| Generally,the cabin structure is composed of plate,shell and rib elements.It is widely used in aircraft,submarine or hull,unmanned underwater vehicle and other engineering fields.Under the external excitation,the cabin structure will produce vibration,cause structural fatigue and even damage,which will have a negative impact on production operation and safety reliability.Therefore,it is important to reveal the vibration response characteristics of the cabin structure and its substructures to study the vibration isolation and vibration reduction of the system and reduce the acoustic radiation.In this paper,the vibration characteristics of open plate,cylindrical shell,ring stiffened cylindrical shell and cabin coupling structure are studied and analyzed.By introducing Chebyshev polynomials as the displacement tolerance function of each structural member.Based on the principle of minimum potential energy and Ritz method,the theoretical solution model of vibration characteristics of the above structure is established.A series of theoretical and experimental studies on vibration characteristics are carried out.The main work is as follows:Firstly,the bending vibration characteristics of rectangular plates with complex openings under elastic boundary conditions are studied.In this paper,a Chebyshev-Ritz method is proposed to solve the bending vibration of rectangular plates with complex openings.The transverse displacement of the plate is expanded into double Chebyshev polynomials.The opening is regarded as a special film with zero physical property.The constraint spring is introduced to simulate the elastic boundary.Based on the principle of minimum potential energy,the vibration characteristic equation of open plate is constructed.Ritz method is used to solve the problem,and the natural frequency and the corresponding mode shape are obtained.The accuracy of the theoretical results is verified by comparing the theoretical results with the literature results and simulation results.The theoretical model is used to analyze the vibration characteristics of the plate,and the effects of the stiffness coefficient,the opening area and the opening shape of the restraint spring on the vibration characteristics of the plate are studied.The vibration modal test of rectangular plate with opening is carried out to verify the accuracy of the theoretical model from the experimental point of view.The results show that:(1)The maximum relative error between the theoretical results and the literature results is 1.71%,and the maximum error between the theoretical results and the simulation results is 1.85%,which verifies the accuracy of the theoretical results.(2)The influence of stiffness coefficient of normal restraint spring on the stiffness of open plate is much greater than that of torsional restraint spring;with the increase of the opening area,the fundamental frequency of the plate decreases;by changing the shape of the opening,the average change of the first two frequencies of the plate is 0.48%,and the change of the third to the sixth order is 2.35%.It shows that the change of the opening shape has little effect on the low-order natural frequency of the plate,but has a great effect on the high-order natural frequency.(3)Through the modal test,the maximum relative error between the theoretical results and the test results is 4.09%,and the deformation of the vibration pattern is basically the same.The accuracy of the theoretical model is verified from the experimental point of view.Secondly,the vibration characteristics of cylindrical shell and ring stiffened cylindrical shell under elastic boundary conditions are studied.Based on Sanders shell theory,a Chebyshev Ritz method is proposed to solve the vibration characteristics of shell under elastic boundary conditions.Four sets of constrained springs are used to simulate the elastic boundary.Chebyshev polynomials and trigonometric orthogonal functions are introduced to describe the case of shell vibration displacement.The Lagrangian equation is constructed by using the principle of minimum potential energy.Using Ritz method,the characteristic equation of vibration is derived and the theoretical modal parameters are obtained.On this basis,the ring stiffener is regarded as a discrete beam structure element,and the theoretical solution model of the vibration characteristics of the ring stiffened cylindrical shell is established by the principle of energy superposition.Compare the theoretical results with the simulation results,and verify the accuracy of the theoretical model from the perspective of simulation.The theoretical model is used to analyze the vibration characteristics of the shell.The effects of stiffness coefficient and ring rib parameters on the vibration characteristics are studied,and the forced vibration response is analyzed.Finally,the vibration modal test of the shell is carried out to verify the accuracy of the theoretical model.The results show that:(1)The maximum error in the theoretical results of cylindrical shell is 0.67%,the maximum error of ring stiffened cylindrical shell is 0.88%.Compared with the simulation results,the maximum error of the theoretical results is 1.18%,which verifies the accuracy of the theoretical model.(2)The stiffness coefficient of the circumferentially restrained spring has the greatest influence on the vibration characteristics of the shell,while that of the rotating restrained spring has the least influence on the vibration characteristics of the shell.(3)When the rib width is changed,the average change of the basic frequency of the shell is 5.55%,and when the rib height is changed,the average change is 14.97%.Therefore,the influence of the rib height on the vibration characteristics is greater than that of the rib width.(4)Through the modal test,the maximum relative error between the theoretical results and the test results is 0.47%,and the vibration mode is in good agreement.The accuracy of the theoretical model is verified from the experimental point of view.Finally,the vibration characteristics of coupled cabin structure are studied.In order to solve the problem of the vibration characteristics of the coupled cabin structure under the elastic boundary condition,the theoretical model of the vibration characteristics of the coupled cabin structure is established by using the principle of minimum potential energy and Ritz method.Two sets of displacement admissible functions based on Chebyshev polynomials are used to describe the displacement of the opening plate and the shell respectively.Four sets of coupled springs are used to simulate the displacement effect of plate shell coupling boundary.The elastic boundary conditions of plate and shell are simulated by boundary constrained spring.The accuracy of the theoretical results is preliminarily verified by simulation.The vibration characteristics of the coupled structure are analyzed by using the theoretical model,and the effects of the coupling angle and the opening size on the vibration characteristics of the structure are studied.Design and build the vibration test platform of the cabin coupling structure,carry out the modal test research,compare and analyze the test results and theoretical results,and verify the accuracy of the theoretical model from the experimental point of view.The results show that:(1)Compared with the numerical simulation results,the maximum error of the first eight frequencies is 1.97%,and the modal results are in good agreement,which verifies the accuracy of the theoretical model.(2)The natural frequencies of the coupling structure increase with the increase of the coupling angle.The low-order natural frequencies of the coupling structure increase with the increase of the opening on the coupling plate.(3)Through the modal test research,the maximum relative error between the theoretical results and the experimental results is-6.71%,and the vibration patterns of each stage are basically the same.The accuracy of the theoretical model is verified by experiments. |
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