Optimization of vibration and noise reduction in sigmoid functionally graded plates using mode localization

Abstract

The acoustic and vibrational properties of thin plates made of aluminum and aluminum oxide with a sigmoidally functionally graded material (SFGMs) with physical neutral surface are investigated in this study through use of mode localization and varying boundary conditions. This approach facilitates an in-depth analysis of how differences in material gradation impact the vibrational response and sound emission of the plates. The materials follow a sigmoidal gradation law with indices of k = 0, 1, 5, and 10. Mode localization is assessed by imposing a 20% mass constraint, either concentrated at a point or distributed across the structure. With the use of MATLAB, the governing equation – which was derived using Kirchhoff’s plate theory – is analytically solved to determine the normal velocity and far-field sound radiation fields. Numerical simulation in ANSYS are used to validate the sound power levels, and the result shows a notable level of agreement. The ‘A’-weighted sound power levels (dBA) indicate a rise in sound power level as the sigmoid-law index increases. Across all gradation indices, plates with distributed mass exhibit reduced sound power levels compared to those with point mass. This research delivers a comprehensive analysis of the vibroacoustic properties of SFGM plates, offering important insights for designing quieter structural components in engineering applications.