A discretely damped SDOF model for the rocking response of freestanding blocks

This paper presents a single-degree-of-freedom(SDOF)constitutive model for assessing the performance of freestanding block contents of buildings.The model incorporates a bespoke damper to account for energy dissipation associated with rocking.It is advantageous in its direct correlation,via energy conservation,to the restitution coefficient for impact during rocking.A comparative study with the existing SDOF rocking models shows that the proposed model significantly improves the accuracy of free-rocking simulations,in which inherent damping predominantly affects response.It provides a promising and efficient tool for computationally intensive performance evaluation of nonstructural components.

THE FREE-INTERFACE METHOD OF COMPONENT MODE SYNTHESIS FOR SYSTEMS WITH VISCOUS DAMPING

This paper presents a new free-interface method of component mode synthesis for linear systems with arbitrary viscous damping. The left and right projection matrices described by state-variable vectors are first introduced for components with rigid-body freedom. The operator function of projection matrices for state displacement and state force is proved, and then the state residual flexibility matrix and the state residual inertia-relief attachment mode are defined and employed. The results of three examples demonstrate that the method proposed in this paper leads to very accurate system eigenvalues and high mode-synthesis efficiency

Experimental studies on behavior of fully grouted reinforced-concrete masonry shear walls

An experimental study is conducted on fully grouted reinforced masonry shear walls (RMSWs) made from concrete blocks with a new configuration. Ten RMSWs are tested under reversed cyclic lateral load to investigate the influence of different reinforcements and applied axial stress values on their seismic behavior. The results show that flexural strength increases with the applied axial stress, and shear strength dominated by diagonal cracking increases with both the amount of horizontal reinforcement and applied axial stress. Yield displacement, ductility, and energy dissipation capability can be improved substantially by increasing the amount of horizontal reinforcement. The critical parameters for the walls are derived from the experiment: displacement ductility values corresponding to 15% strength degradation of the walls reach up to 2.6 and 4.5 in the shear and flexure failure modes, respectively; stiffness values of flexure- and shear-dominated walls rapidly degrade to 17%–19% and 48%–57% of initial stiffness at 0.50 Dmax (displacement at peak load). The experiment suggests that RMSWs could be assigned a higher damping ratio (～14%) for collapse prevention design and a lower damping value (～7%) for a fully operational limit state or serviceability limit state.

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.

Self-excited vibration of driveline for vehicle launch

The launch shudder phenomenon induced by self-excited vibration of driveline was stud- ied with a compact car equipped with AMT as research object. The research showed that self-excited vibration was closely related with damping of driveline, the variation of friction coefficient, equiva- lent radius of friction plate and applied force of pressure plate. Six DOFs torsional vibration model of vehicle driveline was established according to the parameters of the certain compact car. The simula- tion was carried out and the result was compared with test data. It was found that the negative slope of friction coefficient with relative slip speed does not necessarily lead to self-excited vibration and the frequency of self-excited vibration on 1st gear is near to the 1st order of torsional natural frequen- cy. The influence of each viscous damping in driveline on self-excited vibration was analyzed by sim- ulation and the results showed that increasing the torsional dampings of half-axles and tires properly was effective to improve launch shudder phenomenon.

Loss of energy dissipation capacity from the deadzone in linear and nonlinear viscous damping devices

In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper＇s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of ＂deadzone＂. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect ofdeadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 3 5 6 for calculation of equivalent damping if a deadzone is to be considered.

Equivalent damping of SDOF structure with Maxwell damper

To predict the maximum earthquake response of an SDOF structure with a Maxwell fluid damper or supplemental brace-viscous damper system using the seismic design response spectrum technique,a new approach is presented to determine the first-and second-order equivalent viscous damping and stiffness,the peak responses,and the damper force of the above structure.Based on the fact that the dynamic characteristics of a general linear viscoelastically damped structure are fully determined by its free vibration properties and the relaxation time constants of a Maxwell fluid damper and supplemental brace-viscous damper system in engineering practice are all small,the method of improved multiple time scales and the equivalent criterion in which all free vibration properties are the same are used to obtain the first-and second-order equivalent viscous damping and stiffness of the above structure in closed form.The accuracy of the proposed method is higher and significantly better than that of the modal strain energy method.Furthermore,in the parametric range of the requirements of the Chinese ＂Code for Seismic Design of Buildings＂,the error of the proposed second-order equivalent system for the abovementioned engineering structure is not more than 0.5%.

Time-delay damping theory

In this paper,existing damping theories are briefly reviewed.On the basis of the existing damping theories,a new kind of damping theory,i.e.,the time-delay damping theory,is developed.In the time-delay damping theory,the damping force is considered to be directly proportional to the increment of displacement.The response analysis of an SDOF time-delay damping system is carried out,and the methods for obtaining the solution for a time-delay damping system in the time domain as well as the frequency domain are given.The comparison between results from different damping theories shows that the time-delay damping theory is both reasonable and convenient.

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Effects of residual stress and viscous and hysteretic dampings on the stability of a spinning micro-shaft

This study examines the effects of the residual stress and viscous and hysteretic dampings on the vibrational behavior and stability of a spinning Timoshenko micro-shaft.A modified couple stress theory(MCST)is used to elucidate the sizedependency of the micro-shaft spinning stability,and the equations of motion are derived by employing Hamilton’s principle and a spatial beam for spinning micro-shafts.Moreover,a differential quadrature method(DQM)is presented,along with the exact solution for the forward and backward(FW-BW)complex frequencies and normal modes.The effects of the material length scale parameter(MLSP),the spinning speed,the viscous damping coefficient,the hysteretic damping,and the residual stress on the stability of the spinning micro-shafts are investigated.The results indicate that the MLSP,the internal dampings(viscous and hysteretic),and the residual stress have significant effects on the complex frequency and stability of the spinning micro-shafts.Therefore,it is crucial to take these factors into account while these systems are designed and analyzed.The results show that an increase in the MLSP leads to stiffening of the spinning micro-shaft,increases the FW-BW dimensionless complex frequencies of the system,and enhances the stability of the system.Additionally,a rise in the tensile residual stresses causes an increase in the FW-BW dimensionless complex frequencies and stability of the micro-shafts,while the opposite is true for the compressive residual stresses.The results of this research can be employed for designing spinning structures and controlling their vibrations,thus forestalling resonance.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.

Damping Solitary Wave in a Three-Dimensional Rectangular Geometry Plasma

The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ ＋∞.

Exponential stability of a pendulum in dynamic boundary feedback with a viscous damped wave equation

In this paper,we continue the earlier work[Lu,L,&Wang,D.L.(2017).Dynamic boundary feed-back of a pendulum coupled with a viscous damped wave equation.In Proceedings of the 36th Chinese Control Conference(CCQ)(pp.1676-1680)]on study the stability of a pendulum coupled with a viscous damped wave equation model.This time we get the exponential stability result which is much better than the previous strong stability.By a detailed spectral analysis and opera-tor separation,we establish the Riesz basis property as well as the spectrum determined growth condition for the system.Finally,the exponential stability of the system is achieved.

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.

SURFACE WAVE PATTERNS AND INSTABILITY IN A VERTICALLY OSCILLATING CIRCULAR CYLINDRICAL VESSEL

The natural frequency of surface wave, which has been derived from avertically oscillating circular cylindrical vessel in inviscid fluid, was modified by consideringthe influence of surface tension and weak viscosity. Many flow patterns were found at differentforced frequencies by numerical computation. In addition, the nonlinear amplitude equation derivedin inviscid fluid was modified by adding viscous damping and the unstable regions were determined bystability analysis.