Study On Dynamic Characteristic Analysis And Modal Modification Method Of Shafting System

Shafting system as an important part of the ship,the stability of its dynamic performance is an essential prerequisite to ensure the safe operation of the ship.At the same time,shafting as its key components,its dynamic characteristics are very important for the low noise design of the ship.Therefore,the research on the dynamic characteristics and the exploration of the law of shafting has always been one of the important research topics in the field of ship engineering.With the development of high-tech ships,shafting system becomes more and more complex.Shafting with multiple auxiliary structures and supporting structures becomes particularly common.The research on the dynamic characteristics of such complex shafting system is still insufficient: there are inevitable differences between the numerical model and the actual structure,and the vibration control methods of complex shafting need to be further studied.For this reason,the dynamic characteristics of the complex shafting and its supporting system are analyzed,and a feasible method for vibration control of the complex shafting is proposed.This paper mainly focuses on the analysis of natural vibration characteristics and forced vibration characteristics of shafting with auxiliary structures and elastic supports,the correction of partial eigenvalues of complex shafting,and the analysis of the bending and torsion coupling characteristics of the axially loaded Timoshenko beam considering the effect of warpage.The specific research contents are as follows:Firstly,based on Hamilton's principle,the differential equations of motion of a continuum with multiple auxiliary structures and elastic supports are derived to study the vibration characteristics of a shafting system with multiple concentrated inertia elements and elastic supports.Then,combining the variable separation method and the Laplace transform method,the analytical solution expression of the natural characteristics of the torsional free vibration of the shaft system with auxiliary structures and elastic supports is obtained.The accuracy of the results of this paper is verified by comparison with the calculation results of the known literature and the experimental results.Finally,the calculation results of the method in this paper are compared with the calculation results of the lumped mass method and the finite element method.The results show that the accuracy of the natural frequency results calculated by the lumped mass method is more dependent on the number of discrete inertias.In other words,to get the higher order natural frequency,the number of discrete inertias needed to be more,and the accuracy of some shafting modes calculated by the lumped mass method is obviously insufficient.For the finite element method,in order to get the same accuracy as the method in this paper,we need to use high-precision interpolation function,and the number of elements should be as many as possible,and the shaft segment should be divided as evenly as possible.Then,a new method based on Laplace-Fourier integral transformation is proposed,which can successfully obtain the analytical solution of the torsional forced vibration of a shaft with multiple any size of concentrated inertia and elastic support at any position under any boundary condition and any excitation form.By comparing with the results of the eigenfunction expansion method and the finite element method,it is fully proved that the method has good convergence and the operation speed is better than the two methods.Finally,the effects of some parameters,including the stiffness and position of the elastic support and the time interval of the impact load,on the torsional forced vibration of the shafting are discussed.Then,based on the Lanczos method and the gradient flow method,the distribution of partial eigenvalues in the torsional vibration control of the complex ship propulsion shafting is studied.Through a simplified model of a "real" marine diesel engine propulsion system,three different shafting torsional vibration control schemes are given.Through the comparison of the two methods,it is found that although the Lanczos method can achieve the goal of redistributing part of the natural frequencies of the complex system,the method is greatly affected by the initial value,which will cause large differences in the calculation results,and sometimes appear no solution.In addition,this method cannot realize the correction of the inertia and stiffness of a specific position.In most cases,all relevant parameters can be changed to realize the partial distribution of natural frequencies,which cannot meet the needs of actual system structure modification.The gradient flow method can realize the distribution of partial natural frequencies by modifying the inertia and stiffness values of specific positions in the system,while keeping the inertia and stiffness values of other designated positions unchanged.Therefore,it is more suitable for the natural frequency correction of the actual system than the Lanczos method.In addition,the gradient flow method can also realize the correction of the eigenvalues of the structural parts with similar natural frequencies.This fully shows that the gradient flow method is effective and feasible in solving the partial frequency distribution problem of the torsional vibration of the complex shafting.Finally,based on the Green function method,the flexural-torsional coupled vibration response of Timoshenko beam subjected to axial force under the influence of warping stiffness and damping is studied.Firstly,without considering damping,the inherent characteristics of the beam are calculated by ignoring the effects of warpage,moment of inertia,shear stiffness,and axial force,respectively,and compare them with known literature to fully demonstrate the method in this paper.The correctness of the results can also see the influence of warping stiffness and axial force on the inherent characteristics of the beam.Then,by comparing the degenerated model with the known literature,the effectiveness of the model and method in calculating the forced vibration response is demonstrated.Finally,the influence of warping stiffness,damping and axial force on the vibration response characteristics of the beam is further analyzed.