Research And Application Of The Spreading Residue Harmonic Balance Method For Several Nonlinear Vibration Systems

Because the phenomenon of nonlinear vibration exists in all fields,it is very important to study the nonlinear vibration system.Nonlinear vibration system is a complex system,so it is difficult to solve the exact solution.Therefore,many scholars have proposed a large number of methods to analyze the approximate solution.However,this paper mainly adopts the spreading residue harmonic balance method to study three types of nonlinear vibration systems.The first one is a strong nonlinear system of a restrained cantilever beam,the second one is the nonlinear vibration system of the electrostatically act.uated micro-beam and the third one is the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction.And then the paper use the above method to research the approximate periodic solutions of these three systems.The content of this paper is divided into four chapters.The first chapter mainly introduces the research background and research status.The second chapter mainly em-ploy the spreading residue harmonic balance method to study the restrained cantilever beam,and the approximate solution of this system is obtained.Then the paper com-pare the results from the second-order harmonic approximation with the energy balance method,the homotopy analysis method,the Runge—Kutta method.Meanwhile,the time history responses and the phase portrait are given for different parameters.The third chapter continues to use the spreading residue harmonic balance method to solve the nonlinear vibration of an electrostatically actuated microbeam.And numerical sim-ulations are carried out.The results are compared with the other three methods.In the fourth chapter,the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction is solved the spreading residue harmonic balance method.When the large amplitudes axe selected,the approximate solutions are in good agreement with the numerical solution of Runge—Kutta method.Through the above three chapters,the paper verify the feasibility and effectiveness of the spreading residue harmonic balance method for three systems.Further the paper prove that this method is also applied to the other nonlinear vibration systems.