Size Effects Of Nonlinear Microbeams Based On The Modified Couple Stress Theory

With the rise and development of MEMS technology,MEMS devices with different functions have been developed,and have been widely used in biomedicine,aerospace,automotive and other fields.Microbeam is a typical structure widely used in MEMS.Due to the miniaturization of the geometric dimensions and the specialization of the process,its mechanical properties differ from those in the macroscopic state,and the size-effect cannot be ignored.Time-delay is a common phenomenon in MEMS devices.A great number of dynamical systems not only depend on the current state,but are also related to a certain moment in the past period of time.Under the feedback of time-delay,we study the mechanical properties of nonlinear microbeams by the modified couple stress theory.First of all,we establish a size-effect model with von Karman geometry nonlinear beam based on modified couple stress theory.The effect of electrostatic drive and time delay feedback is considered in the model.The Hamiltonian variational principle is used to derive the equations of motion and boundary conditions.The Galerkin method and the multi-scale method are used to approximate the vibration equation of the microbeam.The amplitude-frequency response curves of main resonance,superharmonic resonance and subharmonic resonance are analyzed.When the time-delay is taken,the influence of the thickness variation of the microbeam on the amplitude-frequency response curve is analyzed.When the thickness and width of the beam are taken,the effects of the time delay feedback and the time delay feedback coefficient on the amplitude-frequency response curve and amplitude peak are analyzed.Then we discuss the characteristic analysis of the pull-in and voltage of nonlinear microbeam with von Karman geometry under modified couple stress theory.The variational principle is used to derive the equations.Considering the electrostatic drive and proportional feedback in this model,and the pull-in phenomena are investgated.We study the influence of the length,thickness and gap variation of the microbeam on the pull-in voltage and deflection,and compare the voltage-deflection curves of the linear microbeam with nonlinear one.The classical elastic theory and the modified couple stress theory were used to the difference of pull-in voltage.The effect of the size-effect on the voltage and deflection is also analyzed.Finally,as for the nonlinear microbeam vibration equation with time-delay feedback,the particle swarm algorithm is used to find its periodic solution.We analyze the effects of the difference in the number of points,the number of fitting orders,and the solution range on the error size of the solution.