Study On Modeling And Characteristics Of In-plane Vibration Of Circular Annular Plate Structure Under Complex Boundary Conditions

As an important type of basic structural element,circular annular plates are frequently encountered in mechanical engineering,shipbuilding industry,rail transit and other various engineering branches.For example,key components such as gear transmission system,high-speed wheel/rail system and sawing machine can be simplified to such structures for research in many cases,therefore,a deep understanding of its dynamic characteristics is the prerequisite and foundation for performing the optimization design of relevant complex system.According to the different directions of vibration,it can be divided into bending and in-plane vibrations.In-plane vibration is increasingly attracting research attention due to its impact on various aspects,such as built-up structure and energy transmission.Considering the application mode and service environment in different occasions,there are a series of important factors that affect the vibration characteristics of circular annular plate structure,such as boundary constraint,material property,rotational motion and structural coupling.In this thesis,the in-plane vibration analysis model of circular annular plate structure under complex conditions is established,and the following research is performed:The Fourier series and the boundary smoothed polynomial are superposition,and the in-plane vibration displacement function of annular plates with uniform elastic restraints is constructed.The polynomial is introduced to overcome the differential discontinuities of displacement function on the inner and outer boundaries of circular annular plate,and satisfies the arbitrary stress balance at boundaries.Based on the principle of harmonic balance,the matrix equation which satisfies the differential governing equation and uniform elastic boundary condition of circular annular plate is obtained,and the equivalent weak solution is also derived by energy description and Rayleigh-Ritz method.Through the coordinate transformation,the in-plane displacement field function that accurately meets the differential governing equation and boundary conditions is constructed under the inertial reference system.Analytical solution for the in-plane vibration analysis of rotating circular annular plate structure under linear theory is obtained by harmonic balance of series expansion.For more complicated arbitrary boundary constraints and internal support problems,continuous or discrete distributed constraint stiffness is introduced,and the boundary stiffness distribution function is expanded into a Fourier series,and harmonic balance is used to achieve accurate satisfaction of arbitrarily boundary conditions and simultaneous solution with in-plane differential equations.Introduction of the constrained potential energy at any point in circular annular plate through the two-dimensional Dirac?function,the standard eigenvalue matrix for the in-plane vibration of circular annular plate with arbitrary constraints is obtained by Rayleigh-Ritz method.In terms of such set of point constraints,the vibration frequency and mode shape under in-plane line constraint and local area constraints is realized.Elastic mechanical coupling points between multiple circular annular plates are introduced through the Dirac?function.Circular annular plates are systematically coupled according to the stress balance relationship,and the analysis model of in-plane vibration characteristics of coupled circular annular plate system is established.An improved Fourier series with additional smoothed terms is used to ensure the differential continuity of two in-plane vibration displacement fields in the whole solution domain.Using the principle of harmonic balance,a system characteristic matrix that simultaneously meets the differential governing equations and coupling conditions of multiple circular annular plates system is derived.By solving the system characteristic matrix,in-plane vibration characteristic parameters of the coupled circular annular plate structure are obtained,and the correctness and effectiveness of the constructed model are verified through numerical examples.For circular annular plate made of functionally graded material(FGM),based on the thermal stress in circular annular plate under thermal environment,system Lagrangian is used to describe the in-plane dynamics of the FGM circular annular plate in thermal environment.In-plane vibration analysis model of the FGM circular annular plate is obtained by Rayleigh-Ritz method,which reveals the influence of thermal environment conditions,functionally graded material index and other important parameters on its in-plane vibration characteristics.Based on the obtained in-plane vibration characteristics of circular annular plates under complex boundaries,in-plane modal sensor design of the circular annular plates is studied.Taking the polarization distribution of piezoelectric film as the design variable and combining with the objective function of charge output,the polarization distribution of in-plane modal sensor is solved by linear optimization method.Efficiency and correctness of the designed modal sensor for the target order frequency extraction and non-target frequency filtering are verified through frequency response curve.Based on this,the influence of complex factors such as boundary constraint on the in-plane modal sensor is revealed by numerical examples,which provides useful reference for the design of in-plane modal sensor of circular annular plate structure.