Viscoelastic Link Research Articles

Modeling of flexible damped coupling and its influence on rotor dynamics

A long transmission shaft is typically constructed by connecting multiple shafts through couplings. Joining two non-collinear shafts causes misalignment, which is one of the primary faults in the shaft system. The flexible coupling can compensate for the misalignment up to some extent. However, in this process, the system dynamics may be affected by the coupling characteristics. The present research proposes flexible disk coupling in a misaligned propeller shaft. The coupling is modeled by segmenting the disk into multiple viscoelastic links exhibiting restoring and dissipating behavior. A combination of parallel and angular misalignment is taken to obtain coupling characteristics. Finite element formulation considering the Timoshenko beam theory is applied to obtain the laminated composite shaft equation, and coupling characteristics are integrated. Operator based constituted relationship is utilized to incorporate material damping of both the shaft and coupling. The stiffness and damping of the coupling rotate with the spin synchronized rotor frame and modify the overall system matrices. Therefore, the coupling influences the modal characteristics and response of the rotor shaft system. A comparative study between the coupled and the uncoupled shafts is performed based on the eigenvalue analysis to show the effect of coupling behavior.

Seismic pounding mitigation of asymmetric-plan buildings by using viscoelastic links

Connection of adjacent buildings with viscoelastic links (VE) has been proved to be an efficient method for preventing or at least attenuating the structural collisions during earthquakes. The efficiency of this pounding mitigation method was extensively studied in the past, mostly based on assuming a two-dimensional problem without addressing the effects of plan irregularities. In this paper, the effect of VE links between adjacent asymmetric-plan buildings is studied in detail. First, two adjacent one-story models with various structural as well as link-wise dynamic parameters are analyzed under white-noise input. The inelastic behavior of the adjacent buildings is also taken into account. The response of two adjacent 5 story buildings is then evaluated under the actual earthquake record to validate the findings obtained under white-noise analysis. Results demonstrate that not only plan asymmetries do not necessarily lead to higher responses compared to the symmetric adjacent buildings, but the linked-to-unlinked response ratio would be efficiently reduced by providing supplemental damping in the link elements. As the link stiffness decreases, the reduction in the relative displacement of the buildings due to supplemental damping could be up to 80% and even more. Results also reveal that it is possible to obtain a dominant modal damping ratio up to twice than that in symmetric plans for certain plan eccentricities.

Mitigating the seismic pounding of multi-story buildings in series using linear and nonlinear fluid viscous dampers

Seismic-induced pounding between adjacent buildings may have serious consequences, ranging from minor damage up to total collapse. Therefore, researchers try to mitigate the pounding problem using different methods, such as coupling the adjacent buildings with stiff beams, connecting them using viscoelastic links, and installing damping devices in each building individually. In the current paper, the effect of using linear and nonlinear fluid viscous dampers to mitigate the mutual pounding between a series of structures is investigated. Nonlinear finite-element analysis of a series of adjacent steel buildings equipped with damping devices was conducted. Contact surfaces with both contactor and target were used to model the mutual pounding. The results indicate that the use of linear or nonlinear dampers leads to the significant reduction in the response of adjacent buildings in series. Moreover, the substantial improvement of the performance of buildings has been observed for almost all stories. From the design point of view, it is concluded that dampers implemented in adjacent buildings should be designed to resist maximum force of 6.20 or 1.90 times the design independent force in the case of using linear or nonlinear fluid viscous dampers, respectively. Also, designers should pay attention to the design of the structural elements surrounding dampers, because considerable forces due to pounding may occur in the dampers at the maximum displaced position of the structure.

Evaluation of the repartition of the particles in Pickering emulsions in relation with their rheological properties

HypothesisThe distribution of particles in Pickering emulsions can be estimated through a percolation-type approach coupled to the evolution of their rheological features with the dispersed phase volume fraction ϕ. ExperimentsThe rheological behavior of water-in-dodecane Pickering emulsions stabilized with hydrophobic silica nanoparticles is addressed. The emulsions viscosity and elastic modulus are investigated at ϕ varying from 0.1 to 0.75. Various rheological models are adjusted to the experimental data. FindingsThe comparison of the elastic modulus evolution of the Pickering emulsions with those of emulsions stabilized with surfactants confirms a major contribution of the particles to the rheological behavior of Pickering emulsions and supports the existence of a three-dimensional network between the droplets. The applied percolation approach allows to quantitively estimate a nanoparticles viscoelastic link between the droplets and opposes the classic vision of interfacial monolayers stabilizing the Pickering emulsions. This network of interconnected particles and droplets contributes significantly to the viscosity as well as the elastic modulus of these emulsions. To our knowledge, the applied percolation-based model is the only one capable of providing a structural explanation while describing the abrupt viscosity and elastic modulus growth of Pickering emulsions across the range of ϕ.

A Nonlinear Reduced-Order Model of the Corpus Callosum Under Planar Coronal Excitation.

Traumatic brain injury (TBI) is often associated with microstructural tissue damage in the brain, which results from its complex biomechanical behavior. Recent studies have shown that the deep white matter (WM) region of the human brain is susceptible to being damaged due to strain localization in that region. Motivated by these studies, in this paper, we propose a geometrically nonlinear dynamical reduced order model (ROM) to model and study the dynamics of the deep WM region of the human brain under coronal excitation. In this model, the brain hemispheres were modeled as lumped masses connected via viscoelastic links, resembling the geometry of the corpus callosum (CC). Employing system identification techniques, we determined the unknown parameters of the ROM, and ensured the accuracy of the ROM by comparing its response against the response of an advanced finite element (FE) model. Next, utilizing modal analysis techniques, we determined the energy distribution among the governing modes of vibration of the ROM and concluded that the demonstrated nonlinear behavior of the FE model might be predominantly due to the special geometry of the brain deep WM region. Furthermore, we observed that, for sufficiently high input energies, high frequency harmonics at approximately 45 Hz, were generated in the response of the CC, which, in turn, are associated with high-frequency oscillations of the CC. Such harmonics might potentially lead to strain localization in the CC. This work is a step toward understanding the brain dynamics during traumatic injury.

Use of viscoelastic links for seismic pounding mitigation under random input

Purpose The purpose of this paper is to study the effects of viscoelastic links between two adjacent buildings for pounding mitigation under white-noise seismic input. Design/methodology/approach A formulation is first extracted for the effective modal damping ratios of the system. Then, two single DOF linear buildings connected by viscoelastic links are considered with both classical and non-classical damping schemes. The inelastic behavior is also taken into account by using equivalent natural frequencies and damping ratios of the buildings. The effect of ground dominant frequency and damping on the displacement response is also investigated by using Kanai‒Tajimi filtered white noise as the random input. Findings The difference between classical and non-classical damping is shown to be less than 20 percent, implying the permission in using the simpler classical damping scheme. Finally, the problem is extended to two-storey buildings, where using viscoelastic links only at the top story level of the buildings is shown to be sufficient for controlling individual, as well as relative, motions of the structures. Originality/value Results demonstrate that the use of link with a moderate stiffness may reduce the stiffer building displacement up to approximately 20 percent in comparison to the free displacement, while the seismic pounding of the adjacent buildings is effectively controlled. Further, an upper limit of link stiffness is obtained for preventing the increase in the stiffer building displacement, which may be exceeded by the minimum link stiffness necessary for pounding prevention if small gap size exists.

Derivation of motion equation for mobile manipulator with viscoelastic links and revolute–prismatic flexible joints via recursive Gibbs–Appell formulations

This paper investigates the dynamic equations of an N-flexible link manipulator with revolute–prismatic joints while considering the effects of manipulator locomotion by the mobile platform bound by non-holonomic kinematic constraints. Such constraints, in addition to creating dynamic interaction between manipulator and platform, cause serious motion limitations and introduction of more computational complexity. The manipulator’s flexible links are modeled by the assumed mode method, where the Timoshenko beam theory is used for the substitution of the assumed mode shapes. The internal and external damping effects are also studied for the model precision. Moreover, revolute–prismatic joints in each arm are exploited to develop the robot mobility. The new joint structure makes it possible to use mobile manipulators with long flexible links. However, in regard to the variations of links length caused by prismatic joints, time-varying dynamic equations are obtained, leading to comparatively complex and lengthy formulations. Therefore, the Gibbs–Appell formulation is utilized as an alternative to the Lagrange equations to facilitate the process of deriving the motion equations. In addition, the non-dimensional form of the Timoshenko beam theory mode shapes is recommended to circumvent the computation of time step mode shapes. It is also necessary to examine the system tip-over stability based on long and variable-length arms, lightweight base, and widespread environmental factors using the zero moment point methods. Finally, a numerical simulation for a mobile manipulator, with two flexible links and revolute–prismatic joints is carried out to demonstrate the performance of the presented model for such complex systems. Different amounts of link elasticity and the effects of internal and external damping coefficients are separately studied. The results are verified by recent fixed base flexible manipulators employing revolute–prismatic joints as well as the IUST Revolute–Prismatic joints experimental setup incorporating rigid links.

Vertical isolation of a structure based on different states of seismic performance

In vertical seismic isolation (VSI), a building is partitioned intentionally by vertical layers into two dynamically different substructures for seismic response reduction. Initially, a 1-story frame was partitioned into two substructures, interconnected by viscous and visco-elastic links, and seismic responses of the original and the vertically isolated structures (VIS) were obtained, considering a large number of stiffness and mass ratios of substructures with respect to the original structure. Color contour graphs were defined for presentation and investigation of large amounts of output results. Dynamic characteristics of the isolated structures were studied by considering the non-classical damping of the system, and then the effects of viscous and visco-elastic link parameters on the modal damping ratios were discussed. On this basis, three states of mass isolation, interactional state, and control mass were differentiated. Response history analyses were performed by Runge-Kutta numerical method. In these analyses, interaction of isolation ratios and link parameters, on response control of VIS was studied and the appropriate ranges for link parameters as well as the optimal ranges for isolation ratios were suggested. Results show that by using the VSI technique, seismic response reduction up to 50% in flexible substructure and even more in stiff substructure is achievable.

Use of Co-polymer of Styrene Butadiene Rubber-a Seismically Innovative Approach towards Energy Dissipation

Analysis, monitoring and control of vibration and displacement is the prime concern for structural engineers during any seismic activity. This paper presents the design, development and seismic performance of new and innovative visco-elastic links made by using ’ply’ of old & used radial rubber tyres (co-polymer of styrene butadiene rubber) coupled with interlinked concrete blocks of grade M-20. The study is conceptualized on frictional as well as viscous damping. The whole system is integrated to restrict translation and rotation of the concrete blocks during the extreme earthquake forces. The system is conceptualized on the principle of capacity based design by keeping the yielding capacity of visco-elastic links lower in comparison to concrete blocks. Full scale models are tested and analyzed on shake table and shock table under artificial earthquake excitations. Three shocks with the base acceleration ranging between 0.6g to 2.5g are applied under shock table test. Same type of model is tested on shake table also corresponding to an artificial accelerogram compatible with design spectrum as per IS: 1893 (Part 1): 2002 considering Design Basis Earthquake (DBE) and Maximum Considered Earthquake (MCE) in zone v (for soft soil condition). Effective peak ground acceleration of 0.18g &0.36g is used as the base excitation in horizontal direction and its 2/3 is considered for its vertical motion. A high speed camera with the capturing capacity of 1000 frames per second is used for the analysis of the results and various parameters. A significant performance of inter-linked block masonry system is endorsed under both types of testing. The concept of block masonry with visco-elastic link is successful since the energy is completely released through yielding of links at the bottom portion of the model and the top of the model remains intact, even not a single block of parapet wall under shock table test is displaced from its original undamaged position.

Model reduction and optimal control for an electromechanical structure with viscoelastic links

Motions of a flexible electromechanical structure consisting of two joined beams clumped on a mobile carriage controlled with an electric driver are studied. An optimal control problem is considered to transfer the structure from its initial state to terminal one in a fixed time and to minimize the mean mechanical energy of the beams. The numerical solution of the inverse dynamic problem, which is based on the method of integrodifferential relations and a model reduction technique, is presented and discussed.

Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

In this paper, based on the Voigt-Kelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the model's dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamilton's principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude. 'n Voigt-Kelvin saamgestelde model word in 'n nie-reglynige dinamiese oplossingsruimte gebruik om 'n soepel hanteringsrobot te ontleed. Die modellering is daartoe instaat om nie-linere dinamiese vertoning van styfheid wat ontstaan wees sentrifugale en Corioliskragte te ontleed. Die modelvergelykings is gebaseer op die Hamiltonbeginsel. Simulasieresultate toon betekenisvolle verbetering van sisteemgedrag. Verdere ontledings handel oor strukturele demping en vibrasie-amplitude.

Numerical and Experimental Testing of Normality in the Functioning of the Bearings System

A highly efficient seismic protection of bridges have been demonstrated by the passive control systems with me- chanical links with selective viscoelastic energy dissipation through viscous friction and dry friction. These systems are able to take over the deformations and movements caused by temperature variations, those due to seismic activities and from road traffic. A number of natural factors such as atmospheric and anthropogenic parameters, such as shock and vibration from road traffic, lead to the degradation of the viscoelastic bonds of passive control systems based on rubber molding. The presence of the elastic and dissipative nonlinear forces in the functioning of antiseismic systems inevitably leads to quantitative and qualitative changes of the structural responses of bridges and viaducts both in time and spectral domains. The implications of these changes on the integrity and stability of the bridge or viaduct sections may be from the simplest to the most severe depending on the type of seismic excitation to which they are subjected. For these reasons, it is imperative that we should identify and quantify the degree of nonlinearity of antiseismic systems embedded in the structure of bridges and viaducts in order to prevent accidents with severe socioeconomic implications. In this way can determine the dependence of the nonlinear behavior of the bearing system and the degree of degradation of their viscoelastic links. From a theoretical point of view the following parameters of the vi- bration of the system will be comparatively analyzed: the displacement and acceleration of the bridge deck in time and frequency domains, the hysteretic loop, the representation in the plane of phases, the power spectral density and the spectrograms of the acceleration signals. From an experimental point of view there will be identified and plotted the parameters able to provide information regarding the abnormal operation of the bearings from the elastomer: system acceleration, representations in time and frequency and its spectrogram.

Numerical and Experimental Testing of Normality in the Functioning of the Bearings System

A highly efficient seismic protection of bridges have been demonstrated by the passive control systems with mechanical links with selective viscoelastic energy dissipation through viscous friction and dry friction. These systems are able to take over the deformations and movements caused by temperature variations, those due to seismic activities and from road traffic. A number of natural factors such as atmospheric and anthropogenic parameters, such as shock and vibration from road traffic, lead to the degradation of the viscoelastic bonds of passive control systems based on rubber molding. The presence of the elastic and dissipative nonlinear forces in the functioning of antiseismic systems inevitably leads to quantitative and qualitative changes of the structural responses of bridges and viaducts both in time and spectral domains. The implications of these changes on the integrity and stability of the bridge or viaduct sections may be from the simplest to the most severe depending on the type of seismic excitation to which they are subjected. For these reasons, it is imperative that we should identify and quantify the degree of nonlinearity of antiseismic systems embedded in the structure of bridges and viaducts in order to prevent accidents with severe socioeconomic implications. In this way can determine the dependence of the nonlinear behavior of the bearing system and the degree of degradation of their viscoelastic links. From a theoretical point of view the following parameters of the vibration of the system will be comparatively analyzed: the displacement and acceleration of the bridge deck in time and frequency domains, the hysteretic loop, the representation in the plane of phases, the power spectral density and the spectrograms of the acceleration signals. From an experimental point of view there will be identified and plotted the parameters able to provide information regarding the abnormal operation of the bearings from the elastomer: system acceleration, representations in time and frequency and its spectrogram.

Determination of the steady state response of portal frames with intermediate viscoelastic links

Steady state response of portal frames whose members are connected to each other continuously or by infinitesimally small rotational link elements (intermediate viscoelastic hinges) are investigated under a periodic external force within the Euler-Bernoulli beam theory by using energy based finite element method. The effect of damping of the members of portal frames, the values of rotational spring coefficient and damping coefficient of intermediate viscoelastic hinges on the steady state response are investigated numerically. Optimum damping coefficients of intermediate viscoelastic hinges are investigated for different damping coefficients of members. The results of frames constituted by connecting the members continuously and by connecting the members with intermediate viscoelastic hinges in some desired joints are compared and presented in graphics and tables. Convergence studies are made. The obtained results are compared with the results of same models constituted on the structural analysis software package SAP 2000. It is seen that the results obtained from this study are harmonious with the results obtained by using SAP 2000 package. Key words: Portal frames, finite element method, viscoelastic hinge, steady state response, optimum damping coefficients.

Substructure method in high-speed monorail dynamic problems

Substructure method in high-speed monorail dynamic problems

Nonequilibrium properties of fluid interfaces: aperiodic diffusion-controlled regime 2. Experiments

We have investigated the surface dilational properties of a submicellar aqueous solution of n-dodecyldimethyl-phosphine oxide. We compared (a) the steady-state responses of dynamic surface tension, induced by small-amplitude harmonic disturbances of surface equilibrium (at different frequencies), and (b) the transient response induced on the same sample by a single trapezoidal-pulse disturbance. Using the equations for a diffusive model, we determined the fit parameters from the observed response values both in the frequency and in the time domains. The results enabled us to predict satisfactorily the harmonic dynamic behaviour of the surface, from the relaxation data. The prediction-bservation agreement supports the theoretical treatment and, in particular, the assertion that the viscoelastic link, between surface excitation and response, is a constitutive property of a liquid solution. The experiments also show the existence of a linearity range and the repeatability of measurements.

Anwendung balkenförmiger schwingungstilger für biegeschwingungssysteme

Tuned viscoelastic dampers, comprising a mass connected through a viscoelastic link to a vibrating structure, have been considered from many points of view. For effective operation, the resonant frequency of such a damper must be made somewhat lower than the undamped resonant frequency of the structure. If the resonant frequency of the structure is low, some difficulty is encountered in constructing a good tuned damper system. In such a damper system the viscoelastic materials must be both soft and strong enough to give the necessary tuning frequencies without the damper being too heavy. For this reason a damper, based on a different principle for lateral vibrating structures is described in this paper. The main vibrating system is a clamped-free beam. The damper is also a clamped-free beam which is accomodated in an opening of the main system. The damper beam can vibrate freely in this opening and creates a new degree of freedom in the total system. The different equations for the lateral vibrations of the main and of the damper beam can be formulated according to the classical Bernoulli - Euler theory. For theoretical analysis, the system has been simplified. The main beam has partially constant rectangular sections. The auxiliary beam has a constant rectangular section. The total system has four different parts with constant sections. Structural damping of both beams has also been considered by a complex modulus of elasticity. For vibrations in a normal mode, the Euler - Bernoulli equation can be formulated as an ordinary differential equation. A general solution for each beam section is a sum of trigonometric and hyperbolic functions. The coefficients in the general expressions can be determined from the 16 boundary conditions of the beam damper system. The equations for the forced vibrations of the main beam, which can be excited by a prescribed motion at some point in the system or by a harmonic force are written in matrix notation: |A| · |X| = |B| The components of the matrix |A| are functions of the dimensionless frequency parameter and the geometric and the dynamic properties of the system. The matrix |B| contains the exciting functions, and the matrix |X| contains the unknown coefficients of the general solutions. For the solution of matrix |X| the Wilkinson method is used. The computed examples show, for a given beam-damper system, the amplitude of the vibration of the main beam as a function of frequency; the effect of tuning on the natural frequencies of the main beam; the effect of damping on the amplitudes of the main beam; the effect of the mass ratio MDamper/MBeam on the natural frequencies and resonant amplitudes of the main system; and the effect of the attaching point of the damper on the natural frequencies and resonant amplitudes of the main beam.

Dynamics of circular periodic structures

The frequency response matrix is determined for a periodically supported, periodically damped, closed circular beam structure which is an approximate model of a skin-stringer aircraft fuselage structure. The analytical technique which is developed depends on the periodic nature of the structure to simplify the analysis. The analysis is a complementary approach to the transfer matrix method for determining frequency response. One purpose of the analysis is to circumvent the numerical and/or computer storage difficulties commonly found in computing the frequency response for typical aircraft fuselage structure from a transfer matrix analysis. Numerical difficulty is avoided by using the properties of the transfer matrix for one periodic unit and a consequence of the Cayley-Hamilton theorem to obtain an analytical solution for the frequency response matrix. The second purpose of the analysis is to investigate the spatial decay of response from a point or region of the structure which is being excited. This spatial decay isolates the response to a region of structure near the excitation and reduces the over-all dynamic stress level of the structure for a general excitation. Three damping devices that utilize a viscoelastic link to produce spatial decay are evaluated. Several numerical examples are shown.

A Resonant Beam Tuned Damping Device

A resonant beam tuned damping device, comprising a flexible beam joined by way of visco-elastic links at the ends, to a vibrating structure, is described. This device has the advantage of relying on the interaction between the beam stiffness and the link stiffness for tuning, rather than on the link stiffness alone as for the conventional tuned damper, so that a weight-saving potential exists. An analysis is developed and verified experimentally.