Research On Structural Nonlinear Dynamics Of Frictional Joints

As an important form of mechanical joints for fastening, frictional joints arewidely used in the structures of vehicles and other industrial products. In fact, thistype of connections are not fully tightened, for slipping often take place on thecontact interface during vibration of the structure, which may have an importantimpact on loads transfer between substructures as well as the mechanicalcharacteristics of the composed whole structures. In this thesis, the nonlinearvibration of the structures under the influence of the slipping on the interface offrictional joints is concerned. The solution methods for nonlinear vibration of aseries of vibration systems, including oscillators, beams and a high-dimensionalself-excited vibration system with Iwan model, which can be used for friction jointsmodeling, will be deeply studied in this thesis. The main contents of the thesis are asfollows:When the joint is modeled by a discrete Iwan model, the correspondingvibration systems shows piecewise linear hysteresis nonlinear characteristics. Forsuch nonlinear systems, we proposed an analytical method to calculate the vibrationresponse of the system. In the method, when the general analytical expression of thesolution for each linear phase is obtained, by the continuity of displacement and ve-locity, substituting the parameters of each linear phase into the analytical expressionsequentially during the vibration process, then the solution of entire time domain isconstituted. For an oscillator with a discrete Iwan model, by variable substitution,the equation of motion for arbitrary linear phase can be transformed into the formwhich can be solved analytically. For an continuious beam with an piecewise linearhysteresis boundary modeled by a discrete Iwan model, by displacement conversion,the piecewise linear hysteresis boundary problem is then converted into linearboundary problem which can be solved by linear vibration theory. The results ofnumerical examples show that, as the excitation magnitude increases, slipping onthe friction surface would take place, which makes the peaks of ampli-tude-frequency curves left drifted as well as damping enhancement. Finally, The ra-tionality of frictional joint modeling and the calculation results is verified by a sinesweep vibration test of the beam model in a vibration shaker.The continuous Iwan model, which contains infinite number of Jenkinselements, is more appropriate to depict the microslip on the frictional interfaces ofstructures. Based on the expressions of restoring force of the continous Iwan model,we solved the nonlinear vibration problems of a dry friction oscillator with continuous Iwan model. For the free vibration problem, the half-harmonic motioncorresponding to each monotone loading/unloading movement independently isanalyzed, then based on the harmonic balance method, the analytical solution of thesystem response is obtained. For the forced vibration of the oscillator undermicrosilp, on the basis of the harmonic balance, the amplitude-frequency relation-ship as well as the nonlinear relationship of damping and the vibration amplitude areboth obtained. Simulation results show that the numerical results agree well withthose of analytical solutions, which verified the validity of the both methods.The nonlinear vibration of a clamped-clamped beam with microslip at one endunder harmonic base excitation is also studied. When the slip is small, the hysteresisforce at the nonlinear boundary can be rewritten in a form containing a smallparameter. Taking into account that hysteresis boundary condition which describedIwan model containing displacement amplitude items, we expand both thedisplacement and its amplitude into a power series of the small parameter. Then, bythe method of multiple scales, the second-order approximate solution and theamplitude-frequency relationship of system’s primary resonance are obtaind. Andbased on Lyapunov linearity stability theory, the stability boundary of the responseof the system is derived. Simulation results show that an unstable multi-valuedregion would arise in the frequency response curve when the excitation amplitude,viscous damping and joint stiffness are in a specific range. When the slip is large,the governing equation and the nonliear boundary condition are reconstructed, thenamplitude-frequency relationship can be obtained by the first harmonic balancemethod. The simulation results show that there are no unstable region in theamplitude-frequency for the significant influence of the friction damping.In the final chapter of the thesis, the Iwan model is introduced for modeling thehysteresis nonlinearity in a class of high-dimensional self-excited system. Whensolving the high-dimensional nonlinear differential equations by the higher orderharmonic balance method, as the number harmonic terms increases, the dimensionsof the harmonic balance equations wound increase manyfold, which makes it toughto solve the equtions directly. For this problem, an strategy for init valuesdetermination is proposed. In the strategy, the results of the first order harmonicsolution are considered as the initial values of the corresponding coefficients of thehigh order harmonic solutions, and the initial value of the higher order harmonicscoefficients are assigned to zero. This strategy is verified by seccessfully solving ofthe limit cycle oscillations of an airfoil with an external store under microslip.