Study On Vibration Characteristics Of Triangular And Quadrilateral Laminates And Vibro-acoustics Characteristics Of Enclosed Acoustic Cavity

With the rapid development of modern science and technology,the fiber composite material has been already applied widely.Structures composed of arbitrary triangular and straight quadrilateral structures filled with fibrous composites,have been widely used in aerospace,ship,building and other engineering fields.In general,the working environment of such structures is complex,and often stimulated by complex external disturbances,which then induce their own forced response and radiate energy to the surrounding environment.In addition,due to the application of arbitrary triangle and straight quadrilateral shape structure,some enclosed cavities of triangle and straight quadrilateral have been produced in engineering.The energy radiated from the structure during vibration,acting together with the medium in the cavity,will cause coupled vibration and form a complex acoustic-vibration coupling phenomenon,which is the main source of noise.Therefore,it is of great theoretical significance and application value to understand the vibration characteristics of triangular and straight quadrilateral structures with arbitrary shape,the inherent characteristics of triangular and straight quadrilateral enclosed cavities and the vibro-acoustics characteristics of the acoustic-vibration coupling system composed of them.(1)An analysis model for vibration characteristics of arbitrary triangular laminates with elastic boundary conditions is established.Firstly,based on the unified coordinate transformation,the arbitrary triangle area is transformed into the regular unit isosceles right triangle area,and the displacement admissible function of isosceles right triangle plate is constructed by the improved Fourier series.Secondly,the elastic boundary is obtained by introducing three groups of boundary displacement restraint springs and one group of torsional restraint spring.Then,based on the chain derivation principle,the strain energy,kinetic energy and boundary spring potential energy of arbitrary triangular laminates are derived.Finally,combined with Ritz method,vibration characteristics of triangular laminates are solved.By numerical examples,the good convergence characteristics and calculation accuracy of the analysis model is verified.Meanwhile,it also can be found from the literature that it's the first time to study vibration characteristics of arbitrary triangular laminates with elastic boundary conditions,which can enrich and develop the research results of triangular laminates.(2)An analysis model for vibration characteristics of arbitrary straight quadrilateral laminates with elastic boundary conditions is established.Firstly,by introducing the four-node coordinate transformation,an arbitrary rectangular quadrilateral in Cartesian coordinate system is transformed into a unit square in natural coordinate system.Secondly,based on the first-order shear deformation theory,the strain energy,kinetic energy and boundary spring potential energy of arbitrary straight quadrilateral laminated plates in natural coordinates are derived.Then using the improved Fourier series,the displacement admissible function of equal unit square plate is constructed.Finally,using Ritz method,iterate the displacement admissible function in the strain energy,kinetic energy and boundary spring potential energy,carry out the partial differential operation,and then the structural vibration characteristic are obtained by solving the equation.The numerical results show that the established analysis model for vibration characteristics of arbitrary straight quadrilateral laminates with elastic boundary conditions has good convergence characteristics and computational accuracy.On this basis,extend the model by using the virtual coupling spring technology,and the analysis model for vibration characteristics of arbitrary laminated plate coupling structure is then established.The linear spring and torsional spring are used to simulate the coupling boundary conditions between substructures,where coupling effects of bending moment,bending force,in-plane shear force and longitudinal force are comprehensively considered,so it can ensure the continuity of displacement and rotation in three directions at the boundary.By comparing with the results from relevant literature and the Finite Element Method(FEM),the accuracy of the analysis model for vibration characteristics of arbitrary laminated coupled structures is also verified.(3)An analysis model for sound field characteristics in arbitrary triangular and quadrilateral prism enclosed acoustic cavity with an arbitrary impedance wall boundary is established.According to the coordinate transformation,arbitrary triangular and quadrangular enclosed acoustic cavity is converted into the standard isosceles right angle triangular prism and unit square prism.The unified expression for the sound pressure admissible function in a prismatic cavity is then constructed based on the improved Fourier series.On this basis,expressions of kinetic energy,potential energy,energy dissipated due to boundary and work done by the point sound source of prismatic acoustic cavity are derived further.Then the sound pressure admissible function is substituted for the above expression,and the analysis model of sound field characteristics in an enclosed acoustic cavity under arbitrary impedance wall conditions is obtained by Ritz method.The comparison with calculated results by FEM and experimental data shows the validity of the proposed model.The study expands the research sypstem in this field,since there is no relevant report in the field of closed cavity research.(4)An analysis model for vibro-acoustics characteristics of coupling system of arbitrary shaped triangular,straight quadrilateral laminates and prismatic enclosed acoustic cavity is established.Firstly,based on the study of triangular and quadrilateral laminates with arbitrary shapes and enclosed acoustic cavities with arbitrary triangular and quadrilateral prisms,their energy functions are constructed respectively.On this basis,according to the velocity continuity condition of the interface coupling,the coupling energy functional produced by the interaction between the elastic structure and the interface of the acoustic cavity is established.By superposing it with the structural energy functional and the acoustic cavity energy functional,the energy function of the acoustic-vibration coupling system is obtained.Then,the displacement admissible functions of each subsystem are constructed according to the Fourier series.By substituting the displacement admissible function into the energy functional of the system and solving the extreme value,the study of vibro-acoustics characteristics of coupled systems can be simplified to solving the equations of acoustic-vibration coupling.Similarly,the FEM results and experimental data are still used as the basis for comparison,which shows the good prediction accuracy and convergence accuracy of the analysis model.This research can be used as an extension of the research category and enrichment of the research results.since there is no relevant report in the field of the vibro-acoustics characteristics of structure-acoustic cavity coupling system.The advantages of this method are parameterization and versatility.The present method can be further extended to study the vibro-acoustics coupling system consisting of arbitrary triangular and straight quadrilateral laminates with internal openings of arbitrary shapes,closed cavities with arbitrary superimposed shapes subjected to arbitrary impedance wall conditions.Furthermore,by considering the multi-field effect,a whole set of analytical techniques for structure,enclosed acoustic cavity and vibro-acoustics coupling system can be formed,which can be used for reference in the theory and application of this field.