A UNIVERSAL MATRIX PERTURBATION TECHNIQUE FOR COMPLEX MODES

A universal matrix perturbation technique for complex modes is presented. This technique is applicable to all the three cases of complex eigenvalues: distinct, repeated and closely spaced eigenvalues. The lower order perturbation formulas are obtained hy performing two complex eigensubspace condensations, and the higher order perturbation formulas are derived hy a successive approximation process. Three illustrative examples are given to verify the proposed method and satisfactory results are observed.

Complex modes and traveling waves in axially moving Timoshenko beams

Complex modes and traveling waves in axially moving Timoshenko beams are studied. Due to the axially moving velocity, complex modes emerge instead of real value modes. Correspondingly, traveling waves are present for the axially moving material while standing waves dominate in the traditional static structures. The analytical results obtained in this study are verified with a numerical differential quadrature method.

Extraction of real modes and physical matrices from modal testing

A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.

A NEW MATRIX PERTURBATION METHOD FOR ANALYTICAL SOLUTION OF THE COMPLEX MODAL EIGENVALUE PROBLEM OF VISCOUSLY DAMPED LINEAR VIBRATION SYSTEMS

A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.

Complex Mode Frequency Iteration Method for Flutter Analysis of 2-DOF Systems

For a vibration system with 2 DOF of bend and torsion, its critical flutter wind speed can be calculated by using complex mode frequency iteration (CMFI) method based on MatLab 5.2, the results of which are in agree with those acquired by wind tunnel test. Not only critical flutter wind speed, but also vibration characteristic of a system under different wind speeds can be determined. CMFI method is suitable for both of separated flow torsional flutter and classic coupling flutter analysis, which is presented by flutter analysis of an ideal thin plate and a bluff bridge deck. Furthermore, it is proved through the investigation of the relationship between flutter derivatives and its critical flutter wind speed that coupling aerodynamic derivatives are necessary for classic coupling flutter to occur.]

COMPLEX NUMBER MODE APPROACH FOR REDUCING VIBRATION OF STRUCTURAL FLEXIBLE REDUNDANT ROBOT MANIPULATORS

A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify the modal exciting force of flexural motion, and the approach can be freely used when the degree of freedom of flexural motion is much greater than the available degree of reundancy. The availability and effectiveness of the proposed approach are demonstrated through numerical simulation with a four link spatial robotic manipulator possessing an end flexible link.

A New Fuzzy Controlled Antenna Network Proposal for Small Satellite Applications

This research contributes to small satellite system development based on electromagnetic modeling and an integrated meta-materials antenna networks design for multimedia transmission contents.It includes an adaptive nonsingular mode tracking control design for small satellites systems using fuzzy waveless antenna networks.By analyzing and modeling based on electromagnetic methods,propagation properties of guided waves from metallic structures with simple or complex forms charge partially or entirely by anisotropic materials such as metamaterials.We propose a system control rule to omit uncertainties,including the inevitable approximation errors resulting from the finite number of fuzzy signal power value basis functions in antenna networks.Moreover,both the stability and the tracking performance of the closed-loop robotic system are experimentally validated.The research lies within the scope of the improvement of speed,effectiveness,and precision of numerical methods applied to electro-magnetic modeling with complex structures,essentially rectangular metallic waveguides filled with isotropic or anisotropic metamaterials.Three axes of our research are presented:waveguides,filters,and antennas.The proposed controller does not require prior knowledge about the dynamics of the fuzzy system controller for antenna networks or the offline learning phase.In addition,this work contributes to solving the problem of non-visibility stations to ensure data transmission in wireless networks.The proposed solution maximizes inter-connection by using a fuzzy controlled antenna network,and the novelty guarantees nonlimited interconnection in wireless networks compared to traditional methods.

Application of complex nonlinear modes to determine dry whip motion in a rubbing rotor system

Dry whip motion is an instability of rubbing rotor system and may cause catastrophic failures of rotating machinery.Up to now,the related mechanisms of the dry whip is still not well understood.This paper aims to build the relationship between the complex nonlinear modes and the dry whip motion,and propose an effective method to predict the response characteristics and existence boundary of the dry whip through complex nonlinear modes.For the first time,the paper discusses how to use the complex nonlinear modes to predict the dry whip systematically,and as a consequence,the mechanism of the relationship between the complex nonlinear mode and the dry whip is revealed.The results show that the Backward Whirl(BW)mode motion of the rubbing rotor system dominates the response characteristics and the existence boundary of dry whip.The whirl amplitude and whirl frequency of dry whip are equal to the modal amplitude and modal frequency of the BW mode at the jump up point where the modal damping is equal to zero.The existence boundary corresponds to the critical rotation speed where the minimum of the modal damping of the BW mode motion is exactly equal to zero.Moreover,the proposed nonlinear modal method in this article is very effective for the prediction of dry whip of the more complicated practical rotor system,which has been verified by applying the predicted method into a rubbing rotor test rig.

Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

Influence of Girder Vibration on Cable Damper's Performance of A Cable-stayed Bridge

The model combined by cable,girder and damper is founded to study the influence of girder vibration on cable damper 's performance of a cable-stayed bridge. The complex mode method and nondimensionalization are used to analyze the relationship between the girder's parameters and the performance of cable-related damper. The results indicate that the performance of cable-related damper will decrease greatly when the girder frequencies are near the frequencies of cable. The smaller absolute displacement of damper's piston caused by the very small vibration phase shift of girder and cable is the physical cause of the negative impact mentioned above.

Complex eigenvalues and group velocities of normal modes in shallow water with a lossy bottom

For the stratified shallow water with a lossy bottom, the distribution and asymptotic behavior of mode eigenvalues in the complex plane are discussed on the basis of the Pekeris cut. The analysis shows that even in the shallow water with a low-speed lossy bottom there may be the proper modes which satisfy the radiation condition at infinite depth. It is also shown that when the ratio between the densities of the seawater and seabottom is close to one, there exist only a finite number of improper modes . An iterative method for evaluating the complex eigenvalues and group velocities of normal modes is presented and some numerical results are given.

A Brief Review of Design and Simulation Methodology in Silicon Photonics

Powerful electronic design automation tools have enabled the rapid development of electronic Integrated Circuits(ICs). Similar to electronic ICs, silicon photonics technology has sufficiently matured, and large-scale photonic circuits can now be implanted into a single chip. Design tools have also evolved from primary devices to complex photonic circuits. In this paper, we review the current state of photonic design automation in terms of device modeling methods and circuit simulation methodologies, and compare the photonics design flow with mature electronic design automation design flows. Key challenges and opportunities are also discussed.

Non-random vibration analysis for general viscous damping systems

The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to be an effective supplement of the traditional random vibration theory. In this paper, we further extend the nonrandom vibration analysis into the general viscous damping system, and formulate a method to calculate the dynamic response bounds of a viscous damping vibration system under uncertain excitations. Firstly, the unit impulse response matrix of the system is obtained by using a complex mode superposition method. Secondly, an analytic formulation of the system dynamic response middle point and radius under uncertain excitations is derived based on the Duhamel’s integral, and thus the upper and lower response bounds of the system can be obtained. Finally, two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Study on triaxial test method and failure criterion of asphalt mixture

Asphalt mixture is the most widely used pavement material all over the world. In China, more than 90% of service expressways are asphalt pavement. However, current asphalt pavement design method still has irrationality. Even though maximum tensile stress theory is used as failure criterion, pavement structure under the effects of wheel load is in three-dimensional complex stress state. Obviously, one-dimensional strength theory cannot reflect the failure characteristics and the resistance of pavement structure. So it is necessary to study the failure criterion of asphalt mixture under three-dimensional com- plex stress state. Due to limitations of test equipment, there are almost no studies in related area. Under this background, this paper develops a new triaxial test method, ac- cording to the investigation of strength characteristics of asphalt mixture under complex stress state through plane isobaric/axial tensile test, plane isobaric/axial compression test, plane tensile and compression/axial tensile test, to reveal the general rules of asphalt mixture＇s strength failure. The failure mode is divided into three types： tensile failure, shear failure and rheological failure. The tensile meridian and compression meridian in the stress space and strength envelope in the π plane where hydrostatic pressure is greater than zero are obtained, and the failure criterion of asphalt mixture under complex stress state is established, providing theoretical method and scientific basis for structure design as well as strength check of asphalt pavement under three-dimensional stress state.

Some Modal Relations and Generalized Velocity Method in State Space

Real mode theory in configuration space has shown that the mode acceleration method converges faster than the mode displacement method. This paper demonstrates a similar conclusion in the state space. Some new expressions on modal parameter matrices were set up first. A generalized velocity method (GVM) is then demonstrated in a systematic way. This method is the so\|called complex mode velocity method, but the expressions and schemes are given in terms of parametric matrices in configuration space. Theoretical comparison of this GVM with the traditional complex mode method shows some interesting conclusions. The latter approach is actually a generalized displacement method (GDM). Without mode reduction, the displacement responses of the concerned system resulting from both approaches are identical. On the other hand, both approaches have to adopt mode reduction to become practical. Under this situation, GVM has advantages because it compensates for the contribution of the omitted high\|order modes to the displacement responses.