TY - JOUR
T1 - Scale effect on the nonlinear vibration of piezoelectric sandwich nanobeams on Winkler foundation
AU - Luo, Tianxi
AU - Mao, Qibo
AU - Zeng, Shan
AU - Wang, Kaifa
AU - Wang, Baolin
AU - Wu, Jinwu
AU - Lu, Zhao
PY - 2021
Y1 - 2021
N2 - Purpose: Goal for the present research is investigating the effect of scale effect on free vibration of piezoelectric sandwich nanobeams on Winkler foundation. For this purpose, the effects of nonlocal parameters and strain gradient parameters on the free vibration of the model are studied. Methods: Based on the nonlocal strain gradient theory and Timoshenko beam theory, the nonlinear vibration of piezoelectric sandwich nanobeams on Winkler foundation is investigated. The nonlinear governing equations and boundary conditions are derived using the Hamilton's principle. The partial differential equation is transformed into ordinary differential equation by Galerkin's method, and then the nonlinear vibration of piezoelectric nanobeam is numerically analyzed using the Runge-Kutta method. Results and Conclusions: The results show that the nonlinear frequency ratio decreases with the increase of length-to-thickness ratio. When the nonlocal parameter is not less than the strain gradient length scale parameter, the piezoelectric nanobeam exhibits stiffness softening effect. When the nonlocal parameter is not greater than the strain gradient length scale parameter, the piezoelectric nanobeam exhibits stiffness hardening effect. It is also observed that both large length-to-thickness ratios and shear deformation can attenuate the nonlocal strain gradient effect. In addition, changes in the external applied voltage have a significant effect on the natural frequency of the piezoelectric nanobeams and increasing the thickness of the piezoelectric layer can enhance the structural stiffness.
AB - Purpose: Goal for the present research is investigating the effect of scale effect on free vibration of piezoelectric sandwich nanobeams on Winkler foundation. For this purpose, the effects of nonlocal parameters and strain gradient parameters on the free vibration of the model are studied. Methods: Based on the nonlocal strain gradient theory and Timoshenko beam theory, the nonlinear vibration of piezoelectric sandwich nanobeams on Winkler foundation is investigated. The nonlinear governing equations and boundary conditions are derived using the Hamilton's principle. The partial differential equation is transformed into ordinary differential equation by Galerkin's method, and then the nonlinear vibration of piezoelectric nanobeam is numerically analyzed using the Runge-Kutta method. Results and Conclusions: The results show that the nonlinear frequency ratio decreases with the increase of length-to-thickness ratio. When the nonlocal parameter is not less than the strain gradient length scale parameter, the piezoelectric nanobeam exhibits stiffness softening effect. When the nonlocal parameter is not greater than the strain gradient length scale parameter, the piezoelectric nanobeam exhibits stiffness hardening effect. It is also observed that both large length-to-thickness ratios and shear deformation can attenuate the nonlocal strain gradient effect. In addition, changes in the external applied voltage have a significant effect on the natural frequency of the piezoelectric nanobeams and increasing the thickness of the piezoelectric layer can enhance the structural stiffness.
UR - https://hdl.handle.net/1959.7/uws:63142
U2 - 10.1007/s42417-021-00297-8
DO - 10.1007/s42417-021-00297-8
M3 - Article
SN - 2523-3920
VL - 9
SP - 1289
EP - 1303
JO - Journal of Vibration Engineering and Technologies
JF - Journal of Vibration Engineering and Technologies
IS - 6
ER -