| Products such as aerospace,automobile,electronics,and home appliances all have microelectromechanical system Systems to realize the functions of sensors,actuators,signal processing,and micro energy.In order to ensure the stability and reliability of Micro-Electro-Mechanical Systems,it is necessary to analyze the dynamic characteristics of the beam and plate structure.Therefore,in this paper,the dynamic characteristics of the micromechanical systems are analyzed using the modified couple stress theory and Lagrange dynamic equations.The strain energy and kinetic energy of the microplate are determined using the modified couple stress theory.Then,the assumed mode method is used to discretize the lateral displacement of the microplate.Finally,substitute the discretized energy into the Lagrange equations to obtain the dynamic equations of the simply supported microplate and the cantilever microplate system.Considering the nonlinear coupling deformation caused by the surface deformation in the microplate,the lateral displacement of the microplate is discretized by the combination of boundary conditions and Chebyshev polynomials.In the static analysis of simply supported microplates,with the increase of DC voltage,the pull-in phenomenon appears in the system,and the DC voltage at this time is the pull-in voltage of the system.The pull-in voltage of the system decreases with the increase of the aspect ratio of the simply supported microplates and increases with the increase of the distance between the plates.In the dynamic analysis,the natural frequency of the system decreases with the increase of DC voltage and instability near the pull-in voltage;under the combined action of DC and AC voltage,with the increase of AC voltage,the nonlinear vibration amplitude of the system increases and the hard nonlinear behavior is more obvious.For the rotating cantilever microplate,the nonlinear coupling deformation caused by the surface deformation in the microplate is taken into account to establish the dynamic equations.In a given rotational motion,with the increase of the dimensionless rotational angular velocity,the zero-order approximated coupling modeling method without considering the nonlinear coupling deformation diverges when the angular velocity reaches the first stationary natural frequency of the microplate,so the firstorder approximated coupling modeling method with considering the nonlinear coupling deformation is more suitable for the engineering practice.The change of dimensionless natural frequency and mode shape of the microplate is analyzed by changing the rotating angular velocity and aspect ratio of the cantilever microplate.When increasing the rotational angular velocity,the dimensionless natural frequency of the microplate increases gradually,which reflects the dynamic rigidity phenomenon,and the third and fourth-order,the fifth and sixth order,the fourth and fifth-order successively appear the frequency loci veering and mode shape switching phenomenon.With the increase of aspect ratio,the fundamental and 3rd dimensionless natural frequencies remain basically the same,and the other order natural frequencies increase.In the fourth and fifth-order,the fifth and sixth order,the frequency loci veering and mode shape switching phenomenon appear successively.Based on the modified couple stress theory,the system dynamics model is established for the rotating cantilever microplate and the additional stiffness brought by the size effect is introduced.The diverged angular velocity of the zero-order approximated model when considering the size effect is larger than that when the size effect is not considered in the dynamic response analysis,and the lateral displacement of the middle point outside the system considering the size effect is smaller than that without considering the size effect by using the same motion equations;because of the additional stiffness brought by the size effect,the corresponding natural frequency is larger. |
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