Computing Natural Frequencies and Mode Shapes of Thin Plates

Using MATLAB software enables the computation of natural frequencies and mode shapes for thin plates. Based on these calculations, frequency response curves can be plotted to further analyze the vibration characteristics of the plates. These analytical results provide fundamental support for vibration analysis and control of thin plates. For plates with different geometries and materials, various computational methods and analytical approaches can be employed to achieve more accurate results. Common MATLAB implementations include using the PDE Toolbox for finite element analysis or programming custom solutions with eigenvalue solvers like "eig" function for modal analysis. The process typically involves defining plate properties (density, elasticity), applying boundary conditions, and solving the governing vibration equations. Therefore, MATLAB-based computation and analysis play a significant role in vibration studies and control strategies for thin plates, offering both numerical accuracy and visualization capabilities through functions like "contour" or "surf" for mode shape plotting and "plot" for frequency response visualization.