Nonlinear Dynamics

, Volume 73, Issue 3, pp 1697–1714 | Cite as

Theoretical and experimental studies on nonlinear oscillations of symmetric cross-ply composite laminated plates

Original Paper


The nonlinear oscillations and resonant responses of the symmetric cross-ply composite laminated plates are investigated theoretically and experimentally. The governing equations of motion for the composite laminated plate are derived by using the von Karman type equation, Reddy’s third-order shear deformation plate theory, and Galerkin method with the geometric nonlinearity. The four-dimensional averaged equation is obtained by using the method of multiple scales. The frequency-response functions are analyzed under the consideration of strongly coupled of two modes. The influences of the resonance case on the softening and hardening type of nonlinearity are analyzed with different parameters for the composite laminated plates. The numerical results indicate that there exist the hardening and softening types of the composite laminated plate in the specific resonant case. The variation of the response amplitudes is studied for the composite laminated plate under combined the transverse and in-plane excitations. A sweep frequency experiment is performed to obtain the hardening and softening nonlinearities of a composite laminated plate. The experimental results coincide with the numerical results qualitatively. The influences of the excitation amplitudes on the softening and hardening types of nonlinearity are also analyzed for the composite laminated plate. The amplitude spectrums of the test plate also demonstrate that the change of the nonlinear dynamic responses may be caused by the subharmonic resonance.


Composite laminated plate Nonlinear oscillations Frequency-response curves Theoretical and experimental study 



The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through grant Nos. 11290152, 11072008, and 10732020, and the Funding Project for Academic Human Resources Development in the Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of Mechanical EngineeringBeijing University of TechnologyBeijingP.R. China

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