Vibration,Buckling And Control Analysis Of Stiffened Cantilever Plate Structures

Cantilever plate structures are widely used in aerospace,ships and naval vessels,mechanical engineering and other fields.In order to improve the stiffness,strength,stability and load-bearing capacity of cantilever plate structures,reinforcement ribs are usually attached to the plate structures.For example,aircraft wing structures are composed of cantilever plates coupled with longitudinal and transverse stiffeners.Therefore,due to the practical needs of engineering,it is of great theoretical guidance and practical application value to study and analyze the vibration characteristics and stability of ribbed cantilever plate structures in depth for the initial design of complex engineering structures.This paper covers the establishment and analysis of the dynamic model of ribbed cantilever Kirchhoff thin plate,dynamic model of ribbed cantilever Mindlin thick plate,vibration response model of flexural characteristics and static model of buckling characteristics of ribbed orthotropic cantilever Mindlin thick plate,and the theoretical model of vibration control of ribbed cantilever plate.The main research work of the thesis is as follows:(1)A dynamic model of the vibration response of a reinforced cantilever Kirchhoff thin plate is developed based on the finite integral transform technique.The finite integral transform method requires no artificial preselection of the vibration displacement functions and enables direct integration to the governing differential equations,which overcomes the boundary condition of zero torque at the free corners and solves the coupling problem of plate and beam.The effects of single rib,periodic ribs and orthogonal ribs on the vibration characteristics of the cantilever plate are analyzed using the analytical solutions obtained for the ribbed cantilever thin plate.According to the minimum inertia axis and torsion center line of the cantilever plate,the vibration mode of the cantilever plate is divided into bending vibration mode and torsional vibration mode.According to the distribution of the mode vibration shape,the position of the rib insertion,and the change of the curvature of the insertion position before and after the rib insertion,the role played by the rib in the mode vibration can be judged.The effect of the periodic ribs on the modal vibration of the cantilever plate depends on whether the mass loading effect or the stiffness enhancement effect of all the rib is dominant.If another rib is inserted in the torsion center line of the periodically ribbed cantilever plate,the ribs as a whole will show a stiffness enhancement effect.(2)As the plate thickness and study frequency increase,the vibration prediction of the model of the ribbed cantilever thin plate will produce large deviation,so a dynamic model of the vibration response of the ribbed cantilever Mindlin thick plate considering shear deformation and rotational inertia is developed using the finite integral transform method.The effects of inserting single rib in the direction parallel to the clamped edge,inserting single rib in the direction perpendicular to the clamped edge,and inserting a pair of orthogonal ribs in the plate on the frequency response and steady-state kinetic energy of the cantilever plate are investigated using the obtained analytical solutions,and it is found that the orthogonal ribs could effectively suppress the vibration of the cantilever plate.However,for cantilever plate structures such as aircraft wings,the dynamic stress concentration problem at the clamped edge is also an important factor affecting the safety of the aircraft.Therefore,the effects of inserting a rib in different coordinate directions and orthogonal ribs on the shear force distribution at the clamped edge of the cantilever plate are investigated.Finally,taking the steady-state kinetic energy and the maximum shear force of the clamped edge for the cantilever plate as the objective functions,the optimal arrangement strategy of the orthogonal ribs is obtained by using the multiobjective particle swarm algorithm to optimize the insertion position of the orthogonal ribs.(3)The effect of shear deformation on orthotropic plates is greater,and this effect becomes more severe as the degree of orthotropy becomes greater and the width-tothickness ratio becomes smaller.This is because the transverse shear modulus is comparable to the smaller elasticity modulus of plate in magnitude,so the relative shear stiffness is relatively small,and shear deformation is likely to occur in the vibration and buckling deformation of the plate.Therefore,based on Mindlin thick plate and Timoshenko thick beam theory,a complete set of mechanical models for solving the vibration response and buckling characteristics of(ribbed)orthotropic cantilever plates is established in this paper.The analytical solutions of free vibration,forced vibration,critical buckling loads and buckling modes of a ribbed cantilever plate with any number of stiffener inserted in the plate coordinate direction can be obtained.It is found that the structural stiffness and critical buckling loads of cantilever plate can be effectively improved by increasing the stiffness in the direction perpendicular to the clamped edge,and structural stiffness and buckling resistance of orthotropic cantilever plates can be improved more effectively by inserting a rib in the direction perpendicular to the clamped edge than in the direction parallel to the clamped edge.(4)An experimental platform for vibration test of cantilever plate is designed.The vibration modal tests and frequency response tests of the cantilever base plate and the ribbed cantilever plate with a stiffener in different coordinate directions are completed.The results are compared with the calculation results of the dynamic model of the vibration response of the ribbed cantilever Mindlin plate established in this paper and the finite element analysis,and it is found that the three are in satisfactory agreement.It provides another supporting proof for the accuracy of the analytical solution of the ribbed cantilever plate obtained in this paper,thus laying the foundation for the practical application of the theoretical model in engineering.(5)Based on the analysis of vibration characteristics and the propagation mechanism of structural waves of ribbed cantilever plate,the vibration control of the cantilever base plate and ribbed cantilever plate is realized by combining with elimination volume velocity method.The vibration control performance of unribbed and ribbed cantilever plate with different structural sizes is studied by several examples.The effects of single stage point force control and multistage point force control on the vibration energy of the ribbed cantilever plate and the effect of the position of the control source on the vibration control effect are analyzed.It is found that a relatively satisfactory damping effect can be obtained after vibration control of the cantilever plate structures.However,for the control system of single stage point force,the vibration control effect for frequency points of individual resonant peak is not ideal,while a multistage point force control system can perfectly solve the failure of vibration control of these resonance modes.When the ribbed cantilever plate structures are under the vibration control of single stage point force and the rib acts as the effective boundary in the process of modal vibration,the vibration reduction effect will be weakened if the rib suppresses the modal vibration of the plate surface near the control source,while the vibration reduction effect will be enhanced if the rib suppresses the modal vibration of the plate surface near the excitation source.