New exact solutions for free vibrations of thin orthotropic rectangular plates

• Published in: Composite structures Vol. 89; no. 4; pp. 567 - 574
• Main Authors: Xing, Y.F., Liu, B.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2009; Elsevier
• Subjects: Exact sciences and technology; Free vibration; Frequency; Fundamental areas of phenomenology (including applications); Orthotropic; Physics; Separation of variables; Solid mechanics; Structural and continuum mechanics; Thin plates; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Frequency; Separation of variables; Orthotropic; Free vibration; Thin plates; Thin plate; Simple support; Modeling; Orthotropic material; Exact solution; Finite element method; Separation method; Orthotropic plate; Rectangular plate
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2008.11.010

In this paper, a novel separation of variables is presented for solving the exact solutions for the free vibrations of thin orthotropic rectangular plates with all combinations of simply supported (S) and clamped (C) boundary conditions, and the correctness of the exact solutions are proved mathematically. The exact solutions for the three cases SSCC, SCCC, and CCCC are successfully obtained for the first time, although it was believed that they are unable to be obtained. The new exact solutions are further validated by extensive numerical comparisons with the solutions of FEM and those available in the literature.