Natural Frequencies of Beams with Axial Material Gradation Resting on Two Parameter Elastic Foundation
DOI:
https://doi.org/10.48048/tis.2022.3048Keywords:
Axially functionally graded beam, Timoshenko beam, Free vibration, Elastic foundation, Energy methodAbstract
Free vibration analysis is carried out on axially inhomogeneous beams resting on Winkler-Pasternak elastic foundation. The material properties of the beam like Young’s modulus, modulus of rigidity and material density are considered to be varying along the length direction following constant, linear and exponential material models. The beam is subjected to different combinations of clamped and simply supported boundary conditions. The formulation is based on Timoshenko beam theory and energy method along with Hamilton’s principle is used to derive the governing equations. The effect of material gradation and the 2 parameters of elastic foundation on the natural frequencies are studied in detail. The present results are validated by comparing them with established ones and satisfactory matching is observed.
HIGHLIGHTS
- Free vibration behavior of axially functionally graded beams in investigated
- Three different material models and three boundary conditions are considered
- Effect of two parameter elastic foundation is considered
- Timoshenko beam theory and Rayleigh Ritz method are employed
- It is found that the stiffness of elastic foundation significantly affects the natural frequency of the beam
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