: Free vibration; Axially graded beams; Nonhomogeneity; Natural frequency.