Science China Technological Sciences

, Volume 61, Issue 11, pp 1654–1665 | Cite as

Nonlinear dynamic behavior of inhomogeneous functional plates composed of sigmoid graded metal-ceramic materials

  • YanQing WangEmail author
  • Jean W. Zu


This paper presents a study on nonlinear vibration of inhomogeneous functional plates composed of sigmoid graded metal-ceramic materials. The material properties vary continuously along the thickness direction according to a sigmoid distribution rule, which is defined by piecewise functions to ensure smooth distribution of stress among all the interfaces. The geometric nonlinearity is considered by adopting the von Kármán geometrical relations. Based on the d’Alembert’s principle, the nonlinear out-of-plane equation of motion of the plates is developed. The Galerkin method is employed to discretize the motion equation to a series of ordinary differential ones, which are subsequently analyzed via the use of the method of harmonic balance. Then, the analytical results are validated by the comparison to numerical solutions, which are obtained by using the adaptive step-size fourth-order Runge-Kutta method. The stability of the steady-state response is examined by the perturbation technique. Results show the first and third modes are both activated while the second mode is not activated for the plates under harmonic point excitation. The frequency response relationships of activated modes exhibit very complicated curves due to the nonlinear modal interaction. In addition, influences of key system parameters on nonlinear vibrational characteristics of the present inhomogeneous plates are illustrated.


inhomogeneous functional plates sigmoid graded metal-ceramic material nonlinear vibration response harmonic balance method 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MechanicsNortheastern UniversityShenyangChina
  2. 2.Key Laboratory of Ministry of Education on Safe Mining of Deep Metal MinesNortheastern UniversityShenyangChina
  3. 3.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

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