This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal direc...This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.展开更多
We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from whic...We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained. Numerical solutions by the Runge-Kutta method show that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant. As resonators are to be made smaller and thinner in the future with about the same power requirement, nonlinear effects will become more important and need more understanding and consideration in resonator design.展开更多
文摘This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.
基金supported by the Program for New Century Excellent Talents in Universities(No.NCET-12-0625)the Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province(No.SBK2014010134)+2 种基金the Fundamental Research Funds for Central Universities(No.NE2013101)the National Natural Science Foundation of China(No.11232007)a project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained. Numerical solutions by the Runge-Kutta method show that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant. As resonators are to be made smaller and thinner in the future with about the same power requirement, nonlinear effects will become more important and need more understanding and consideration in resonator design.
