Vibration Transfer Path Analysis And Response Prediction For Multi-point-coupled Mechanical Systems

In order to reduce the vibration and noise of products,it is necessary to analyze the vibration characteristics of mechanical structures and modify the structures base on the analysis.Modern mechanical products are often composed of many parts,which are assembled together in a certain way.Generally speaking,such a mechanical structure can be regarded as a multi-point-coupled system.There are many available theories to address the dynamics of multi-point-coupled systems.Transfer path analysis(TPA)is a widely used method in engineering to analyze the vibration transfer characteristics.By analyzing the contribution of each transfer path to the total response,the most important transfer path can be found to improve the structure.The efficiency of product design will be greatly improved if the dynamic characteristics of products,especially the dynamic response,can be predicted directly before the products are manufactured.Response prediction can also effectively evaluate the quality of the structural modification.Therefore,the combination of TPA and response prediction technologies can solve many key problems related to vibration and noise in engineering.There are still many shortcomings in the existing TPA and response prediction techniques.For example,the implementation efficiency of TPA is relatively low;some improved methods improve the efficiency while reducing the accuracy of the analysis;and response prediction technology needs to measure the dynamic forces,etc.These problems have caused some practical difficulties in the applications.This paper mainly focuses on some problems in TPA and response prediction techniques and carry out in-depth research on multi-point-coupled system dynamics.The main work of this paper are summarized as follows:(1)In order to solve the problem that the passive part needs to be removed from the structure when measuring the frequency response functions(FRFs)from the coupling points to the target response points in TPA,which greatly reduces the implementation efficiency,the relationship between the FRFs of the subsystem and the FRFs of the coupled system is addressed in detail.The so-called virtual decoupling method is proposed.The proposed method allows to obtain the FRFs of subsystems directly from the measured FRFs of the coupled system without disassembling the coupled structure.(2)In this paper,the existing operational transfer path analysis(OTPA)methods are investigated deeply.The concept and properties of transmissibilities are discussed in detail,and an improved OTPA method based on the response differences between active and passive coupling points is proposed.The path contributions calculated by the improved method have the same physical meaning as those in classical TPA,while the test process of the improved OTPA is similar to that of OTPA.This method can greatly reduce the path crosstalk in OTPA.The test accuracy is higher than that of OTPA,and the implementation efficiency is higher than that of classical TPA.(3)In order to avoid measuring the blocked forces of subsystems in the existing component TPA method,an advanced component TPA method is proposed.The proposed method can predict the responses of a coupled system according to the blocked responses and the transmissibility matrices of the subsystems.Compared with the classical component TPA,the proposed method only needs to measure the blocked response and transmissibility matrices of the subsystems,and does not need to measure the blocked force and FRF matrices.Hence,the proposed advanced component TPA method completely avoids the measurement of forces,which makes the test process easier.(4)The physical meaning of the coupling problem is successfully explained by making use of the Neumann series.The couplings of mechanical systems are usually represented mathematically as the non-zero elements on the non-diagonal of the dynamic stiffness matrix.However,it is difficult to explain this problem in physics.In this paper,the responses of coupled systems are expressed as the form of the Neumann series.Each term in the Neumann series represents the contribution of corresponding order’s vibration transfer to the final responses.This interpretation is of great significance to understand the nature of coupling problems.(5)In this paper,the issue of structural modification is addressed in detail.The method of predicting the modified structural responses based on the known structural responses and local structural modification characteristics,is proposed systematically.First,seven typical cases of structural modification are introduced and investigated.Then,these seven typical cases of modifications are considered equivalent to some additional forces which can be expressed by the dynamic characteristics of the modifications and the responses of the new structure.Finally,the dynamic response expressions of the new structure can be easily obtained by substituting the equivalent additional force expressions into the system dynamic equation.This paper not only investigates the case of single modification,but also discusses how to predict the responses of modified structures when multiple modifications are made at the same time.(6)Based on the research of structural modification,the issues of coupling and decoupling are discussed again.To some extent,a coupled system composed of two subsystems can be regarded as the outcome of modifying one of the subsystems.Similarly,the decoupling problem can also be regarded as a special structural modification problem,that is,subtracting a part from the whole structure.The response relationship between the coupled system and its subsystems is derived,and then their FRF relationship is obtained.By analyzing the expression of the responses of coupled structures,it is found that the responses of a coupled system can also be expressed in terms of the Neumann series.Thus,the coupling and decoupling problems are analyzed more deeply.In summary,this paper systematically addresses some key issues of TPA and response prediction for multi-point-coupled systems.The research results are of great value for the analysis of vibration and noise problems in engineering.At the same time,this paper also improves and complements the relevant theories of multi-point-coupled system dynamics.