Analytical Investigation of Sound Radiation from Functionally Graded Thin Plates Based on Elemental Radiator Approach and Physical Neutral Surface

Abstract

This paper analyzes the sound radiation behavior of a clamped thin, functionally graded material plate using the classical plate theory and Rayleigh Integral with the elemental radiator approach. The material properties of the plate are assumed to vary according to the power-law distribution of the constituent materials in the transverse direction. The functionally graded material is modeled using a physical neutral surface instead of a geometric middle surface. The effects of the power-law index, elastic modulus ratio, different constituent materials, and damping loss factor on the sound radiation of functionally graded plate are analyzed. It was found that, for the considered plate, the power-law index significantly influences sound power level and radiation efficiency. There exists a critical value of the power-law index for which the corresponding peak of sound power level is minimum. In a wide operating frequency range, approximately 500–1500 Hz, this research suggests that the radiation efficiency is lower for the power-law index equal to 0 and 1. However, for very low frequencies (less than 250 Hz), the power-law index does not affect radiation efficiency significantly. Further, as the modulus ratio increases, the sound power peak decreases for a given power-law index. For the given material constituents of the functionally graded plate, the different values of damping loss factors do not significantly influence radiation efficiency. However, the selection of material constituents affects the radiation efficiency peak.

Computational and Theoretical Investigation of Acoustical and Vibrational Properties of Rigid Thin Material

“…A recent study has been performed on composite recycled glass bead panels sandwiched between two fiberglass composite sheets to evaluate the appropriateness for built environment and construction industry applications, particularly for loud built-up situations where they could be used as physical structural parts that could propose sound attenuation, or they could be utilized to reduce outdoor sound as noise screeners [22]. The classical plate theory and Rayleigh integral with the elemental radiator method were applied to analyze the acoustic radiation behavior of constrained thin functionally graded plates; it was found that the different values of the damping values could not significantly impact the acoustic radiation efficiency [23]. A mathematical model combining the classical forced plate theory with the combination of Green's function was presented to analyze the stress of thin plates and their vibration modes at different eigenfrequencies [24].…”