NON-LINEAR VIBRATION CHARACTERISTICS OF CLAMPED LAMINATED SHALLOW SHELLS

✍ Scribed by A. ABE; Y. KOBAYASHI; G. YAMADA

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 259 KB
• Volume: 234
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2877

✦ Synopsis

This paper examines non-linear free vibration characteristics of "rst and second vibration modes of laminated shallow shells with rigidly clamped edges. Non-linear equations of motion for the shells based on the "rst order shear deformation and classical shell theories are derived by means of Hamilton's principle. We apply Galerkin's procedure to the equations of motion in which eigenvectors for "rst and second modes of linear vibration obtained by the Ritz method are employed as trial functions. Then simultaneous non-linear ordinary di!erential equations are derived in terms of amplitudes of the "rst and second vibration modes. Backbone curves for the "rst and second vibration modes are solved numerically by the Gauss}Legendre integration method and the shooting method respectively. The e!ects of lamination sequences and transverse shear deformation on the behavior are discussed. It is also shown that the motion of the "rst vibration mode a!ects the response for the second vibration mode.