Research On Nonlinear Dynamics Of Two Types Of Fluid-Solid Coupling System

Pipes conveying pulsating fluid and moving plates immersed in liquid are two types of fluid-solid coupling system,which have been widely used in engineering fields.Fluid-conveying pipes exist in the fields of aerospace engineering,nuclear industry,submarine pipeline engineering,hydrodynamic engineering and so on.The nonlinear oscillations of the pipes conveying pulsating fluid will lead to the damage of the system under serious conditions,so it is being paid more and more attention in engineering practice.Additionally,axially moving plates is a kind of common engineering structures.In marine engineering and mechanical engineering,axially moving plates often contact with liquid,which results in fluid-structure coupling vibrations.With the rapid development of science and technology,and the continuous development and perfection of nonlinear dynamics theory,more and more researchers start focusing their attention on the nonlinear oscillations of fluid-conveying pipes and immersed moving plates,and have found some new nonlinear phenomena.In this dissertation,the multiple scale method,Galerkin method and energy-phase method are used to analyze the nonlinear vibration characteristics of vertical cantilever fluid-conveying pipes under parametric and external excitations.Additionally,the parametric vibration and nonlinear vibration of axially moving rectangular plates immersed in liquid are studied.The main contents consist of the following parts:(1)In view of the nonlinear dynamics of a cantilever fluid-conveying pipe under the joint action of parameter excitation and external excitation,the geometric nonlinearity and the viscoelastic constitutive relation of the pipe are considered.The dynamic model of the vertical cantilever fluid-conveying pipe under the joint action of pulsating flow and lateral load is established by using the Hamilton principle.(2)In the cases of principal parametric resonance,1/2 subharmonic resonance and 1:2 internal resonance,the method of multiple scales and Galerkin's method are employed to transform the partial differential governing equation of motion to the averaged equations in the Cartesian coordinate form.The amplitude-frequency curves of the cantilevered pipe conveying pulse fluid are obtained by using numerical simulations.The bifurcation diagram,planar phase portrait,three-dimensional phase portrait,waveform and frequency spectrum of the averaged equations are obtained.The influence of parametric and external excitations on the nonlinear vibration of cantilevered pipe conveying pulse fluid is studied.When the other parameters of the system are fixed and only the fluid velocity or excitation frequency is changed,the system presents the alternating law of periodic motion and chaotic motion.The resonance response curve of the nonlinear system contains jump and saturation phenomenon,and the curve has multiple solutions.(3)The method of multiple scales and Galerkin's method are employed to analyze the partial differential governing equation of motion of the fluid-conveying pipe.The average equations in the cases of 1:3 internal resonance and principal parameter resonance are obtained.The amplitude-frequency equations of the system are derived and the resonance response is studied.The bifurcation diagram,phase diagram,waveform diagram and Poincare section diagram of the system are obtained by numerical simulation of the average equation.The results show that the system has the characteristics of hard spring.The amplitude-frequency curve shows jump phenomenon,and the nonlinear motion form is complex.With the increase of fluid velocity or external excitation,the system can exhibit periodic motion and chaotic motion alternately.(4)The multi-pulse orbit and chaotic dynamics of a cantilever pipe conveying pulsating fluid under the action of simple harmonic excitation and pulsating inner flow are studied using the energy-phase method for the first time.The nonlinear governing equation of motion of the system is determined using the Hamilton principle.The four-dimensional average equations in the cases of primary parametric resonance,1/2 sub-harmonic resonance and 1:2 internal resonance are obtained by using the method of multiple scales and Galerkin approach.Then,the normal form theory is used to simplify the averaged equations.Based on the normal form,it is found that there is a multi-pulse chaotic jump phenomenon in the system.Numerical simulation results also verify the existence of multi-pulse chaotic jump in the cantilever fluid-conveying pipe.Combining the theoretical and numerical results,the existence of chaotic motion in the sense of Smale horseshoe in the fluid-conveying pipe is proved.(5)An axially moving viscoelastic plate immersed in liquid,which have variable speed,is considered.According to the classical thin plate theory and d'Alembert's principle,the governing equation of the transverse vibration of the system is derived.The liquid is assumed as ideal fluid and thus is inviscid,irrotational,and incompressible.The dynamic pressure of fluid on the plate can be described by the added mass.The partial differential equations and boundary conditions of the system are analyzed by the method of multiple scales.Based on the solvability conditions and the Routh-Hurwitz criterion,the instability regions for sum-type and difference-type combination resonances of the system are determined.The effects of different parameters on the instability regions of the two kinds of combination resonance are discussed.(6)Based on the classical thin plate theory and von Karman nonlinear geometrical relationships,the nonlinear vibrational differential equations of a vertically moving rectangular plate immersed in liquid is derived.The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the moving plate.The system is solved by applying directly the method of multiple scales to the nonlinear partial-differential equations.Based on the solvability condition,the nonlinear frequencies of the system are obtained.The 1:1 and 1:3 internal resonances of moving plate-fluid system are investigated.The effects of system parameters on the nonlinear dynamic characteristics of the fluid-structure coupling system are discussed in detail.