Vibration Analysis of Straight FGM Beam with Different Parameters

Abstract

This paper deals with the vibration analysis of Straight functionally Graded Beam (FGM) considering various parameters. It is analysed with different boundary conditions like simply supported, clamped clamped. The FGM beam is analysed for different L/h ratio and different volume fraction index. is analysed with different L/h ratios using higher order shear deformation theory. It was found that for a fixed value of L/h ratio as the volume fraction index is increased the frequency of vibration is reducing. Again, if the value of volume fraction index is kept constant and the L/h ratio is increased the frequency is decreasing. The dependence of support conditions on the frequency response is highlighted. Comparison and convergence study has been performed to validate the present formulation. The result and the analysis of the frequency of vibration can be used to optimize the frequency of a leaf spring treating it as a straight beam to have better ride. Thus, we observe that for both clamped -clamped and simply supported condition, for a fixed value of of L/h ratio as the volume fraction index is increased the frequency of vibration is reducing. Again if the value of volume fraction index is kept constant and the L/h ratio is increased the frequency is decreasing.

Introduction

The spring, particularly the leaf spring, is a critical component in automobiles for absorbing vibrations and providing a comfortable ride, especially in heavy vehicles. Leaf springs offer the advantage of guided deflection along a fixed path, functioning as both a structural member and an energy absorber. Considerable research has focused on reducing leaf spring vibrations to improve ride comfort.

This paper models the master leaf spring as a curved beam and analyzes its vibration behavior across various materials, length-to-radius (L/R) ratios, and boundary conditions.

Several referenced studies contribute to this field:

• Analysis and optimization of composite leaf springs using software like ANSYS.

• Fatigue life assessments and parameter optimization of elliptic springs.

• Vibration studies on straight and curved beams using different theoretical approaches including shear deformation theories and finite element methods.

• Investigation of geometrically nonlinear vibrations, thermo-elastic vibration in functionally graded materials (FGM), and effects of microstructural defects.

• Modal analysis of different materials and beam configurations.

• Studies on nonlinear free vibration, dynamic stability, and eigenvalue problems of Timoshenko and shear deformable beams.

• Research on the influence of initial static loading, nonlinear vibrations, and finite element techniques on curved beams and arches.

The text also presents the mathematical formulation of displacement fields and strain-displacement relations for curved beams, incorporating nonlinearities due to curvature, thickness, and deformation modes. It defines displacement components, strain components, and their relations for a curved beam using higher-order shear deformation theory and considers boundary conditions by varying the curvature radius.

Conclusion

The vibration analysis straight FGM was done under various conditions. MATLAB was used for the analysis. The effect of end condition on the vibration of straight FGM beam was studied for L/ h =5,20,50 and 100. The effect of change in volume fraction index and support condition is also studied. The volume fraction index was taken as 0.5,2,5 and 10.The result was also validated. During the analysis it was found that as the L/h ratio is increased the value of frequency of vibration in both the clamped-clamped condition and simply supported condition decreases. but for clamped-clamped condition the frequency decreases much rapidly compared to simply supported condition. We also tried to observe the effect on frequency on volume fraction index and it was found that it decreases with increase in volume fraction index for both clamped and simply supported condition.

References

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Copyright

Copyright © 2025 Md Rashid Akhtar, Aas Mohammad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.