Abstract
This research paper deals with a numerical method which is modified and applied, by the authors to derive an eigenvalue of a thick plate having cut‐out in which geometries of plate and cut‐outs are different, through a deflection matching condition by including shear deformation and rotary inertia effects, with less computational efforts and high accuracy. The modified Independent Coordinate Coupling Method (ICCM) is validated with FEM package (ANSYS) and applied to know the change in eigenvalues for a plate with cut‐out by varying various parameters like aspect ratios, cut‐out size, and thickness ratios. Trigonometric functions considered at the boundary level conditions of a simply supported plate should be satisfied. Free vibrational exploration on a thick isotropic plate with various aspect ratios and an elliptical plate with various sizes is carried out through the modified ICCM. Independent coordinates are applied for a plate domain and for a hole domain individually followed by equating the deflection condition of hole and plate, a reduced mass to express with cut‐out from which eigenvalues can be obtained. The deflection matching condition facilitates the analysis even though the geometries of plate and cut‐outs are different.
Highlights
A plate with a cut-out is a commonly existing structure in the domain of aeronautics, civil, marine, and mechanical engineering to accommodate mountings or accessories under the action of various forces
Eigenvalues of thin plates may be calculated using classical plate theory and obtained, whereas they cannot be applied directly in thick plate analysis due to the effect of rotary inertia. is leads to an overestimation of results. e expression of strain and potential energies of plate must contain the terms of shear and rotary inertia to improve the accuracy of eigenvalues while computing
Based on the various combinations of aspect ratios and cut-out sizes, the derived numerical results were plotted in Figures 3 and 5. e frequency occurs due to a large hole, and maximum variation was observed compared to a plate without a cut. ese observations were tabulated as follows so that the designers can change the natural frequency of a structure up to maximum limit of scope by introducing a cut-out
Summary
A plate with a cut-out is a commonly existing structure in the domain of aeronautics, civil, marine, and mechanical engineering to accommodate mountings or accessories under the action of various forces. Using the ICCM, a Mindlin elliptical and rectangular plate’s first six natural frequencies with various sizes of cut-outs under supported boundary conditions were derived to show the variation of natural frequencies with respect to various hole sizes, and the same is validated through ANSYS software including mode shapes, which was not covered in the literature in view of the authors.
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