Vibration of MEE Composite Conical Shell Surrounded by Nonlinear Elastic Foundation Considering the Effect of Geometrical Nonlinearity

This paper is investigated vibration of magneto-electro-elastic (MEE) composite conical shell on a nonlinear elastic foundation and under electric or magnetic potential while the influence of geometrical nonlinearity is taken into account. The conical shell is modeled based on the von Karman approach while the influences of shear deformation and rotary inertia are heeded. Coupled relations of MEE material are utilized to derive the vectors of stress, electric displacement as well as magnetic induction.  Quasi-static Maxwell equations, Gauss' laws as well as thin shell assumptions are used to determine electric and magnetic fields. The nonlinear ordinary differential equation of the shell is derived through the Lagrange approach. Lindstedt-Poincare method and modal analysis are hired in order to obtain nonlinear vibration responses of the MEE composite conical shell. For validation intention, some results of the literature are compared with some results of this study. The effects of several parameters including nonlinear and linear constants of foundation, electric and magnetic potentials, thickness as well as length on the values of fundamental linear frequency, nonlinear parameter, and the curves of nonlinear frequency ratio versus amplitude parameter are investigated. The results show that the increase of the nonlinear constant of elastic foundation or thickness causes the increase of the nonlinear frequency ratio. On the other hand, the nonlinear frequency ratio gets smaller values with an increase in the linear constants of the elastic foundation or length.