摘要 :
Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However...
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Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However, in large scale industrial applications, there is no general methodology for dynamicists to extract nonlinear parameters from measured vibration data so that these can be then included in the associated numerical models. In this paper, a simple method based on the information contained in the frequency response function (FRF) properties of a structure is studied. This technique falls within the category of single-degree-of-freedom (SDOF) modal analysis methods. The principle upon which it is based is effectively a linearisation whereby it is assumed that at given amplitude of displacement response the system responds at the same frequency as the excitation and that stiffness and damping are constants. In so doing, by extracting this information at different amplitudes of vibration response, it is possible to estimate the amplitude-dependent 'natural' frequency and modal loss factor. Because of its mathematical simplicity and practical implementation during standard vibration testing, this method is particularly suitable for practical applications. In this paper, the method is illustrated and new analyses are carried out to validate its performance on numerical simulations before applying it to data measured on a complex aerospace test structure as well as a full-scale helicopter.
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Structural nonlinearity is a common phenomenon encountered in engineering structures under dynamic loading. In several cases, linear theory can suffice to analyze nonlinear systems to some extent. However, there are cases where no...
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Structural nonlinearity is a common phenomenon encountered in engineering structures under dynamic loading. In several cases, linear theory can suffice to analyze nonlinear systems to some extent. However, there are cases where nonlinear effects and therefore nonlinear analysis become unavoidable. In most of the engineering applications it is usually very difficult if not impossible to model nonlinearity theoretically, especially for nonlinear effects stemming from structural connections. Then it becomes necessary to detect, localize and parametrically identify nonlinear elements from measured vibration data. In this study, two different methods, one being a method suggested recently by two of the authors of this paper, and the other being again a method developed in an earlier work, are implemented on a test rig containing a nonlinear element. Both methods are capable of parametrically identifying nonlinearities from measured frequency response functions. It is aimed in this paper to asses the validity of each method by applying them to a real test structure and thus parametrically identifying the nonlinear element in the system to obtain a mathematical model, and then employing the model in harmonic response analysis of the system in order to compare predicted responses with measured ones.
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Increased system stress has brought about the need for a better understanding of nonlinearities in power system dynamic behavior. The relationship between system stress and the nonlinearity of the differential equations should be ...
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Increased system stress has brought about the need for a better understanding of nonlinearities in power system dynamic behavior. The relationship between system stress and the nonlinearity of the differential equations should be quantified. The similarity transformation used to determine the Jordan canonical form of a linear system provides a view of the system in a 'modal' state space where the linear parts are decoupled and easily accounted for. The nonlinear system can also be transformed to the modal state space using the linear variable transformation. In the transformed state space the effects of nonlinearities and linearities are clearly separated and are expressed in terms of their effects on the system modes. Thus the nonlinear interactions between the modes are viewed directly. The effects of the nonlinearities on the modes are measured by considering the signal energy associated with the nonlinearities in the Jordan-form state space. The concept of nonlinear signal energy provides a numerical value to gauge the influence of nonlinearities on a given mode. Application to the IEEE 50-generator test system shows the relationship between interarea modes and nonlinear interactions between low- and high-frequency modes.
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This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investig...
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This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investigate the need to include higher order terms for small signal (modal) analysis. The focus of the work reported here is on establishing and documenting the practical significance of these terms in stability analysis using the method of Normal Forms. Special emphasis was placed on determining and describing conditions when higher order terms need to be included to accurately describe modal interactions. Test cases were developed on a standard test system to demonstrate the application of appropriate indices to detect the occurrence of nonlinear interaction and hence the need for higher order terms in stability analyzes. The use of the higher order terms in the site selection for a damping controller is also documented.
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摘要 :? 2018, Editorial Department of Journal of Southeast University. All right reserved.? 2018, Editorial Department of Journal of Southeast University. All right reserved. In order to consider the effect ...
展开? 2018, Editorial Department of Journal of Southeast University. All right reserved.? 2018, Editorial Department of Journal of Southeast University. All right reserved. In order to consider the effect of geometrical nonlinearity and multi-mode contributions in the pushover analysis of the seismic response of planar steel arches, a modified factored modal combination method is proposed. First, a nonlinear stiffness ratio α k is introduced to quantify the effect of geometrical nonlinearity on the initial structural frequency. Then, a limit value β is defined for selecting dominated modes, and the combined load profiles are established based on the dominated modes. Finally, the structural responses are obtained by pushover analysis based on the combined load profiles. The results of two planar steel arches with the span-rise ratio of 1/4 and 1/5 show that the modified method is convenient and effective. Compared with the results of response history analysis, when the peak ground acceleration is 0.3g, the average errors of the steel arches in the x direction peak displacement with the span-rise ratios of 1/4 and 1/5 are 2.7% and -7.2%, respectively, and -6.5% and 5.8% in the y direction. The average errors in the peak member stress are -5.0% and -4.3%, respectively. With the increase of the peak ground acceleration, the average errors of the peak displacement and the peak member stress keep stable in the x and y directions. In order to consider the effect of geometrical nonlinearity and multi-mode contributions in the pushover analysis of the seismic response of planar steel arches, a modified factored modal combination method is proposed. First, a nonlinear stiffness ratio α kk is introduced to quantify the effect of geometrical nonlinearity on the initial structural frequency. Then, a limit value β is defined for selecting dominated modes, and the combined load profiles are established based on the dominated modes. Finally, the structural responses are obtained by pushover analysis based on the combined load profiles. The results of two planar steel arches with the span-rise ratio of 1/4 and 1/5 show that the modified method is convenient and effective. Compared with the results of response history analysis, when the peak ground acceleration is 0.3g, the average errors of the steel arches in the x direction peak displacement with the span-rise ratios of 1/4 and 1/5 are 2.7% and -7.2%, respectively, and -6.5% and 5.8% in the y direction. The average errors in the peak member stress are -5.0% and -4.3%, respectively. With the increase of the peak ground acceleration, the average errors of the peak displacement and the peak member stress keep stable in the x and y directions.
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The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-perio...
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The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.
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The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled sys...
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The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.
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Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to com...
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Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources.
Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration.
Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as:
equivalent reduced model technique (ERMT);
modal modification response technique (MMRT); and
component element method (CEM);
are presented in this paper and are compared to traditional methods.
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A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedu...
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A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the first step, a multiharmonic analysis of the autonomous system is performed to directly compute the amplitude-dependent characteristics of the considered nonlinear mode. In the second step, these modal properties are used to construct a two-dimensional reduced order model (ROM) that facilitates the efficient computation of steady-state and unsteady dynamics provided that nonlinear modal interactions are absent. The proposed methodology is applied to several nonlinear mechanical systems ranging form single degree-of-freedom to Finite Element models. Unsteady vibration phenomena such as approaching behavior towards an equilibrium point or limit cycles, and resonance passages are studied regarding the effect of various nonlinearities such as cubic springs, unilateral contact and friction. It is found that the proposed ROM facilitates very fast and accurate analysis of the slow dynamics of nonlinear systems. Moreover, the ROM concept offers a huge parameter space including additional linear damping, stiffness and near-resonant forcing.
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The Smooth Decomposition (SD) is a statistical analysis technique for finding structures in an ensemble of spatially distributed data such that the vector directions not only keep the maximum possible variance but also the motions...
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The Smooth Decomposition (SD) is a statistical analysis technique for finding structures in an ensemble of spatially distributed data such that the vector directions not only keep the maximum possible variance but also the motions, along the vector directions, are as smooth in time as possible. In this paper, the notion of the dual smooth modes is introduced and used in the framework of oblique projection to expand a random response of a system. The dual modes define a tool that transforms the SD in an efficient modal analysis tool. The main properties of the SD are discussed and some new optimality properties of the expansion are deduced. The parameters of the SD give access to modal parameters of a linear system (mode shapes, resonance frequencies and modal energy participations). In case of nonlinear systems, a richer picture of the evolution of the modes versus energy can be obtained analyzing the responses under several excitation levels. This novel analysis of a nonlinear system is illustrated by an example.
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