Comparison of Vibration Response from Various Annulated Circular Plates attached with Holes and Concentrated Stiffened Patches under Thermal Environment

Abstract

This study investigated the comparative vibration characteristics of annulated circular plates, annulated circular concentrated stiffened plates, and annulated circular hole plates through finite element analysis (FEA), while maintaining a constant mass for the plates. The temperature is held constant across all scenarios. The analysis of these plates is conducted under both free-free and clamped-free boundary conditions. Parametric studies are performed to assess the impact of Eigen frequencies, aspect ratio, and radius ratio on various stiffened plates, with the results being thoroughly examined and outlined.

Introduction

This study investigates the vibration behavior of circular annulated stiffened plates in a thermal environment, a topic that remains underexplored despite its relevance in fields like aerospace, automotive, naval architecture, and civil engineering. The focus is on out-of-plane flexural vibration modes using Finite Element Analysis (FEA).

Background & Literature Review:

Numerous researchers have analyzed circular annular plates under various conditions using methods such as:

• Differential Transforms Method (DTM)

• Asymptotic approximation

• Multipole Trefftz Method

• Finite Element Analysis (FEA)

• Indirect Boundary Integral Equations Method (BIEM)

However, studies on stiffened plates in thermal environments are limited. This research aims to fill that gap by analyzing Eigen frequencies under constant thermal conditions (T = 273 K) for:

• Unstiffened annular circular plates

• Plates with holes (2 and 4)

• Plates with stiffener patches (2 and 4)

Methodology:

• FEA Modeling: Conducted in ANSYS using 8-node Plane 185 elements.

• Geometry: Outer radius = 151.5 mm; inner radius = 82.5 mm; thickness = 31.5 mm.

• Materials: Steel with Young’s modulus = 218 GPa, density = 7905.9 kg/m³, Poisson’s ratio = 0.305.

• Boundary Conditions: Free-free and clamped-free.

• Assumptions: Constant mass and volume; uniform thickness; steady temperature.

Validation:

The model’s results for natural frequencies of unstiffened plates were validated against results from Lee and Singh (2005), showing good agreement.

Key Findings:

1. Effect of Radius Ratio (β = b/a):

   • For free-free boundary:

     • Increasing β leads to decreasing natural frequency, due to reduced plate stiffness.

   • For clamped-free boundary:

     • Increasing β leads to increasing frequency, because of increased edge rigidity.

2. Effect of Holes:

   • More holes (2 → 4) reduce stiffness and mass, leading to lower Eigen frequencies.

   • Plates with 4 holes vibrate at the lowest frequencies.

3. Effect of Stiffener Patches:

   • More patches (2 → 4) decrease stiffness, similar to holes.

   • Plates with 4 patches have lower frequencies than with 2 patches, though slightly higher than those with holes.

4. Mode Shapes:

   • The first five out-of-plane structural modes were analyzed.

   • The plain annular plate (no stiffeners or holes) showed the highest natural frequencies across all modes.

5. Comparison:

   • Unstiffened plate > Stiffened with patches > With holes in terms of natural frequencies.

   • Clamped-free boundary always yields higher frequencies than free-free.

Conclusion

This research examined the comparative vibration characteristics of annulated circular plates, annulated circular concentrated stiffened plates, and annulated circular hole plates using finite element analysis (FEA), while ensuring a consistent mass for the plates. The temperature remains constant across all scenarios. The evaluation of these plates is performed under both free-free and clamped-free boundary conditions. It is noted that the Eigen frequency (?) decreases as the radius ratio increases for free-free boundary conditions, while the Eigen frequency rises with an increasing radius ratio for clamped-free boundary conditions. Notably, the Eigen frequency for the clamped boundary condition demonstrates greater vibration sensitivity compared to the free-free boundary condition. Nevertheless, as the aspect ratio increases, the Eigen frequency also increases for both free-free and clamped-free boundary conditions. Furthermore, it is found that the un-stiffened annulated circular plate possesses the highest Eigen frequency across all cases. The analysis indicates that as the number of holes and patches increases, the natural frequency decreases. The configuration with 4-holes and 4-patches shows the lowest frequency under all conditions. Additionally, it has been observed that the clamped-free boundary condition results in a shorter plate compared to the free-free boundary condition.

References

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Copyright

Copyright © 2025 Swagata Ghosh, Abhijeet Chatterjee. 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.