Boundary constraint induced inhomogeneous effects are important for mechanical responses of nano/micro-devices.For microcantilever sensors,the clamped-end constraint induced inhomogeneous effect of static deformation,...Boundary constraint induced inhomogeneous effects are important for mechanical responses of nano/micro-devices.For microcantilever sensors,the clamped-end constraint induced inhomogeneous effect of static deformation,so called the clamped-end effect,has great influence on the detection signals.This paper is devoted to developing an alternative mechanical model to characterize the clamped-end effect on the static detection signals of the DNA-microcantilever.Different from the previous concentrated load models,the DNA adsorption is taken as an equivalent uniformly distributed tangential load on the substrate upper surface,which exactly satisfies the zero force boundary condition at the free-end.Thereout,a variable coefficient differential governing equation describing the non-uniform deformation of the DNA-microcantilever induced by the clamped-end constraint is established by using the principle of minimum potential energy.By reducing the order of the governing equation,the analytical solutions of the curvature distribution and static bending deflection are obtained.By comparing with the previous approximate surface stress models,the clamped-end effect on the static deflection signals is discussed,and the importance of the neutral axis shift effect is also illustrated for the asymmetric laminated microcantilever.展开更多
In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric vo...In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric voltage between the horizontal part of T-shaped tip mass and an opposite electrode plate. The cantilever microbeam is modeled as an Euler-Bernoulli beam. The T-shaped tip mass is assumed to be a rigid body and the nonlinear effect of electrostatic force is considered. An equation of motion and its associated boundary conditions are derived by the aid of combining the Hamilton principle and Newton’s method. An exact solution is obtained for static deflection and mode shape of vibration around the static position. The differential equation of nonlinear vibration around the static position is discretized using the Galerkin method. The system mode shapes are used as its related comparison functions. The discretized equations are solved by the perturbation theory in the neighborhood of primary and subharmonic resonances. In addition, effects of mass inertia, mass moment of inertia as well as rotation of the T-shaped mass, which were ignored in previous works, are considered in the analysis. It is shown that by increasing the length of the horizontal part of the T-shaped mass, the amount of static deflection increases, natural frequency decreases and nonlinear shift of the resonance frequency increases. It is concluded that attaching an electrode plate with a T-shaped configuration to the end of the cantilever microbeam results in a configuration with larger pull-in voltage and smaller nonlinear shift of the resonance frequency compared to the configuration in which the electrode plate is directly attached to it.展开更多
基金the National Natural Science Foundation of China (Nos.11772182, 11272193,and 10872121)the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)。
文摘Boundary constraint induced inhomogeneous effects are important for mechanical responses of nano/micro-devices.For microcantilever sensors,the clamped-end constraint induced inhomogeneous effect of static deformation,so called the clamped-end effect,has great influence on the detection signals.This paper is devoted to developing an alternative mechanical model to characterize the clamped-end effect on the static detection signals of the DNA-microcantilever.Different from the previous concentrated load models,the DNA adsorption is taken as an equivalent uniformly distributed tangential load on the substrate upper surface,which exactly satisfies the zero force boundary condition at the free-end.Thereout,a variable coefficient differential governing equation describing the non-uniform deformation of the DNA-microcantilever induced by the clamped-end constraint is established by using the principle of minimum potential energy.By reducing the order of the governing equation,the analytical solutions of the curvature distribution and static bending deflection are obtained.By comparing with the previous approximate surface stress models,the clamped-end effect on the static deflection signals is discussed,and the importance of the neutral axis shift effect is also illustrated for the asymmetric laminated microcantilever.
文摘In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric voltage between the horizontal part of T-shaped tip mass and an opposite electrode plate. The cantilever microbeam is modeled as an Euler-Bernoulli beam. The T-shaped tip mass is assumed to be a rigid body and the nonlinear effect of electrostatic force is considered. An equation of motion and its associated boundary conditions are derived by the aid of combining the Hamilton principle and Newton’s method. An exact solution is obtained for static deflection and mode shape of vibration around the static position. The differential equation of nonlinear vibration around the static position is discretized using the Galerkin method. The system mode shapes are used as its related comparison functions. The discretized equations are solved by the perturbation theory in the neighborhood of primary and subharmonic resonances. In addition, effects of mass inertia, mass moment of inertia as well as rotation of the T-shaped mass, which were ignored in previous works, are considered in the analysis. It is shown that by increasing the length of the horizontal part of the T-shaped mass, the amount of static deflection increases, natural frequency decreases and nonlinear shift of the resonance frequency increases. It is concluded that attaching an electrode plate with a T-shaped configuration to the end of the cantilever microbeam results in a configuration with larger pull-in voltage and smaller nonlinear shift of the resonance frequency compared to the configuration in which the electrode plate is directly attached to it.
