FREE VIBRATION OF ORTHOTROPIC SQUARE PLATES WITH A SQUARE HOLE

• Published in: Journal of sound and vibration Vol. 259; no. 1; pp. 63 - 80
• Main Authors: SAKIYAMA, T., HUANG, M., MATSUDA, H., MORITA, C.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 2003; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Variable section; Perforated plate; Free vibration; Characteristic equation; Rectangular plate; Numerical method; Green function; Structural analysis; Orthotropic material; Variable thickness plate
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2002.5181

An approximate method is extended for analyzing the free vibration problem of orthotropic square plate with a square hole. In this paper, a square plate with a square hole is transformed into an equivalent square plate with non-uniform thickness by considering the hole as an extremely thin part of the equivalent plate. Therefore, the dynamic characteristics of a plate with a hole can be obtained by analyzing the equivalent plate. The Green function, which is the discrete solution for the deflection of the equivalent plate, is used to obtain the characteristic equation of the free vibration. The effects of the side to thickness ratio, hole side to plate side ratio and the variation of the thickness on the frequencies are considered. Some numerical analyses are carried out for the simply supported orthotropic square plate with a square hole. The efficiency and accuracy of the numerical solutions by the present method are investigated.