Nonlinear dynamic instability analysis of laminated composite thin plates subjected to periodic in-plane loads

• Published in: Nonlinear dynamics Vol. 91; no. 1; pp. 187 - 215
• Main Authors: Darabi, M., Ganesan, R.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2018; Springer Nature B.V
• Subjects: Amplitudes; Aspect ratio; Automotive Engineering; Classical Mechanics; Composite structures; Control; Dynamic stability; Dynamical Systems; Engineering; Equations of motion; Galerkin method; Geometric nonlinearity; Laminates; Mathematical analysis; Mechanical Engineering; Nonlinear analysis; Nonlinear dynamics; Nonlinear equations; Original Paper; Stability analysis; Steady state; Thin plates; Transverse waves; Vibration; Thin plate; Composite laminates; Nonlinear vibrations; Dynamic stability; Parametric resonance
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-017-3863-9

In this paper, the dynamic instability of thin laminated composite plates subjected to harmonic in-plane loading is studied based on nonlinear analysis. The equations of motion of the plate are developed using von Karman-type of plate equation including geometric nonlinearity. The nonlinear large deflection plate equations of motion are solved by using Galerkin’s technique that leads to a system of nonlinear Mathieu-Hill equations. Dynamically unstable regions, and both stable- and unstable-solution amplitudes of the steady-state vibrations are obtained by applying the Bolotin’s method. The nonlinear dynamic stability characteristics of both antisymmetric and symmetric cross-ply laminates with different lamination schemes are examined. A detailed parametric study is conducted to examine and compare the effects of the orthotropy, magnitude of both tensile and compressive longitudinal loads, aspect ratios of the plate including length-to-width and length-to-thickness ratios, and in-plane transverse wave number on the parametric resonance particularly the steady-state vibrations amplitude. The present results show good agreement with that available in the literature.