Viscous Dashpot Research Articles

Micromechanical study of dispersion and damping characteristics of granular materials

The wave-propagation characteristics of dense granular materials have been studied from the micromechanical viewpoint, in which relationships are sought between properties at the micro-scale of particles and interparticle contacts and properties at the continuum, macro-scale. The dispersion and damping characteristics have been determined from a three-dimensional lattice analysis in which the particle interaction is modeled with linear elastic springs and linear viscous dashpots. Due the presence of rotational degrees of freedom of the particles, optical branches are observed in the dispersion and damping characteristics, besides the acoustical branches. The influence of the micromechanical characteristics on the macroscopic dispersion and damping characteristics has been determined for a face-centered cubic lattice and a body-centered cubic lattice. For small wave numbers (large wave lengths) the damping of the optical branches is very large. This means that the optical branches will not be observed in conditions where a continuum-mechanical description is appropriate.

Energy harvesting from axial fluid-elastic instabilities of a cylinder

A flexible cylindrical system unstable to flutter oscillations is analysed from the perspective of energy harvesting. In this work we analyse the non-linear reduced order model of a two-degree of freedom system of cylinders modelled with discrete stiffness and damping. The non-linear system of equations is solved in terms of cylinder deflection angles. We seek the flow speed range over which flutter oscillations are stable and correspondingly amenable to energy harvesting. Energy harvesters are modelled as viscous dashpots and the coefficients of damping are parametrised in order to determine combinations that harvest maximum power. We show that for harvesting the maximum possible energy the viscous dashpot should be placed away from the region driving the instability and for this model the optimal location is the fixed end. This result is robust to flow speed variation, action of viscous drag and to variations in cylinder geometry.

Elastic and viscoelastic properties of a type I collagen fiber

A new mathematical model is presented to describe the elastic and viscoelastic properties of a single collagen fiber. The model is formulated by accounting for the mechanical contribution of the collagen fiber's main constituents: the microfibrils, the interfibrillar matrix and crosslinks. The collagen fiber is modeled as a linear elastic spring, which represents the mechanical contribution of the microfibrils, and an arrangement in parallel of elastic springs and viscous dashpots, which represent the mechanical contributions of the crosslinks and interfibrillar matrix, respectively. The linear elastic spring and the arrangement in parallel of elastic springs and viscous dashpots are then connected in series. The crosslinks are assumed to gradually break under strain and, consequently, the interfibrillar is assumed to change its viscous properties. Incremental stress relaxation tests are conducted on dry collagen fibers reconstituted from rat tail tendons to determine their elastic and viscoelastic properties. The elastic and total stress–strain curves and the stress relaxation at different levels of strain collected by performing these tests are then used to estimate the parameters of the model and evaluate its predictive capabilities.

Relationship between Q-factor and sample damping for contact resonance atomic force microscope measurement of viscoelastic properties

Contact resonance AFM characterization techniques rely on the dynamics of the cantilever as it vibrates while in contact with the sample. In this article, the dependence of the quality factor of the vibration modes on the sample properties is shown to be a complex combination of beam and sample properties as well as the applied static tip force. Here the tip-sample interaction is represented as a linear spring and viscous dashpot as a model for sample (or contact) stiffness and damping. It is shown that the quality factor alone cannot be used to infer the damping directly. Experimental results for polystyrene and polypropylene are found to be in good agreement with predictions from the model developed. These results form the basis for mapping viscoelastic properties with nanoscale resolution.

Recent Advancements in Fractal Geometric‐Based Nonlinear Time Series Solutions to the Micro‐Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin‐Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed‐form solutions, are displayed graphically for selected values of the systems′ parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro‐ and nano‐electronic devices, circuits and systems.

Iterative analysis of concrete gravity dam-nonlinear foundation interaction

This paper deals with finite element analysis of the soil–structure systems considering the coupled effect of elastic structure and materially nonlinear soil. The equations of motion of both soil and structure have been expressed in terms of displacement variable. The structure and the soil domain are treated as two separate systems. The solution of the coupled system is accomplished by solving the two systems separately and then considering the interaction effects at the soil–structure interface enforced by a developed iterative scheme. Emphasis has been laid on the study of material nonlinearity of the foundation material in the interaction analysis. The results show the pronounced effects of displacements and stresses for the structure when the foundation is assumed to be composed of nonlinear materials. A widely popular model called Duncan-Chang model has been used for representing nonlinear material behavior of soil/rock. In order to represent the semi-infinite nature of the foundation domain, the Lysmer-Kuhlemeyer boundary condition consisting of viscous dashpots have been used. Studies show the accuracy of the proposed algorithm, while comparing with the results reported in the literature. Keywords: Concrete gravity dam; dam-foundation interaction; iterative algorithm; Duncan-Chang model; viscous dashpots.

Internal stress model for pre-primary stage of low-stress creep

Initial transient stage in low-stress creep experiments was observed in all such experiments. Recently, evidences were presented that this stage cannot be considered as a normal creep primary stage, though the shape of the creep curve is similar. The strain reached during this so called pre-primary stage is fully recoverable upon unloading; the internal stresses must play important role in the effect. Model of standard linear anelastic solid was modified by introduction of creeping body instead of viscous dashpot. Both power law and hyperbolic sine creep law were used to fit observed creep curves of model and structural materials. Mainly the model using hyeprbolic sine creep law provides good fit to individual creep curves and sets of creep curves at different stresses.

Invariant elastic modulus of viscoelastic materials measured by rate-jump tests

It is demonstrated that, when polyethylene is subject to a tensile test with a jump in the loading rate, an elastic modulus, given as the ratio of the jump in stress rate to the resultant jump in strain rate, is invariant with respect to the magnitude of jump in the loading rate, at a given strain at which the jump is imposed. However, such an elastic modulus measured from rate jumps applied at different strains in the polymer can be different. These observations are consistent with a constitutive description of the mechanical behaviour of the polymer in terms of a network of linear elastic springs and (in general) nonlinear viscous dashpots. During the rate jump, the dashpots are infinitely stiff and do not respond, and the response of the elastic springs in the network gives an overall elastic modulus which is invariant with respect to the magnitude of the rate jump. As the polymer is deformed to different strains, the spring–dashpot network itself may change as a result of evolution of the microstructure, hence the overall elastic modulus describing the collective behaviour of the springs in the network may change. These findings illustrate that an effective elastic modulus can be defined from a spring–dashpot network description of an (in general) nonlinear viscoelastic material, and such a modulus can be measured by a rate-jump test.

Fractal Geometry-Based Hypergeometric Time Series Solution to the Hereditary Thermal Creep Model for the Contact of Rough Surfaces Using the Kelvin-Voigt Medium

This paper aims at constructing a continuous hereditary creep model for the thermoviscoelastic contact of a rough punch and a smooth surface of a rigid half-space. The used model considers the rough surface as a function of the applied load and temperatures. The material of the rough punch surface is assumed to behave as Kelvin-Voigt viscoelastic material. Such a model uses elastic springs and viscous dashpots in parallel. The fractal-based punch surface is modelled using a deterministic Cantor structure. An asymptotic power law, deduced using approximate iterative relations, is used to express the punch surface creep which is a time-dependent inelastic deformation. The suggested law utilized the hypergeometric time series to relate the variables of creep as a function of remote forces, body temperatures, and time. The model is valid when the approach of punch surface and half space is in the order of the size of the surface roughness. The closed-form results are obtained for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results show good agreement with published experimental results, and the methodology can be further extended to other structures such as the Kelvin-Voigt medium within electronic circuits and systems.

Mechanical model of a mistuned 2DOF‐structure coupled by viscous damping

AbstractIn this paper the vibration amplitude reduction of a mechanical system is investigated when applying a damper between different DOF of that structure. Thereby, an elementary mechanical model consisting of two mass‐spring elements with slightly differing eigenfrequencies and which are connected via a viscous dashpot damper is regarded. To investigate the systems behavior, an analysis of the transfer function and its poles and zeros in the L APLACE domain is performed when varying the damping constant. This reveals that the achievable amplitude reduction depends on the mistuning of the system and that even ideal viscous damping leads to a coupling which results in a shift of eigenfrequencies. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamic Soil–Structure Interaction of Bridge Substructure Subject to Vessel Impact

The paper describes the in situ investigation, site stratigraphy, field monitoring, data reduction, and subsequent time-domain analysis of soil–structure interaction from a full scale vessel impact loading of a bridge pier at the St. George Island Causeway. The in situ investigation included standard penetration testing, electric cone, dilatometer, and pressuremeter testing to identify soil stratigraphy, engineering properties (strength and moduli), and axial and lateral static pile resistance (T–z, and P–y). Field instrumentation included soil total stress and pore pressure gauges in front of and behind the pile cap, a fully instrumented pile (strain gauges along length), dynamic load cells to monitor barge impact loads, and accelerometers to monitor pier accelerations, velocities, and displacements. Analyses of the field data reveal significant dynamic forces within the soil–structure system as a result of the duration and magnitude of the loading. Inertia from the piers, cap, and piles provide significant resistance in the early portion of the impact. However, postpeak inertia (i.e., pier deceleration) resulted in maximum deformations of the pier. Soil damping provided most of the resisting force at the peak barge loading, whereas static soil resistance dominated at the peak lateral displacement. Time-domain finite element analysis of an impact event employing viscous soil dashpots, nonlinear P–y and T–z springs with nonlinear beam, and shell elements for the pier, cap, and piles resulted in reasonable load displacement predictions.

Seismic Response of Liquid Storage Tanks Incorporating Soil Structure Interaction

A frequency domain method is presented to compute the impulsive seismic response of circular surface mounted steel and concrete liquid storage tanks incorporating soil-structure interaction (SSI) for layered sites. The method introduces the concept of a near field region in close proximity to the mat foundation and a far field at distance. The near field is modeled as a region of nonlinear soil response with strain compatible shear stiffness and viscous material damping. The shear strain in a representative soil element is used as the basis for strain compatibility in the near field. In the far field, radiation damping using low strain soil response is used. Frequency dependent complex dynamic impedance functions are used in a model that incorporates horizontal displacement and rotation of the foundation. The focus of the paper is on the computation of the horizontal shear force and moment on the tank foundation to enable foundation design. Significant SSI effects are shown to occur for tanks sited on soft soil, especially tanks of a tall slender nature. SSI effects take the form of period elongation and energy loss by radiation damping and foundation soil damping. The effects of SSI for tanks are shown to reverse the trend of force and moment reduction under earthquake loading as is usually assumed by designers. The reasons for this important effect in tank design are given in the paper and relate to the very short period of most tanks, hence, period lengthening may result in load increase. A comparison is made with SSI effects evaluated using the code SEI/ASCE 7-02. Period elongation is found to be similar for relatively stiff soils when assessed by the code compared with the results of the dynamic analysis. For soft soils, the agreement is not as good. Code values of system damping are found to agree reasonably well with an assessment based on the dynamic analyses for the range of periods covered by the code. Energy loss by material damping and radiation damping is discussed. It is shown that energy loss may be computed using the complex dynamic impedance function associated with the viscous dashpot in the analytical model. The proportion of energy loss in the translation mode compared to that dissipated in the rotational mode is addressed as a function of the slenderness of the tank. Energy loss increases substantially with the volume of liquid being stored.

EFECTOS DE INTERACCIÓN SUELO-ESTRUCTURA EN EDIFICIOS CON PLANTA BAJA BLANDA

Las estructuras con planta baja flexible son muy vulnerables a la acción de sismos. Esto es debido, principalmente, a la falta de rigidez y resistencia en el piso blando. Las Normas Técnicas Complementarias para Diseño por Sismo del RCDF tratan el problema como una condición de irregularidad estructural, limitándose a reducir el factor de comportamiento sísmico que controla las resistencias de diseño. De esta forma se aumenta la capacidad de rigidez y resistencia de toda la estructura, pero no se corrige el contraste que existe entre el piso blando y el resto de los entrepisos. En este trabajo se desarrolló un modelo numérico para estimar la respuesta dinámica de estructuras con planta baja flexible desplantadas sobre suelo blando. El modelo es elástico y tiene en cuenta el alargamiento del periodo estructural debido a la flexibilidad del suelo, así como el incremento en el amortiguamiento debido a la disipación de energía por radiación de ondas en el suelo. Considerando que el amortiguamiento está distribuido a lo largo del edificio, se construye una matriz de amortiguamiento clásico para la estructura sola usando amortiguamiento modal. Para el suelo, en cambio, se considera amortiguamiento elemental haciendo uso de amortiguadores viscosos para los distintos modos de vibrar de la cimentación. Debido a que el sistema acoplado suelo-estructura carece de modos clásicos de vibrar, la respuesta estructural se obtiene con el método de la respuesta compleja en la frecuencia.

Soil interaction effects on the performance of compliant liquid column damper for seismic vibration control of short period structures

The paper presents a study on the effects of soil-structure-interaction (SSI) on the performance of the compliant liquid column damper (CLCD) for the seismic vibration control of short period structures. The frequency-domain formulation for the input-output relation of a flexible-base structure with CLCD has been derived. The superstructure has been modeled as a linear, single degreeof-freedom (SDOF) system. The foundation has been considered to be attached to the underlying soil medium through linear springs and viscous dashpots, the properties of which have been represented by complex valued impedance functions. By using a standard equivalent linearization technique, the nonlinear orifice damping of the CLCD has been replaced by equivalent linear viscous damping. A numerical stochastic study has been carried out to study the functioning of the CLCD for varying degrees of SSI. Comparison of the damper performance when it is tuned to the fixed-base structural frequency and when tuned to the flexible-base structural frequency has been made. The effects of SSI on the optimal value of the orifice damping coefficient of the damper has also been studied. A more convenient approach for designing the damper while considering SSI, by using an established model of a replacement oscillator for the structure-soil system has also been presented. Finally, a simulation study, using a recorded accelerogram, has been carried out on the CLCD performance for the flexible-base structure.

Influence of soil–structure interaction on the response of seismically isolated cable-stayed bridge

Soil conditions have a great deal to do with damage to structures during earthquakes. This paper attempts to assess the influence of dynamic soil–structure interaction (SSI) on the behavior of seismically isolated cable-stayed bridge supported on a rigidly capped vertical pile groups, which pass through moderately deep, layered soil overlying rigid bedrock. In the present approach, piles closely grouped together beneath the towers are viewed as a single equivalent upright beam. The soil–pile interaction is idealized as a beam on nonlinear Winkler foundation using continuously distributed hysteretic springs and viscous dashpots placed in parallel. The hysteretic behavior of soil springs is idealized using Bouc–Wen model. The cable-stayed bridge is isolated by using high-damping rubber bearings and the effects of SSI are investigated by performing seismic analysis in time domain using direct integration method. The seismic response of the isolated cable-stayed bridge with SSI is obtained under bi-directional earthquake excitations (i.e. two horizontal components acting simultaneously) considering different soil flexibilities. The emphasis has been placed on assessing the significance of nonlinear behavior of soil that affects the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. It is observed that the soil surrounding the piles has significant effects on the response of the isolated bridge and the bearing displacements may be underestimated if the SSI effects are ignored. Inclusion of SSI is found essential for effective design of seismically isolated cable-stayed bridge, specifically when the towers are very much rigid and the soil condition is soft to medium. Further, it is found that the linear soil model does not lead to accurate prediction of tower base shear response, and nonlinear soil modeling is essential to reflect dynamic behavior of the soil–pile system properly.

On the Phenomenological Modeling of Electrorheological and Magnetorheological Fluid Preyield Behavior

Phenomenological constitutive models for electrorheological and magneto-rheological fluids and devices in the literature have used various approaches for the representation of the preyield regime. These include modeling the preyield regime using an elastic spring, a viscous dashpot, a Kelvin–Voigt solid, a Maxwell fluid, a three-element (Zener) solid, and a three-element fluid. This paper reviews the behavioral attributes associated with each of the above models. Then, considering the physical phenomena prior to the onset of yield, and experimental data in the preyield regime, and comparing with the behavioral attributes exhibited by the various preyield models, it is concluded that the behavior in the preyield regime is solid-like, not fluid-like, and most conveniently represented as a Kelvin–Voigt viscoelastic solid. In particular, over frequency ranges of interest, the storage modulus does not approach zero at low-frequency limits, as a fluid would exhibit. Effectively modeling the preyield behavior as a Maxwell fluid, as has been done in the literature, yielded frequency-dependent system parameters (specifically the preyield viscosity). This is the result of a viscoelastic fluid model attempting to display the viscoelastic solid-like characteristics exhibited by the test data.

Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials

A model is developed that describes the sharp indentation behavior of time-dependent materials. The model constitutive equation is constructed from a series of quadratic mechanical elements, with independent viscous (dashpot), elastic (spring), and plastic (slider) responses. Solutions to this equation describe features observed under load-controlled indentation of polymers, including creep, negative unloading tangents, and loading-rate dependence. The model describes a full range of viscous–elastic–plastic responses and includes as bounding behaviors time-independent elastic–plastic indentation (appropriate to metals and ceramics) and time-dependent viscous–elastic indentation (appropriate to elastomers). Experimental indentation traces for a range of olymers with different material properties (elastic modulus, hardness, viscosity) are econvoluted and ranked by calculated time constant. Material properties for these polymers, deconvoluted from single load–unload cycles, are used to predict the indentation load–displacement behavior at loading rates three times slower and faster, as well as the steady-state creep rate under fixed load.

Effect of Soil Plasticity on Damping Ratio at Small Cyclic Strains

In soil dynamics, the most common parameter for measuring soil damping is the equivalent viscous damping ratio, which is derived from the theory of a single-degree-of-freedom system with viscous dashpot. The results of a comprehensive literature review on the equivalent viscous damping ratio at small cyclic shear strain amplitudes, yc, between 0.0001% and 0.01% are presented and discussed. On the basis of the published data from different types of laboratory tests two important trends are established. The first is a significant increase of the scatter of the data points as the plasticity index of the soil, PI, decreases. This indicates that damping in low-plasticity clays and sands is more sensitive to factors such as confining stress, overconsolidation ratio and cyclic loading waveform than the damping in high-plasticity clays. The second trend is an increase of the damping ratio with PI. This trend with PI is opposite from the trend at yc > 0.01% established earlier, where damping ratio generally decreases with PI. An explanation is provided that the phenomena responsible for the increase of the damping ratio with PI at small yc are viscous creep and relaxation of the soil.

Mental results and dynamic parameters for the Penguin Vibration Damper (PVD) for wind and earthquake loading

Penguin Engineering Ltd has developed a compact, efficient, hysteretic damping device, the Penguin Vibration Damper (PVD). Experimental test results show that the PVD can provide a significant amount of damping at displacements as small as 50 micro-metres.
 The hysteresis behaviour of the PVD can be described well either by a model having a linear spring in parallel with a viscous dashpot, or by a bi-linear model, with the parameters of both models being displacement-amplitude dependent. For large displacements, the bi-linear model gives an accurate representation of the PVD's hysteresis loops, and the parameters for the bi-linear model can be taken as constants. Non-linear models, such as the hyperbolic, Ramberg-Osgood and multi-surface plasticity models, can also be used and have an advantage of displacement-amplitude-independent parameters. However, it can be shown that nonlinear models do not correctly predict the amount of damping that a PVD provides at large displacement even though the equivalent spring coefficient can be well approximated. When the PVDs are expected to undergo large displacements, it is possibly best to use a simple bi-linear model in dynamic nonlinear structural analyses, because the bi-linear model with suitably selected parameters can produce the correct amount of damping derived from the experimental data.
 The changes of the PVD's dynamic behaviour are small after a fatigue test of 144 000 cycles with a displacement amplitude of 2 mm.
 An analysis of a 6-storey reinforced concrete moment resisting frame is used to demonstrate the effect of the damper. Equivalent first modal damping ratios are estimated for various levels of earthquake excitations. The example shows that the dampers can provide a large amount of damping to the structure and enhance the structural capacity, for resisting earthquakes, by 50-100%.

Nonlinear Seismic Soil-Pile Structure Interaction

Analytical design tools for evaluation of soil-pile-structure interaction during seismic events are evaluated and modified. Several implementations of the “Beam on Nonlinear Winkler Foundation” (BNWF) method were used to predict results of centrifuge model tests of single piles in a soft clay soil profile. This paper shows that calculations from these computer codes can be sensitive to the details of the arrangement of nonlinear springs and linear viscous dashpots. Placing the linear viscous dashpots (representing radiation damping in the far field) in series with the hysteretic component of the p-y elements (representing the nonlinear soil-pile response in the near field) is shown to be technically preferable to a parallel arrangement of the viscous and hysteretic damping components. Preliminary centrifuge data is reasonably modeled by the numerical calculations using this implementation of damping, but additional field or physical model data are needed to fully evaluate the reliability of BNWF procedures.