Dominant frequency control of sound radiation from largely deformed thin plates

Abstract

Aiming to control dominant frequency of sound radiating from a musical saw, a novel vibration analysis method to obtain mode shape and natural frequencies of largely deformed thin plates is proposed and examined. The static large deformation of cantilever rectangular or trapezoidal thin plate due to the tip displacement is calculated based on the ruled surface model and is approximated as the portion of a cylindrical shell. The strain energy of the deformed plate can be calculated with displacement of the cylindrical shell and small vibration on the shell. The Rayleigh-Ritz vibration analysis based on the strain energy calculated with admissible functions of sinusoidal and polynomial functions to reduce calculation time is proposed. The natural frequencies of the confinement mode are calculated with the proposed vibration analysis method in the case where displacement and tilt of the plate tip are given, and are compared with the results obtained with FEM analysis and the experimental modal analysis. The relation among displacement and posture of plate tip and natural frequencies indicates that dominant frequency of sound radiating from the largely deformed thin plate can be controlled.