The Construction And Analysis On Unified Dynamical Model Of Revolve Structures Subjected To Complex Boundary Conditions

As a stand-alone structure or a constituent structural component,revolve structures are widely used in various engineering application fields such as aeronautics and astronautics,ocean engineering,civil engineering and mechanical engineering.The solution of the structure dynamic problems has been one of the important research topics to engineers and designers.In the traditional solution framework,vibrations of revolve structures with different geometry shapes are considered as different boundary value problems and often treated using different solution algorithms and procedures.This problem is further compounded by the fact that the admissible displacement functions for each structure typically needs to be adapted to different boundary conditions.In order to establish the parameterized model,a unified dynamical model for revolve structures with complex boundary conditions is proposed,which can provide a necessary theory and technique support for the design of revolve structures in engineering practical field.It also can make a foundation of studying the formation mechanism of vibration response and sound field essentially.According to the modelling of revolve structure subjected to complex boundary conditions,specific research work of this dissertation is as follows:A unified transverse vibration analysis model of revolve plates(sector,annular and circular plates)with complex boundary conditions is established.Regardless of the shapes of the plates and the types of boundary conditions,the transverse vibration displacement solution is invariably and universally constructed with 2-D spectro-geometric method.In order to eliminate all the relevant discontinuities with the displacement and its space derivatives at the edges,the displacement component along each direction can be expressed as a standard single cosine series supplemented with four sine functions.Translational and rotational restraining springs with independent stiffnesses are uniformly arranged along each edge to simulate the complex boundary conditions.The vibration problems for complex boundary conditions can be solved through changing the stiffness constants of restraining springs.The unknown series expansion coefficients for displacement function are determined with the Rayleigh-Ritz technique.Numerical examples are carried out to validate the admissible displacement function and unified analysis model.On this basis,the influence factors of transverse vibration characteristics for revolve plates are examined.A unified analysis model for in-plane vibration of revolve plates under complex boundary conditions is constructed.In order to ensure the continuity of the displacement functions and its space derivatives along each edge,the radial and circumferential displacement functions are universally represented using the 2-D spectro-geometric method.Two kinds of springs(normal and tangential springs)uniformly attached to each edge are utilized to model the complex boundary conditions.The Rayleigh-Ritz method is employed to derive the characteristic equation of the in-plane motion for revolve plates.All the in-plane vibration characteristic parameters can be obtained by solving a standard eigenvalue problem concerning the unknown displacement expansion coefficient.The current solutions are compared with other analytical method results to check the presented approach and unified analysis model.A 3-D spectro-geometric method(SGM)is proposed.On the basis,a unified analysis model for three-dimensional vibration analysis of revolve plates subjected to complex boundary supports is established.In order to eliminate the discontinuities involved in displacement and its partial differentials of various order along each boundary face,the admissible displacement functions are represented as a modified 3-D trigonometric series with 3-D SGM.Various boundary conditions as well as its combinations can be readily created by modifying the stiffness of boundary restraining spring along each boundary face.The characteristic equation of 3-D free vibration motion for revolve plates is derived with the Rayleigh-Ritz procedure based on energy principle description,from which the dynamic characteristic of structure system can be solved readily.Vibration characteristics of revolve structures with different geometry shapes can be solved from the same boundary value problem.Free vibrations of revolve structures are examined under different boundary conditions.Comparisons with previously published results and finite element analyses are implemented to demonstrate the presented approach and unified model.A unified model for the vibration of a revolve plate-cylindrical shell structure with complex boundary conditions and coupling conditions is constructed.The six displacement functions for the revolve plate and cylindrical shell are represented simultaneously by the 2-D SGM.The boundary conditions and coupling conditions are modeled respectively.The compatibility conditions along the plate and shell structures' conjunctions are generally described in terms of three-dimensional elastic couplers with both translational and rotational stiffnesses.The three-dimensional elastic coupler is generally described by four distributed springs along the coupling common edge,which are utilized to simulate the transverse shearing forces,bending moments,in-plane longitudinal forces and in-plane shearing forces separately.Different coupling conditions can be readily realized by changing the stiffness of the corresponding springs.Ultimately,the double trigonometric series solutions for the dynamic characteristic of the shell-plate structures are determined by the Rayleigh-Ritz procedure.Comparisons with previously published results and finite element analyses are carried out to validate the constructed unified model.On this basis,the forced vibrations of shell-plate structure are studied.Then,numerical simulation for the effects of several relevant parameters on the vibration characteristics for the shell-plate structures are performed,including coupling conditions,axial location and structure parameters.At last,some relevant experimental setups are designed and built up,and then the experimental studies on the vibration problems for revolve plates(re-entrant annular sector plate and circular plate)and elastic circle plate-cylindrical shell coupled structures are carried out.The effectiveness and correctness of the modelling method proposed in this dissertation are examined strongly through comparing the experimental data with the predicted results.And some special experimental phenomena and various potential factors causing measuring error in the experiments are discussed in detail.