Nonlinear Vibration Suppression Of Composite Beam Using NiTiNOL-Steel Wire Ropes

NiTiNOL-steel wire rope is a new type of vibration absorber which is made of shape memory alloy wire and steel wire.It has rich nonlinear dynamic characteristics and can provide nonlinear stiffness and hysteretic damping for the system.The great performance of NiTiNOL-steel wire rope for vibration reduction and vibration isolation has been proved by scholars.It has a wide application in aerospace vibration suppression and earthquake resistance.With the development of material science,laminated beams,plates,shells and other composite structures are increasingly used in these fields.It is urgent to develop a method of analysing the composite structures embedded with NiTiNOL-steel wire rope and study the effect of vibration suppression.Therefore,the complex dynamic behavior of composite laminated beam embedded with NiTiNOL-steel wire rope is thoroughly studied in this paper.The specific research contents are organized as follows:Based on the classical Euler beam theory,a laminated beam model embedded with NiTiNOL-steel wire rope is established.The damping force of NiTiNOL-steel wire rope is described via the Bouc-Wen model.The low order polynomial models of the nonlinear restoring and damping forces are derived by fitting the experimental results.Galerkin truncation method,harmonic balance method and arc length method are used to obtain the dynamic equations describing the nonlinear frequency domain characteristics of the system.The numerical results are obtained by the fourth order Runge-Kutta method,and the correctness of the approximate analytical solution is verified.Based on the frequency response curve of the system,the vibration suppressing effect of various configurations of NiTiNOL-steel wire ropes is analyzed.The relationships between the amplitude of the external excitation,the parameters in the polynomial model and the dynamic characteristics of the laminated beam are discussed respectively.The results show that the vibration amplitude of the laminated beam can be effectively reduced by the NiTiNOL-steel wire rope.The domain decomposition method is carried out.The decomposed energy function of a laminated beam embedded with NiTiNOL-steel wire rope is established via the generalized variational principle.The discrete nonlinear governing equations of laminated beams are obtained through the variational function extremum method.The harmonic response analysis of decomposed laminated beams is carried out and the analytical results are compared.A method combining Newmark method and direct iteration is applied for the time-domain response of the system,and the vibration suppression effect of NiTiNOL-steel wire rope on the laminated beam under different excitation frequencies is analyzed.The performances of different NiTiNOL-steel wire ropes are similar with the results in Chapter 2.By comparing the numerical results with results in Chapter 2,the correctness of the domain decomposition method is verified.The vibration and noise reduction effect of a beam excited by a period of given Gaussian white noise with limited bandwidth is studied.The beam is based on the highorder shear deformation theory and embedded with different types of NiTiNOL-steel wire ropes.The decomposed governing equation of the beam is established by using the domain decomposition method.The necessity of using the high order shear deformation theory is explained with modal analysis.The limited bandwidth white noise with different sound pressure levels is generated via inverse Fourier transforming and its loading mode is discussed.Newmark method is applied to solve the dynamic response of the system,and the suppression effect of NiTiNOL-steel wire rope under acoustic load is verified.The results show that NiTiNOL-steel wire rope has a certain application value in vibration suppression of composite structures under vibro-acoustic excitation.