Application Of Multiple Scales Method In Kinetic Analysis Of Electrostatically Actuated Micropump

The singular perturbation method is a kind of method for solving nonlinear differential equation in the field of mechanics.It is widely used in many fields,such as mechanics,control engineering,economic system and so on.It is a very important way in the field of applied mathematics.The existing methods for solving singular perturbation problems in time domain include Lindstedt-Poincaré(L-P)perturbation method,multiple scales method,and homogenization method.The multiple scales method is to transform the original ordinary differential equation into partial differential equation.This approach allows the solution to have enough general form.And it is more widely applied than the other two methods.This paper investigates the application of time multiple scales method in the dynamic analysis of electrostatically actuated micropumps.The method of time multiple scales is used to obtain an approximate analytical solution to the control equation of the system.That is using the partial differential equation of multiple time scales to replace the original equation.Because of the tiny size,it is necessary to study the kinetic properties of electrostatically actuated diaphragm-type micropumps on the basis of the couple stress theory.And in order to better verify the practicability and accuracy of the time multiple scales method,we studies two kinds of diaphragm-type micropumps,circular and rectangular diaphragm-type micropumps.In this paper,the governing equations of the system and the corresponding boundary conditions are derived by Hamiltonian principle.Then the Galerkin method is used to transform the nonlinear partial differential equations to a set of ordinary differential equations.Finally,the time multiple scales method is used to obtain the approximate solution through converting ordinary differential equations into partial differential equations.And then through MATLAB numerical simulation,we can further study the effects of voltage,couple stress strength,pump chamber height,fluid properties and temperature on the kinetic properties of the system.It is shown that the softening behavior of the system is obvious as the DC voltage increases.And the AC voltage has little influence on the system.The couple stress intensity can not only increase the rigidity of the system,but also increase the working frequency range of the system.Experiments show that the temperature will increase the softening property of the system and weaken the rigidity of the system.The results also show that softening behavior increases with decreasing chamber height.In addition,it is found that the properties of the operating fluid can influence the softening behavior of the system.As the sizes of the micropumps reduce to nanoscale,the effect of sizes on the dynamic characteristics of the micropumps becomes more and more significant.Therefore,studying the dynamic characteristics of the diaphragm-type micropumps under the condition of the couple stress is not only very meaningful for the development of the MEMS,but also provides theoretical support for the design and manufacture of the micropumps in the future.