Linear and geometrically nonlinear vibrations of fiber reinforced laminated plates and shallow shells

✍ Scribed by A.V. Singh

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 385 KB
• Volume: 76
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(99)00155-8

✦ Synopsis

This paper deals with the free ¯exural vibration of laminated quadrilateral plates and shallow shells using the Rayleigh±Ritz method. Equations are derived using the ®rst order shear deformation theory of plates and shells. Nonlinearity is present only in the in-plane strain components. The transverse shear strains, curvature and inertial terms are linear. The geometry is mapped using the natural coordinates. Admissible displacement ®elds are constructed by taking the product of two simple polynomials in each of the two parametric coordinates. By controlling the coecients of these polynomials, the geometric boundary conditions are satis®ed. Numerical results are presented for the four-layer angle-ply plates and cylindrical shallow shells supported on trapezoidal boundary. The in¯uences of the large amplitude and also of the geometry on the natural frequency are examined.