Near resonance vibration isolation on a levered-dual response(LEDAR)Coulomb-damped system by differential preloads/offsets in linear springs

The levered-dual response(LEDAR)Coulomb-damped system attains near resonant vibration isolation by differential preloads/offsets in linear springs.It takes the advantages of both the preloads/offsets in linear springs and the guiderail friction for realizing different levels of vibration isolation.The isolation capacities are investigated on the strategies with both the horizontal and vertical guiderails,with the horizontal rail only,and without guiderails.The compressive preloads generally result in the consumption of most of the initial excitation energy so as to overcome the potential threshold.The isolation onsets at the frequency ratio of 1∓0.095 on the left-hand side(LHS)and the right-hand side(RHS)of the lever are relative to the load plate connector.The observed near resonant isolation thus makes the LEDAR system a candidate for the isolation of the mechanical systems about resonance while opening a path for simultaneous harvesterisolation functions and passive functions at extreme frequencies.

Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems

A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.

Complex complete quadratic combination method for damped system with repeated eigenvalues

A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic combination （CCQC） method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coefficients of high-order modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method. As a result, the formulas for calculating the correlation coefficients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.

Generalized Wigner Functions for Damped Systems in Deformation Quantization

Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function （WF） does not work for these systems. In this paper we show that in order to let WF satisfy a ,-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a ＊-Exponential expansion in deformation quantization.

Optimal Control Designs for a Class of Nonviscously Damped Systems

A scheme for optimal control problem formulation of a class of nonviscously damped system using pseudo-state-space formulation is presented in this paper.Taking the exponentially damped system of nonviscously damped system as an example,a new state space representation is applied to the n-order exponentially damped system.The necessary conditions for the optimality of the exponentially damped system are obtained.A numerical example of a single degree of freedom exponentially damped system is considered to illustrate the methodology and technique.

Vibrational Resonance in an Overdamped System with a Sextic Double-Well Potential

The phenomenon of vibrational resonance(VR)in an overdamped system with a sextic double-well potential under the excitation of two different periodic signals is investigated.The approximate analytical expression of the resonance amplitude Q at the low−frequencyωis obtained.The VR is observed,and the values of B(the amplitude of the high−frequency signal)andΩ(the frequency of the high−frequency signal)at which VR occurs are determined.Moreover,the relationship between B andΩis revealed.The theoretical predictions are found to be in good agreement with the numerical results.

Eigensolution Variability of Asymmetric Damped Systems

The characterization of energy dissipation or damping in rotor dynamic model is of fundamental importance. Noise and vibration are not only uncomfortable to the users, but also may lead to fatigue, fracture and even failure. During the design process of asymmetric damped systems, it is often required to make changes in the design variables such that the design is optimal. This paper is aimed at developing computationally efficient numerical methods for parametric sensitivity analysis. The algebraic method considered here computes the eigenvector sensitivity by assembling the derivatives of eigenproblems and the additional constraints into an algebraic equation. The coefficient matrix may be ill-conditioned since the elements of it are not all of the same order of magnitude. In this study, a new algebraic method is presented to compute the eigensolution variability of asymmetric damped systems. Some weight constants are introduced such that the proposed method is well-conditioned. The method is very compact and highly efficient, and the numerical stability is also demonstrated. Moreover, several special cases can be presented based on the similar idea of the proposed method. Finally, two numerical examples show the validity of the proposed method.

ON THE CAUCHY PROBLEM FOR THE GENERALIZED BOUSSINESQ EQUATION WITH A DAMPED TERM

This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.

Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

A reweighted damped singular spectrum analysis method for robust seismic noise suppression

(Multichannel)Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression.It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem.However,in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers.The presence of this kind of noise,called erratic noise,makes singular spectrum analysis(SSA)reconstruction unstable and has undesirable effects on the final results.We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA(RD-SSA)method.It incorporates the damped SSA,an improved version of SSA,into a reweighted framework.The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise.The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations.The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance.The feasibility of RD-SSA is validated via both synthetic and field data examples.

Review of the Analysis and Suppression for High-frequency Oscillations of the Grid-connected Wind Power Generation System

High-frequency oscillation(HFO)of gridconnected wind power generation systems(WPGS)is one of the most critical issues in recent years that threaten the safe access of WPGS to the grid.Ensuring the WPGS can damp HFO is becoming more and more vital for the development of wind power.The HFO phenomenon of wind turbines under different scenarios usually has different mechanisms.Hence,engineers need to acquire the working mechanisms of the different HFO damping technologies and select the appropriate one to ensure the effective implementation of oscillation damping in practical engineering.This paper introduces the general assumptions of WPGS when analyzing HFO,systematically summarizes the reasons for the occurrence of HFO in different scenarios,deeply analyses the key points and difficulties of HFO damping under different scenarios,and then compares the technical performances of various types of HFO suppression methods to provide adequate references for engineers in the application of technology.Finally,this paper discusses possible future research difficulties in the problem of HFO,as well as the possible future trends in the demand for HFO damping.

THE ANALYTICAL APPROACH FOR LARGE SCALE NON-CLASSICALLY DAMPED DYNAMIC SYSTEM

This paper gives a dynamic decoupling approach for the analysis of large scale non-classically damped system, in which the complex variable computations were completely avoided not only in solving for the eigenvalue problem but also in the calculation of the dynamic response. The analytical approaches for undamped gyroscopic system, non-classically damped system, including the damped gyroscopic system were unified. Very interesting and useful theoretical results, practical algorithms were obtained which are applicable to both non-defective and defective systems.

Controllability of fractional-order damped systems with time-varying delays in control

In this study,we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control.For the linear system based on the Mittag-Leffler matrix function,we define a controllability Gramian matrix,which is useful in judging whether the system is controllable or not.Furthermore,in two special cases,we present serval equivalent controllable conditions which are easy to verify.For the nonlinear system,under the controllability of its corresponding linear system,we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable.Finally,two examples are given to illustrate the theory.

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.

On precise time integration method for non-classically damped MDOF systems

In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom （MDOF） discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method.

Damping characteristics of friction damped braced frame and its effectiveness in the mega-sub controlled structure system

Based on energy dissipation and structural control principle, a new structural configuration, called the megasub controlled structure （MSCS） with friction damped braces （FDBs）, is first presented. Meanwhile, to calculate the damping coefficient in the slipping state a new analytical method is proposed. The damping characteristics of one-storey friction damped braced frame （FDBF） are investigated, and the influence of the structural parameters on the energy dissipation and the practical engineering design are discussed. The nonlinear dynamic equations and the analytical model of the MSCS with FDBs are established. Three building structures with different structural configurations, which were designed with reference to the conventional mega-sub structures such as used in Tokyo City Hall, are comparatively investigated. The results illustrate that the structure presented in the paper has excellent dynamic properties and satisfactory control effectiveness.

Dynamic characteristics of a novel damped outrigger system

This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method(DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and effi ciency are verifi ed in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the infl uences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coeffi cient. Results show that the modal damping ratio is signifi cantly infl uenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.

Perturbation spectrum method for seismic analysis of non-classically damped systems

Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as structure-damper systems. The approach,which is named the perturbation spectrum method,can provide a more accurate evaluation of a non-classically damped system's mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping,all elements are included in the proposed method for seismic analysis of structure,which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover,as has been adopted in the traditional Complete Quadratic Combination (CQC) method,the white noise model is also used to simplify the expressions of perturbation correlation coefficients. Finally,numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exact ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases,the proposed method shows good agreement with direct time-history integration. Also,the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation.

Vibration characteristics of rotor system with tilting-pad journal bearing of elastic and damped pivots

In view of an entire dynamic model of tilting-pad journal bearing(TPJB) in which the pads swing and vibrate along geometric direction of preload, a TPJB of elastic and damped pivots was designed and manufactured. Vibration experiments were carried out under the conditions of different rotor bending stiffness and oil supply pressure to find out the relationship between the new bearing's vibration depression effect and other dynamic parameters of the rotor. The result shows that critical amplitudes can be efficaciously reduced while system's stability can be remarkably improved by this bearing. Besides, the bearing's effect of vibration depression weakens as the rotor bending stiffness increases, but heightens it as the oil supply pressure increases.

Effect of ground motion duration on inelastic displacement ratio of SDOF systems

In this paper,the influence of ground motion duration on the inelastic displacement ratio,C_(1),of highly damped SDOF systems is studied.For this purpose,two sets of spectrally equivalent long and short duration ground motion records were used in an analysis to isolate the effects of ground motion duration on.The effect of duration was evaluated for observed values of C_(1) by considering six ductility levels,and different damping and post-yield stiffness ratios.A new predictive equation of C_(1) also was developed for long and short duration records.Results of non-linear regression analysis of the current study provide an expression with which to quantify the duration effect.Based on the average values of estimated C_(1) ratios for long duration records divided by C_(1) for a short duration set,it is concluded that the maximum difference between long and short duration records occurs when the damping ratio is 0.3 and the post-yield stiffness ratio is equal to zero.