A Detailed Study of the Effect of Radii Ratio and Aspect Ratio of a Uniform Circular Annular Plate under Free and Forced Vibration in Thermal Environment

Abstract

This paper deals with the free and forced vibration of annular circular plate under thermal environment using finite element analysis (FEA). The temperature is kept constant. The effect of Eigen frequency on radii ratio and aspect ratio is investigated for different annular circular plate under thermal environment. The free-free and clamped-free boundary condition is taken to analysis theses plates. The parametric studies are conducted and the results are analyzed and marked off.

Introduction

Circular annular plates are widely used in various engineering fields such as aerospace, automotive, naval, and civil structures. Despite significant research on their structural dynamics, vibration characteristics under thermal environments, especially out-of-plane flexural modes, have not been deeply explored.

The study identifies a research gap in understanding the vibroacoustic behavior of uniform circular annular plates, focusing specifically on out-of-plane vibration modes in thermal environments. It aims to evaluate how geometry (radii ratio and aspect ratio) and boundary conditions (free-free vs. clamped-free) affect the natural frequencies of such plates.

2. Methodology

A. Mathematical Modeling

• The governing equation for free vibration includes mass and stiffness matrices.

• A non-dimensional frequency parameter is derived based on flexural rigidity, geometry, and material properties.

B. Geometric and FEA Modeling

• Plates modeled in ANSYS using Plane 185 elements (8-node elements with 3 DOF per node).

• Dimensions: outer radius = 151.5 mm, inner radius = 82.5 mm, thickness = 31.5 mm.

• Boundary conditions: free-free (F-F) and clamped-free (C-F).

• Thermal environment: constant temperature at 273K.

• Material properties are fixed across cases.

3. Results and Discussion

A. Natural Frequency Trends

• Natural frequencies increase with mode number, due to increasing structural stiffness at higher modes.

B. Boundary Condition Effects

• Clamped-free plates exhibit higher natural frequencies compared to free-free plates.

• This is attributed to increased constraints and resulting stiffness.

C. Effect of Radii Ratio (β = b/a)

• As the radii ratio increases, natural frequencies increase due to higher plate stiffness.

• Smooth increase in frequency with no abrupt changes, indicating consistent behavior across different modes and geometries.

• This trend holds for both F-F and C-F boundary conditions.

D. Effect of Aspect Ratio (h/a)

• With increasing aspect ratio (thickness), natural frequencies rise.

• This is due to increased stiffness as plate thickness grows.

• Higher modes and higher aspect ratios correspond to higher vibration frequencies.

• C-F plates again show higher frequencies compared to F-F plates for the same aspect ratios.

4. Validation

• The results (natural frequency parameter λ²) are compared with the work of Lee & Singh (2005).

• A good match between current and published results confirms the accuracy and reliability of the FEA model and methodology.

5. Conclusion

• The vibration behavior of circular annular plates under thermal environments is significantly influenced by boundary conditions, radii ratio, and aspect ratio.

• Clamped-free conditions lead to higher frequencies due to greater stiffness.

• Increasing the radii or aspect ratio increases the natural frequency, which is crucial in structural design applications.

• The study fills a critical gap in existing literature by providing in-depth analysis of out-of-plane vibration modes under thermal conditions.

Conclusion

In this chapter the free and forced vibration from out-of-plane modes of annular circular plate with different boundary conditions are analyzed. The result of this chapter matches well with the published results. The natural frequency of the uniform circular plate with free-free and clamped-free boundary condition increases with higher modal indices. With an increasing radii ratio for free-free and clamped-free boundary condition the natural frequency increases with different mode. It is also investigated that with an increasing aspect ratio for free-free and clamped-free boundary condition the natural frequency increases with different mode.

References

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Copyright

Copyright © 2025 Swagata Ghosh. 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.