Nonlinear Dashpot Research Articles

Creep-recovery deformation of 304 stainless-steel springs under low forces

The deformation behavior of materials at high temperatures determines the structural stability of mechanical structures under high-temperature service conditions. In this work, we prepare helical springs from 304 stainless-steel wires and study creep-recovery deformation of the helical springs under small forces at temperatures of 475–575 °C. In contrast to most methods reported in the literature, we use Kelvin representation of the Burgers model with a nonlinear dashpot in series connection to analyze the creep-recovery deformation of the helical springs and suggest the deformation mechanisms of the diffusion of interstitial atoms and dislocation generation/annihilation in transient creep and recovery of the helical springs under small forces. For the creep deformation, the stress exponent and activation energy for the plastic flow of the nonlinear dashpot are 2 and 57.8 kJ/mol, respectively, and the activation energy for the deformation flow of the linear dashpot is 41.8 kJ/mol. The nonlinear dashpot does not play any role in the recovery deformation, and the formation energy of defects for the recovery deformation of the helical springs is 51.4 kJ/mol. The approach used in this work provides a simple method to use a phenomenological model with a nonlinear dashpot to capture the power-law creep deformation of metallic materials.

Modified Rheological Model for Deep‐Buried Silty Mudstone and Support Time Analysis Application

The rheological properties of soft rocks should be considered in the long‐term design and maintenance of deep‐buried tunnels using uniaxial single‐stage loading and graded incremental cyclic‐loading methods. In this article, creep tests were performed on deep‐buried silty mudstone from a specific water conveyance tunnel in China, with a buried depth in the range of 1650–2320 m and subjected to high in situ stress. The creep curves of silty mudstone under different loading stresses were obtained, showing evident rheological mechanical behavior under complicated external environmental conditions. Based on the classic Burgers rheological model, a new nonlinear creep model was established based on the creep properties of deep‐buried silty mudstone in the project area. Typically, the designated rheological models for certain projects are unsuitable or inadequate. A nonlinear dashpot was calculated using the Levenberg–Marquardt (L–M) method coupled with origin to account for the deterioration trend in the strength of the silty mudstone over time. With the determined parameters, the modified Burgers model exhibited good qualitative consistency with field monitoring data. The user‐defined material mechanical behavior (UMAT) subroutine of the modified Burgers model was successfully achieved after it was implemented in the numerical code ABAQUS. Based on the full‐rheological effect, the proper supporting time of a deep‐buried tunnel was studied, and it was proposed that a second lining should be cast in situ approximately 150 days after the excavation of the tunnel. The outcomes of the proposed modified rheological model can accurately represent the creep behavior of deep‐buried silty mudstones in a specific engineering instance. The research results can provide a basis for the rheological behavior and supporting time of deep‐buried silty mudstone.

Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams

This paper analyzes delamination of multilayered inhomogeneous beam structure by utilization a non-linear viscoelastic mechanical model. The non-linear time-dependent response is treated by a non-linear spring and a non-linear dashpot connected in series to a system of two linear springs and two linear dashpots. The model is under stress that is a linear function of time. The constitutive law of the model representing a non-linear dependence between stress, strain and time is derived. The main goal of the paper is to obtain a solution of the strain energy release rate for the delamination in the multilayered inhomogeneous beam by applying the non-linear viscoelastic model. Solutions are derived by using the complementary strain energy and by analyzing the balance of the energy with taking into account the non-linear viscoelastic behaviour. For this purpose, the constitutive law of the non-linear viscoelastic mechanical model is used. The solutions are applied to obtain results for multilayered beams with non-linear variation of material properties in longitudinal direction. The influence of different parameters on the time-dependent strain energy release rate is assessed. The study indicates the effectiveness of the viscoelastic mechanical models with non-linear springs and dashpots in time-dependent delamination analyses of multilayered inhomogeneous beam structures.

A novel nonlinear variable damping device and its application for the systems with uncertain parameters

This paper deals with the performance of a novel nonlinear viscous dashpot with variable damping. The new proposed dashpot can be utilized in devices for instance dynamic vibration absorbers (DVAs). When the vibration absorber is tuned to the bridge's fundamental frequency, it represents a robust effect in controlling the vibrations of the bridge; however, a DVA is very sensitive to frequency detuning. The proposed nonlinear dashpot can be applied in a passive vibration absorber and upgrades it to a nonlinear variable damping one. Since the parameter of such DVA can be adjusted, it is the so-called nonlinear adjustable DVA. The mentioned dashpot, provides a quadratic nonlinearity for the damping element. The proposed dashpot in this study possesses a simple mechanism, which can handle large range of flow rates of fluid, smoothly without turbulence, in the oil channel. To investigate the effectiveness of an adjustable vibration absorber, a semi-active DVA with variable damping, and stiffness elements is applied on a footbridge; where, the footbridge is experienced variations of the fundamental frequency over time, and is subjected to a walking pedestrian. For the case study in the present study, a vibration reduction of 31% in comparison with the attached traditional passive DVA with constant parameters was achieved. The results show that, by using the proposed nonlinear dashpot, presented in this study, into an attached DVA, the footbridge will experience about 10% more deflection reduction concerning a classical linear DVA.

Effects of linear and nonlinear dashpots forces on the dynamics of plants vibrating in a vegetation cover situation

This paper considers the nonlinear dynamics of the oscillations of an individual plant forced by the fluctuating aerodynamic drag and significantly influenced by collisions with its close neighbors. In this study, a row of identical and flexible oscillators is considered. The flexible beams theory is used to model the equation of motion of an individual plant and then plant collisions were modelled as a simple spring, linear dashpot and nonlinear dashpot interactions between adjacent plants. The multiple scales method is used to obtain the amplitude of the plant relative to wind forcing in the resonant and nonresonant oscillations cases. Numerically, chaotic oscillations, hysteresis and coexistence of attractors have been found using the bifurcation diagram, the Lyapunov exponents and the phase portraits. The influences of both type of dashpot collisions on the dynamics behaviors of the plant have been analyzed.

Effects of static indeterminacy on the lengthwise fracture in non-linear viscoelastic inhomogeneous beams loaded in torsion

Lengthwise fracture of statically undetermined beam structure that has non-linear viscoelastic behaviour is analyzed in this paper. The beam is loaded in pure torsion. The cross-section of the beam is a circle. The beam exhibits continuous material inhomogeneity along the radius of its cross-section. The mechanical behaviour of the beam is treated by a viscoelastic model structured by non-linear springs and non-linear dashpots. The static indeterminacy is resolved first and then the problem of the time-dependent strain energy release rate is solved by considering the complementary strain energy. The energy balance is analyzed for verification of the solution of the strain energy release rate. A parametric investigation of the strain energy release rate is carried-out.

Seismic response of nonlinear soil-structure interaction systems through the Preisach formalism: the Messina Bell Tower case study

In this paper the seismic response of linear behaving structures resting on compliant soil is addressed through the application of the Preisach formalism to capture the soil nonlinearities. The novel application of the Preisach model of hysteresis for nonlinear soil-structure interaction problems is explored through the study of the seismic response of a real structure. Through a harmonic balance procedure, furthermore, simplified nonlinear springs and dashpots are derived in closed form for a ready and accurate evaluation of the nonlinear soil-structure interaction response. The selected case study is the bell tower of the Messina Cathedral in Italy. The Bell Tower hosts the largest and most complex mechanical and astronomical clock in the world and it has been recently equipped by a permanent seismic monitoring system. A pertinent finite element (FE) model including the superstructure and the soil underneath, has been defined using authentic drawings and engineering design reports. The modal properties of the FE model have been compared with the experimental ones, identified from environmental noise recorded through the seismic monitoring system. Furthermore, the FE model has been validated by means of acceleration time histories recorded at different floors during two independent seismic events. A nonlinear incremental dynamic analysis of the Bell Tower has been also performed. The seismic response obtained by the complete FE analysis, has been compared with the proposed Preisach lumped parameter model, assembled with nonlinear springs and nonlinear dashpots. The results are well in agreement, offering an alternative promising strategy for the nonlinear soil-structure interaction studies.

Improved Maxwell Model Describing the Whole Creep Process of Salt Rock and its Programming

Based on the creep test results of salt rock, three stages of changes in the viscosity coefficient with time during the creep process of salt rock were delimited from the perspective of creep rate, namely, gradually increased stage, basically unchanged stage and gradually decreased stage. According to this variation, a nonlinear dashpot was proposed, and its viscosity coefficient was assumed as a function of creep time. Then, the dashpot in the Maxwell model was replaced by this nonlinear dashpot to establish an improved Maxwell model that can describe the whole creep process of rock. The rationality of the improved Maxwell model was verified based on the uniaxial compression creep test results of salt rock and the triaxial compression creep test results of coal. Comparisons of the theoretical curves of the model and test results show good agreement between them, and the model can describe the three stages of the whole creep process of rock with a unified expression, thereby overcoming the shortcomings of the traditional mechanical model that requires segmentation processing. Based on the secondary development platform of the FLAC[Formula: see text] software, the secondary development of the improved Maxwell model was achieved by using VC++ 6.0 development environment, and the computer application program of the model was obtained. Then, the secondary development program of the model was used to simulate the uniaxial compression creep test of salt rock and the triaxial compression creep test of coal. In general, the numerical simulation results are in good agreement with the test results, proving the correctness of the secondary development calculation program of the model.

Formulation of non-linear viscoelastic–viscoplastic constitutive equation for polyamide 6 resin

In this study, a non-linear viscoelastic–viscoplastic constitutive equation for polyamide 6 (PA6) is formulated and a new model is suggested for the viscoplastic part of the equation. The suggested model is empirical but can accurately predict the viscoplastic strain. In this study, creep and recovery tests are conducted to evaluate the viscoplastic strain. Using a non-linear dashpot, a viscoplastic strain is formulated and its parameters are identified for PA6. In addition, a stress relaxation test is conducted, and the relationship between the viscoelastic strain and stress is identified when considering the viscoplastic strain. In this study, the time–temperature superposition principle is thoroughly applied to include the effect of elevated temperature on the viscoelastic–viscoplastic behavior. All material constants in the non-linear viscoelastic–viscoplastic constitutive equation including the time–temperature superposition principle for PA6 are presented in this study.

Experimental investigation and modeling of nonlinear, adaptive dashpot

In this paper we determine the characteristics of mechanical components of dynamical systems using a specially designed laboratory rig. We present the details of the experiments performed on the prototype device and provide technical documentation of its crucial elements. We validate the accuracy of measurements using a spring and comparing results with manufacturer data. Then, we examine nonlinear dashpot with variable damping coefficient obtained through the usage of the throttling valve. We perform several tests presenting its force characteristics as a function of velocity and damping coefficient. We derive the mathematical model of the dashpot basing on the experimental data. Finally, we perform transient test in which we change the damping coefficient during operation of the dashpot. The comparison of obtained results with the model gives good accordance.

Study on the creep behaviours and the improved Burgers model of a loess landslide considering matric suction

Loess landslides frequently occur in the northwest area of China, leading to serious damage to the society and economy. Under the effects of rainfall and groundwater seepage, the stress–strain behaviours of Malan loess landslides are closely related to the saturated–unsaturated state of slide mass. Hence, it is of great significance to study the creep behaviours of Malan loess considering matric suction. First, the sliding-zone soil of a typical Malan loess landslide is collected to carry out tri-axial creep tests with a confining pressure of 100 kPa and diffident matric suction values of 20, 50 and 80 kPa. Then, a stress–suction–strain–time model (an improved Burgers model) is established by connecting a nonlinear dashpot element in series with the Burgers model and combining this with the functional relationship between the viscoelastic modulus and matric suction. The results show that (1) the Malan loess has obvious creep behaviours with viscoelastic and viscoplastic creep properties, (2) the long-term shear strength of Malan loess increases along with the increase in its matric suction, and (3) the improved Burgers model can more accurately describe the unsaturated creep behaviours of Malan loess with matric suction compared to the traditional Burgers model.

Optimal design and seismic performance of tuned fluid inerter applied to structures with friction pendulum isolators

The hydraulic realization of the inerter, called fluid inerter, is a piston-cylinder device designed to convey a fluid through an external helical channel, thus producing rotational inertia of a fluid mass. This paper proposes a novel base-isolation scheme that combines friction pendulum isolators with a Tuned Fluid Inerter (TFI), wherein a grounded fluid inerter benefits from the interaction with an auxiliary set of low-damping rubber isolators as tuning elements. Based on experiments on a small-scale prototype, the fluid inerter is modeled as a linear inerter in parallel with a nonlinear dashpot, whose power-law damping term is related to the pressure drops in the helical channel. Instead, the hysteretic behavior of friction pendulum isolators is described by a standard Coulomb-type frictional model. Optimal design of the fluid inerter is performed within a probabilistic framework, by modeling the base acceleration as a Kanai-Tajimi filtered random process and handling the nonlinearities of fluid inerter and friction isolators through statistical linearization. An extensive parametric study is conducted to assess the influence of different characteristics of isolators and earthquake excitation and, above all, of the nonlinearity of the fluid inerter. The effectiveness of the TFI is demonstrated through nonlinear response history analysis under a suite of 100 ground-motion records. The proposed isolation scheme not only significantly reduces the displacement demand of the isolators, but also mitigates the acceleration and interstory drift response of the superstructure. Moreover, the benefits of the inherent nonlinear damping effect produced by the fluid inerter proves to be particularly effective to reduce the peak response under pulse-like ground motions that may occur in near-field earthquake events, which indeed represent critical excitations for structures with friction isolators.

Mem-models as building blocks for simulation and identification of hysteretic systems

In this study, mem-springs and mem-dashpots from a newly introduced family of mem-models are used as fundamental building blocks in hysteresis modeling. The usefulness of such assemblies of mem-models is investigated for both simulation and system identification. First, numerical simulations demonstrate the general capability of these models to describe strain ratcheting behaviors. Next, system identification is addressed by extending the concepts of mem-springs to include linear and nonlinear springs and those of mem-dashpots to include linear and nonlinear dashpots. A reconfigurable device made of steel and/or shape memory alloy wires and wire ropes provides a fitting test for the proposed mem-model-based family. A system identification procedure corroborated by physical insights is proposed and the results are validated using physics-based analysis. Multilayer feedforward neural networks are used for static nonlinear function approximation. The model class and system identification procedure proposed here are shown to extract similarities and dissimilarities among different configurations of the device by quantifying the spring and damping effects.

Modified Nishihara model and experimental verification of deep rock mass under the water-rock interaction

During the mining process of deep mines, the instability of surrounding rock caused by rock creep has occurred from time to time. However, it is difficult to study the accelerating creep phase of rock with the classical Nishihara model. Due to the influence of water seepage and different stress, rock creep exhibits non-linear characteristics. For this reason, on the basis of the Nishihara model, the dashpot in the Kelvin model was replaced by the Abel dashpot, and the dashpot in the plastomer model was modified to non-linear dashpot, and the modified Nishihara model and its constitutive equation were established. Based on the creep experimental data of granite, the experimental results of granite under different stress and different osmotic pressures were analyzed. The typical experimental data were fitted by using MATLAB software, and the fitting results showed that the modified Nishihara model was verified. The model can better describe the whole process (decelerating creep phase, stable creep phase, accelerating creep phase) and non-linear characteristics of rock creep. Especially when the load on the rock is greater than the long-term strength, the accelerating creep phase of rock is more obvious. The modified Nishihara model has five parameters, and the method for determining each parameter is simple and has wide applicability. It better reflects the damage and failure process of the surrounding rock subjected to stable creep phase and accelerating creep phase after excavation, which can provide theoretical basis for further revealing the objective law of rock creep.

Dynamic characterization of elastomer buffer under impact loading by low-velocity drop test method

Abstract An approach is proposed to establish a discrete model to characterize the dynamic behavior of a thermoplastic polyurethane elastomer buffer under impact loading. To this end, a series of low velocity drop tests with initial impact velocities 1.77–4 m/s was carried out. The impact force versus time histories for the samples under impact loading were measured with varying initial impact velocities. To obtain acceleration, velocity and displacement of the projectile, Newton's second law of motion and the numerical integration method were applied. The stress-strain, coefficient of restitution, loss factor and dissipated energy of samples were determined. Following, the experimental data were used to establish a mathematical model for the elastomer buffer. To reach this aim, Maxwell and Kelvin-Voigt viscoelastic impact models and one-dimensional viscoelastic free decay oscillation model were employed. It was observed that Kelvin-Voigt and one-dimensional viscoelastic free decay oscillation models underestimated the buffer dynamic characteristics. An approach was proposed to calculate the calibrated nonlinear Maxwell viscoelastic impact model. The proposed model consists of a nonlinear dashpot and nonlinear spring. The calibrated nonlinear Maxwell model predicted the elastomer buffer impact behavior in terms of peak force, maximum deflection, dissipated energy and coefficient of restitution with high accuracy.

Novel fluid inerter based tuned mass dampers for optimised structural control of base-isolated buildings

This work studies the advantageous features of the fluid inerter device for optimised structural control of buildings. Experimental data are first presented to characterise the fluid inerter dynamics, and validate the simplified analytical formulations. Building on these observations, the device is modelled as an inerter in parallel with a nonlinear dashpot representing a power law damping term. The latter dissipative effects are mainly induced by the pressure drops occurring in helical channels due to the fluid viscosity and density. Then, novel passive vibration control schemes are implemented for the earthquake protection of base-isolated buildings by combining the fluid inerter with a tuned mass damper system. To account for the uncertain nature of the earthquake input, the base acceleration is modelled as a Kanai–Tajimi filtered stationary random process. The optimal fluid inerter parameters, namely inertance and damping, are identified numerically by minimising stochastic performance indices relevant to displacement, acceleration, and energy-based measures of the structural response. The nonlinear damping behaviour of the fluid inerter is fully incorporated in the optimal design procedure via the statistical linearisation technique. Nonlinear response history analysis under an ensemble of 44 natural earthquake ground motions is carried out to assess the seismic performance of the system. Since inertance and damping are coupled characteristics in a real fluid inerter, design guidelines are finally outlined to determine the actual geometrical and mechanical properties of the device to achieve targeted parameters resulting from the optimisation procedure.

Seismic performance assessment of steel moment-resisting frames equipped with linear and nonlinear fluid viscous dampers with the same damping ratio

This manuscript presents a comparative study between the seismic collapse performances of steel moment-resisting frames (MRFs) with the same additional damping ratio while equipped with linear and nonlinear viscous dampers. Three steel moment-resisting frames of 6, 8 and 12 stories were designed based on ASCE 7–10 with and without dampers. The characteristics of the linear (α=1) and nonlinear (α=0.5) dampers were then assigned while assuming equal damping ratios (20% for the models of 6 and 8 stories, and 25% for the model of 12 stories). The sophisticated nonlinear model of the structures was then developed in Opensees considering both cyclic strength and stiffness deterioration with lumped plasticity as well as the linear and nonlinear dashpot for dampers while nonlinear geometry was included in all the models. The collapse probability was calculated using well-known incremental dynamic analysis (IDA) under far-field records. The paper demonstrates that the use of damper improves the performance of the steel MRFs and reduces the collapse probability in comparison with the conventional steel MRFs. Moreover, it was observed that steel MRFs with linear dampers have better collapse performance than steel MRFs with nonlinear dampers for the same damping ratio.

A size-dependent viscoelastic normal contact model for particle collision

Considering different energy dissipation mechanisms, many normal contact models have been proposed. However, the size effect and velocity effect of normal restitution coefficient (NRC) cannot always be accurately described. In addition, most of the normal contact models have unphysical tension stage for particles without adhesion during the simulation of particle collisions. Such problems limit the application of discrete element method (DEM) in particle dynamics. Given such limitations, the normal contact model proposed in the present work consists of a nonlinear Hertz spring and a size-dependent nonlinear dashpot, and the model parameters are determined by the NRC obtained in lab tests. Compared with other viscoelastic contact models, the current model can effectively alleviate the influence of unphysical tension force stage on the calculated results, satisfying the accuracy requirement of calculation, and accurately describe the size effect and velocity effect of the NRC of marble spheres at the same time. Besides, due to the viscous force, the contact time calculated by the current model is a little larger than the elastic contact time. The relationship between model parameters and particle size has been analyzed, which shows the law of K1 conforms to exponential decay law and the K2 conforms to hyperbolic tangent function.

Characterization of a thermoplastic foam material with the two-layer viscoplastic model

This article presents the mechanical characterization of a particular thermoplastic foam material applied in thermoforming processes. During the thermoforming process such materials undergo large deformations, which shows elastic, viscous and yielding properties as well. Additionally, the material behavior is strongly temperature-dependent. The only available material model implemented in the commercial finite element software ABAQUS, which can describe such material behavior properly, is the so-called “two-layer viscoplastic model”. This model is comprised of an elastic-plastic network in parallel with a Maxwell-type viscoelastic branch characterized by a nonlinear dashpot. In our investigations mechanical tests have been performed on several temperatures and based on the experimental results, the material parameters have been fitted using the external optimization software ISIGHT, since the analytical stress-solution for the two-layer viscoplastic model is not available.

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

SummaryIn this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.