Symplectic analysis of vibration characteristics of three dimensional corrugated stretchable structures
Due to its excellent ductility and controllability,mechanically-assembled 3D structures are applied in the fabrication of stretchable electronic devices.In order to evaluate the stability of these stretchable electronic devices,the vibration behaviour of 3D corrugated stretchable structures is studied.Firstly,based on the nonlinear Euler-Bernoulli beam theory and Kelvin-Voigt viscoelastic theory,and considering the surface effect of the piezoelectric materials,the theoretical model of the 3D corrugated structure is established.Using the energy method and the extended Lagrange equation,the dynamic governing equations of the 3D stretchable structure are derived and these equations are solved by the symplectic Runge-Kutta method.The advantages of the symplectic algorithm are verified by numerical simulation experiments.The results show that by modulating the external excitation and structural parameters of the 3D stretchable piezoelectric structure,the vibration characteristics of this structure will transform from period doubling to chaos.The conclusions obtained in this paper will provide theoretical guidance for the optimal design and application of the 3D stretchable structures.
stretchable structurebucklingsymplectic Runge-Kutta algorithmpiezoelectric film
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