Propagation Of Waves In Variable-Section Rods With A Random Rough Surface

During the service life of a component,defects in the surface of the component may be caused by wears and corrosions.These defects may reduce the performance of components and thus lead to the failure of components.Surface roughness,as a component defect,has a non-negligible effect on the wave propagation behaviors in components.In order to understand the wave propagation in components with rough surfaces,it is necessary to carry out a systematic study.In this thesis,the propagation of compressional and torsional waves in a variable-section rod with a random rough surface is investigated from both theoretical and numerical ways by combining the perturbation method and the fast Fourier transform.The main contents read:Firstly,a numerical model of a variable-section rod with a random rough surface is developed.A random rough surface satisfying the Gaussian distribution with the root mean square of height and correlation length as statistical parameters is reconstructed via a linear filtering process.The root mean square of height controls the roughness of the rough surface in the vertical direction,and correlation length governs the roughness of the rough surface along the longitudinal direction.Secondly,the corresponding governing equations with a random discrete sequence of source terms are solved by combining the perturbation method and the fast Fourier transform.The nonlinear wave equations with random discrete sequences are decomposed into the zero-order,the first-order and the second-order equations related according to the small parameters in the perturbation method.The zero-order equation is the governing equation of the corresponding smooth rod,the first-order and second-order equations are related to the rough surface.The discrete perturbation solutions of these three equations are obtained sequentially by the sampling theorem and the discrete Fourier transform.Thirdly,propagations of compression waves in a tapered rod with a random rough surface are investigated.Geometrical and physical scale relationships involved in the tapered rod are determined.The corresponding finite element model is built in ABAQUS.The discrete perturbation solution to the problem of compression waves are solved numerically by using the fast Fourier transform.Relative deviations between the perturbation solution and the finite element solution are compared,and the validity of the present solutions is verified.The range of the small parameters is determined.Effects of the root mean square of height and correlation length on the amplitudes of compression waves are discussed.Finally,propagations of torsional waves in a variable-section rod with a random rough surface are investigated.Geometrical and physical scale relationships involved in the quadratic radical rod are determined.The corresponding finite element model is built in ABAQUS.The discrete perturbation solution to the problem of torsional waves are solved numerically by using the fast Fourier transform.Relative deviations between the perturbation solution and the finite element solution are compared,and the validity of the present solutions is verified.The range of the small parameters involved in the torsional wave is determined.Effects of the root mean square of height and correlation length on the amplitudes of torsional waves are discussed.