摘要 :
There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by usi...
展开
There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techniques available for linear structures, unless they work in linear range. Well-established frequency response function (FRF) based model updating methods would easily be extended to a nonlinear system if the FRFs of the underlying linear system (linear FRFs) could be experimentally measured. When frictional type of nonlinearity co-exists with other types of nonlinearities, it is not possible to obtain linear FRFs experimentally by using low level forcing. In this study a method (named as Pseudo Receptance Difference (PRD) method) is presented to obtain linear FRFs of a nonlinear structure having multiple nonlinearities including friction type of nonlinearity. PRD method, calculates linear FRFs of a nonlinear structure by using FRFs measured at various forcing levels, and simultaneously identifies all nonlinearities in the system. Then, any model updating method can be used to update the linear part of the mathematical model. In this present work, PRD method is used to predict the linear FRFs from measured nonlinear FRFs, and the inverse eigensensitivity method is employed to update the linear finite element (FE) model of the nonlinear structure. The proposed method is validated with different case studies using nonlinear lumped single-degree of freedom system, as well as a continuous system. Finally, a real nonlinear T-beam test structure is used to show the application and the accuracy of the proposed method. The accuracy of the updated nonlinear model of the test structure is demonstrated by comparing the calculated and measured nonlinear FRFs of the test structure at several different forcing levels.
收起
摘要 :
In this work, we use a special nonlinear dependence of dielectric permittivity to study theoretically the effect of a decrease in the nonlinear response in near-surface layers of a medium, which occurs with an increase in the ampl...
展开
In this work, we use a special nonlinear dependence of dielectric permittivity to study theoretically the effect of a decrease in the nonlinear response in near-surface layers of a medium, which occurs with an increase in the amplitude of the electric field. We propose a model of nonlinearity in which the Kerr-type nonlinearity abruptly disappears with an increase in the field, and the dielectric permittivity becomes constant and independent of the field. Increasing the electric field leads to the formation of a local zone (optical domain) near the surface with linear optical properties where the dielectric permittivity becomes independent of the electric field. We formulate a nonlinear equation with stepwise dependence of the dielectric permittivity on electric field, and obtain its two types of exact solutions corresponding to the surface waves in media with positive (self-focusing) and negative (defocusing) nonlinear responses. We calculate and analyze the total power flows of thesurface waves of both types. We discuss in detail the features of the obtained solutions in comparison with previously published results. It is shown that the choice of a crystal with an appropriate nonlinear response makes it possible to increase or decrease the field intensity near the crystal surface with practically the same thickness of the near-surface layer with altered optical properties.
收起
摘要 :
In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member ...
展开
In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member forces. The geometric nonlinearioty includes the second-order effects associated with P-δ and P-△. The material nonlinearity at a section is considered using the concept of the P-m hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability functions. The modified incremental displace- ment method is used as the solution technique. The load-displacement relationships predicted by the proposed analysis compare well with those given by other approaches.
收起
摘要 :
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and ...
展开
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
收起
摘要 :
In the present paper, we describe theoretically the disappearance of self-focusing nonlinear response in the layers near the crystal surface with totally shielding cover due to the electric field variation. The regularities of the...
展开
In the present paper, we describe theoretically the disappearance of self-focusing nonlinear response in the layers near the crystal surface with totally shielding cover due to the electric field variation. The regularities of the formation of a linear near-surface layer due to an increase in the field strength are described. The five types of surface waves from nonlinear wave equation satisfying five different sets of boundary conditions are found. The power flows carried by surface waves are calculated for each type of waves in order to analyze the energy redistribution that occurs in the near-surface layers due to the wave propagation. It is found that the redistribution of the surface wave energy between the crystal regions is possible by varying the surface amplitude, surface gradient or gradient of the field at the domain boundary.
收起
摘要 :
Accurate formulas for obtaining the energy, velocity and displacement decay envelopes in purely nonlinear damped oscillators are presented here. These purely nonlinear oscillators have no linear stiffness components, and the new f...
展开
Accurate formulas for obtaining the energy, velocity and displacement decay envelopes in purely nonlinear damped oscillators are presented here. These purely nonlinear oscillators have no linear stiffness components, and the new formulas derived in this paper are found to be highly accurate in determining the decay envelopes, regardless of the system's physical parameters and its initial condition. The mechanism of these new formulas for obtaining the decay envelopes of the nonlinear oscillators is found to be exactly the same as the mechanism of the well-known amplitude decay formulas used for the linear oscillator. Finding such formulas is significant to many scientific applications of these nonlinear oscillators, such as the passive targeted energy transfer through the stiffness-based nonlinear energy sinks (NESs). In these types of NESs, these formulas can be easily applied for system identification and dynamic analysis. In addition, they are expected to have a significant application in different scientific fields for such oscillators.
收起
摘要 :
In this paper, we theoretically study propagation of steady-state ultrashort pulse in dissipative medium. We considered two cases: 1) medium consisting of lossy metallic nanostructures embedded into a gain material and 2) the gai...
展开
In this paper, we theoretically study propagation of steady-state ultrashort pulse in dissipative medium. We considered two cases: 1) medium consisting of lossy metallic nanostructures embedded into a gain material and 2) the gain material is embedded directly into the nanostructures. We found the shape and the velocity of an optical pulse coupled with the polarization wave.
收起
摘要 :
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...
展开
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.
收起
摘要 :
Given a linear semi-bounded symmetric operator , we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators of type (i.e., generators of one-parameter continuous nonlinear semigroups of cont...
展开
Given a linear semi-bounded symmetric operator , we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators of type (i.e., generators of one-parameter continuous nonlinear semigroups of contractions of type lambda) which coincide with the Friedrichs extension of S on a convex set containing the domain of S. The extension parameter ranges over the set of nonlinear maximal monotone relations in an auxiliary Hilbert space isomorphic to the deficiency subspace of S. Moreover, is a sub-potential operator (i.e., the sub-differential of a lower semicontinuous convex function) whenever is sub-potential. Applications to Laplacians with nonlinear singular perturbations supported on null sets and to Laplacians with nonlinear boundary conditions on a bounded set are given.
收起
摘要 :
The objective of this study is to develop, simulate and verify experimentally a model of a nonlinear spring, based on the principle of a cantilevered beam with a mass on its tip, and whose overall lateral vibration is constrained ...
展开
The objective of this study is to develop, simulate and verify experimentally a model of a nonlinear spring, based on the principle of a cantilevered beam with a mass on its tip, and whose overall lateral vibration is constrained by a specially shaped rigid boundary. The focus here is the use of this spring for vibration reduction applications. The modeling approach uses concepts of plane kinematics of rigid bodies, combined with quasi-static analysis to develop suitable equations of motion for a base-excited spring with a ninth-order geometric nonlinearity. In addition, a parametric identification procedure is implemented for obtaining the required coefficients for computational simulations. An approximated analytical solution to the model is completed with the aid of the method of harmonic balance and its stability is assessed through Floquet theory. Finally, the model is experimentally verified, with the use of two specimens, fabricated specifically for this study. The model, simulations and experimental measurements show the hardening and broadband behavior of the nonlinear spring.
收起
原文获取