Time-dependent Loading Research Articles

Transient thermomechanical responses of multilayered viscoelastic composite structure with non-idealized interfacial conditions in the context of generalized thermoviscoelasticity theory with time-fractional order strain

Nowadays, a multilayered viscoelastic composite structure stands as one of the most representative active/passive vibration isolator and high-efficient damper to avoid unwanted vibrations in civil and ocean engineering, which is commonly applied in harsh non-uniform temperature environment (e.g., high heat-flux, drastic changes of temperature, etc.). In such a case, thermoviscoelastic response analysis is of great importance for the safety design of viscoelastic composites, and so a thorough and comprehensive study on this issue is imperatively needed. This work aims to conduct an analytical study of transient thermomechanical responses of multilayered viscoelastic composite structure under time-dependent heating loads. In the context of generalized thermoviscoelasticity theory with time-fractional order strain, a composite laminated viscoelastic plate is chosen as the analytical model while governing equations of each homogeneous layer accounting for non-idealized interfacial conditions are systematically formulated. Then, a semi-analytical approach via Laplace transform is adopted to deal with the problem. The effects of fractional order parameters and material constants’ ratio on the structural dynamic responses are fully discussed to provide new insights and basic guidelines for vibration control and thermal management of viscoelastic composites, especially for the surface coating at the interface between any two adjacent viscoelastic layers.

Memory response in the vibration of a micro-scale beam due to time-dependent thermal loading

This study proposes a computationally efficient approach about the dynamic response of a homogeneous, transversely isotropic, thermoelastic micro-beam resonator subjected to time-dependent thermal loading. Due to the shortcomings of power law distributions in fractional derivatives, the usage of some other forms of derivatives with few other kernel functions are proposed. With this motivation, the heat transport equation is defined in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer which is modeled based on Euler-Bernoulli beam theory. The beam is assumed to be clamped-clamped conditions on its axial ends. Employing the Laplace transform technique, the analytical solutions have been obtained. Further, incorporating residual calculus, the inversion of the transformed solutions are performed. The analytical expressions for the deflection has been computed numerically for a Silicon micro-beam using Maple software. The new approach is able to portray material heterogeneities and the non-locality of the new kernel allows the full describing of the memory within structure and media with different scales, which cannot be described by classical fractional derivative and also that of the memory-dependent derivative.

Time-Dependent Aerodynamic Loads on Single and Tandem Stores in a Supersonic Cavity

To understand time-dependent aerodynamic loads on single and tandem (fore/aft) slender cylinders translated out into the supersonic freestream from a cavity at Mach 1.5, the normal force and pitching moment are experimentally obtained via load cells. For a single long store, the measurements were conducted with two different angles of attack at several static positions and with dynamic motions. For tandem stores, the fore- and aft-positioned stores were translated both independently and simultaneously with various time delays. The single long store results had good repeatability and revealed that the fastest dynamic motions () exhibited unsteady forces and moments that differed from quasi-static results. Moreover, the results from the tandem stores showed that the aft-positioned store had more favorable aerodynamic loads as compared to the front store for the static measurements. However, when stores were ejected simultaneously or with time delay, the aft-positioned store was strongly affected by the forward-positioned store and showed bifurcation on the aerodynamic loads after the shear layer.

A comparison of the Bolotin and incremental harmonic balance methods in the dynamic stability analysis of an Euler–Bernoulli nanobeam based on the nonlocal strain gradient theory and surface effects

This study addresses the dynamic stability of an Euler–Bernoulli nanobeam under time-dependent axial loading based on the nonlocal strain gradient theory (NSGT) and considering the surface stress effects. The studied nanobeam cross-section was rectangular, and simply-supported boundary conditions were assumed. Moreover, a uniform thermal gradient was applied to the nanobeam. The elastic medium was modeled based on the Pasternak theory. The strain–displacement relations were derived using the Von Kármán equations. The governing equations were obtained by the energy method and applying the Hamilton's principle. Furthermore, the Bolotin and Incremental Harmonic Balance (IHB) methods were used to solve the differential equations. This study investigates the impact of such parameters as the small-scale parameter, the material length scale, surface effects, elastic medium parameters, temperature variations, geometry, and the static loading factor on the Dynamic Instability Region (DIR). The results are suggestive of the shift of the DIR to lower frequency zone by increasing the small-scale Eringen's nonlocal theory parameter, whereas an increase in the material length scale from the strain gradient theory moves the region to higher frequencies. In case the said parameters are equal, the result conforms to the classical beam theory. In addition, assuming a Pasternak medium and taking into account the effects of surface stress (Young's modulus and the residual stress of the surface) shifts the DIR to higher frequencies, whereas applying a compressive static load moves the region to lower frequencies. Moreover, depending on the thermal expansion coefficient of the medium, temperature variations can also displace the DIR.

Transient response in an elasto-thermo-diffusive medium in the context of memory-dependent heat transfer

In the present study, in order to provide some flexible and more appropriate tools which can better describe cases of the dynamics with memory effects or of nonlocal phenomena, a novel mathematical model of elasto-thermodiffusion introduced in the context of Taylor's series expansion involving memory-dependent derivative of the function for the dual-phase-lag heat conduction law is proposed. The governing equations of this new model are applied to a one-dimensional half-space, which is taken to be traction free and is subjected to different time-dependent thermal loadings (thermal shock, periodically varying thermal loading and ramp-type heating) and chemical shocks. Laplace transform technique is employed to find out the analytical solutions and the inversion of Laplace transform is carried out using a method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed due to thermodiffusion. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative also.

Semi-analytical solutions to consolidation for unsaturated soils by vertical drains under arbitrary time-dependent loading

This paper presents general semi-analytical solutions to equal strain consolidation for unsaturated soil layer by vertical drains, and the well resistance is considered. Firstly, the coupled governing equations are transformed into ordinary differential equations (ODEs) by Laplace transform and introducing two new variables, and combined with boundary conditions to obtain solutions. On this basis, the semi-analytical solutions in the time domain are achieved by performing inverse Laplace transform with Crump’s method. Secondly, the correctness of the semi-analytical solutions are verified by comparison with the existing analytical solutions of radial consolidation for unsaturated soils under constant loading. Finally, the effect of well resistance factor, permeability coefficient ratio ka/kw and load parameter on the average degree of consolidation was analyzed under exponential loading.

On the transient planar contact problem in the presence of dry friction and slip

This article models a plane strain dynamic contact problem for an infinite elastic body. Contact is established for x > 0 under the action of a time-dependent remote compressive load, and the system is subjected to a time-dependent remote tangential load. The two faces of the contact interface can slide relative to one other to accommodate mismatches between the shear stresses and the existing Coulomb friction. This is shown to be a cause of interfacial waves of slip, which this article models by deriving the general expression for the corrective traction due to an arbitrary slip distribution. This is achieved using a variant of the Wiener-Hopf technique. Combined with existing closed-form expressions for the interfacial tractions due to compressive and shear loads, this enables the formulation of the elastodynamic extension to the stick-and-slip problem of the Cattaneo-Mindlin type. Exploiting self-similarity a simple numerical algorithm is detailed for solving the resulting Volterra integral equations of the first kind. The solution is shown to display a number of features entirely missed in static problems: slip waves are shown to exist irrespective of the magnitude of the applied loads and the friction coefficient; a regime of reverse and forward slip is also shown to exist for low friction coefficients, brought about by the interfacial Rayleigh waves. The practical implications of these solutions are discussed.

Exponential and harmonic forced torsional vibration of single-walled carbon nanotube in an elastic medium

In this study, free torsional vibration and forced torsional vibration analysis under the time-dependent exponential and harmonic torsional loadings in single-walled carbon nanotube are investigated. The SWCNT is embedded in an elastic medium. Eringen's theory among the small-scale theories is selected. The nonlocal differential constitutive relation and corresponding boundary condition are derived via Hamilton's principle. Clamped–clamped boundary condition is utilized. The assumed modes method is employed for the dynamic torsional vibration in order to discretize the derived governing equations. The novelty of this work is devoted to the analysis of forced torsional vibration of a carbon nanotube embedded in an elastic medium under the various loadings. The angular displacement for the resonance frequency neglecting the elastic medium is illustrated. For the free analysis, the first three nondimensional natural frequencies with various small-scale parameters and stiffness of the elastic medium are calculated. The results are compared with another study for the first 10 mode numbers. The effects of the nonlocal parameter, length of carbon nanotube, stiffness of the elastic medium, thickness, time constant, and excitation frequency on the nondimensional and dimensional angular displacements are investigated, dynamically. For the greater values of the stiffness of the medium, the nonlocal parameter becomes negligible. When a time-dependent exponential torque is applied to the model, the angular displacement becomes greater and then lower by an increase in the value of the length, but the nondimensional angular displacement decreases continuously by increasing the value of the length under the time-dependent harmonic loading. Moreover, the angular displacement for a determined time becomes lower first and then becomes greater by increasing the time constant.

The stimuli-responsive properties of doxorubicin adsorbed onto bimetallic Au@Pd nanodendrites and its potential application as drug delivery platform

Bimetallic nanoparticles have continued to attract interest as drug delivery systems in cancer therapy even though their nature of interaction with small molecules is limited. Currently, many delivery systems based on monometallic nanoparticles are being fabricated for loading of drugs, thus prompting the need to explore and get more understanding of dendritic bimetallic nanostructure-drug interaction. The bimetallic gold-core palladium-dendritic shell nanoparticles (Au@PdNDs) were synthesized by hot injection method and stabilized with methoxy polyethylene glycol thiol (mPEG-SH). An anti-cancer drug, doxorubicin (DOX) was conjugated to the bimetallic nanodendrites leading to the formation of DOX/Au@PdNDs.PEG complex. We used TEM, FTIR, and zeta-potential to study the drug-nanodendrites interaction. The effect of DOX binding and release capacity with regards to pH, adsorption kinetics, solvent polarity, isotherms and temperature on Au@PdNDs.PEG were investigated. The results showed a spontaneous heterogeneous binding of DOX on the Au@PdNDs.PEG surfaces and time-dependent loading capacity of ~90% maximum adsorption within 24h. Moreover, the experimental results showed that the adsorption isotherm data fitted well with the Freundlich model and a pseudo-second order adsorption kinetics. The desorption of DOX was triggered under simulated tumor microenvironmental conditions and should open new opportunities for potential multi stimuli-responsive drug delivery applications.

Eigenvector dimension-reduction method for reliability analysis of power systems under the time-dependent load uncertainty

ABSTRACT Power systems have become central pillars of modern society. Various uncertainties in power systems, however, make reliability analysis difficult. To date, the worst-case scenario was usually employed to tackle uncertainties in the system, which could make the overall system design prohibitively expensive especially when more and more uncertainty sources would be considered in modern power grids. This paper proposes reliability analysis of power systems under the time-dependent load uncertainty using an effective uncertainty quantification (UQ) method, i.e., the eigenvector dimension reduction (EDR) method. As such, reliability can be explicitly calculated in the probability manner for meeting the performance constraints without significantly overdesigning the system. Compared to the Monte Carlo simulation (MCS), the EDR method is much more efficient with satisfactory accuracy. Two case studies, including a 12-bus and a modified IEEE 118-bus power system, are used to demonstrate the feasibility of the proposed work.

Finite element for the dynamic analysis of pipes subjected to water hammer

An axisymmetric finite element is developed for the dynamic analysis of pipes subjected to water hammer. The analysis seamlessly captures the pipe response due to water hammer by solving first the water hammer mass and momentum conservation equations, to recover the spatial–temporal distribution of the internal pressure, and then uses the predicted pressure history to form a time-dependent energy equivalent load vector within a finite element model. The study then determines the pipe response by solving the finite element discretized equations of motion. The formulation of the pipe response is based on Hamilton’s principle in conjunction with a thin shell theory formulation, and captures inertial and damping effects. The results predicted by the model are shown to be in agreement with those based on an axisymmetric shell model in Abaqus for static, free vibration and transient responses for benchmark problems. The water hammer and structural models are seamlessly integrated to enable advancing the transient solution well into the time domain to capture the effect of reflected pressure wave due to water hammer. The results indicate that the radial stress/displacement oscillations approach those of the quasi-steady response when the valve closure time exceeds eight times the period of radial vibrations obtained for the case of instantaneous valve closure.

Influence of hydrogen on dwell-fatigue response of near-alpha titanium alloys

The prior studies have investigated the influence of internal hydrogen on dwell-fatigue behavior of near-α titanium alloys primarily in the lamellar microstructural condition. In the current study, the effects of internal hydrogen, in the range 10–230 ppm (by weight), on the dwell-fatigue behavior of Ti-6242Si alloy were investigated. The examined alloy had a bimodal microstructure comprising approximately 70 vol% primary α grains and 30 vol% transformed β regions. The dwell-fatigue life generally increased with increasing hydrogen content. The dwell-fatigue lives were longer by a factor of as high as 6 for high (≥150 ppm) hydrogen contents than for the low (<60 ppm) hydrogen contents, which is reported for a near-α titanium alloy for the first time. The crack-initiation site was essentially faceted for all the hydrogen levels examined in current study. The crystallographic orientations of fracture facets at the crack-initiation sites were similar for the low (<60 ppm) and high (>150 ppm) hydrogen contents. Specifically, these facets were inclined at ∼8 – 17° from the basal plane. Therefore, the longer dwell-fatigue lives observed for the alloys with hydrogen contents ≥150 ppm could not be explained on the basis of any differences in crystallography of the facets at crack-initiation sites. The longer dwell-fatigue lives for higher hydrogen contents can be explained within the framework of time-dependent load shedding from the soft microtextured regions (MTRs) to the hard MTRs if the local stress redistribution at the soft MTR/hard MTR boundary due to the hold at maximum load is reduced with increasing hydrogen content.

Load identification for a viscoelastic solid by an accurate meshfree sensitivity analysis

This article presents a novel inverse method for identification of a space- and time-dependent load, applied to a two-dimensional viscoelastic solid. Measured strains at several points are considered as sampling quantities. An improved meshfree radial point interpolation method is employed to solve the direct problem. The inverse problem is treated by an optimization approach, where the cost function is described in terms of the differences between measured and computed strains. The damped Gauss Newton method is utilized to solve the inverse problem. A new approach for the sensitivity analysis based on direct differentiation of governing equations is presented. The Tikhonov regularization method is employed to eliminate the undesired oscillations of the solutions of the inverse problem. Using a method based on the condition number of the sensitivity matrix, an appropriate configuration for sensors is determined. The effects of the location and the number of sensors on the accuracy of the identified loads are investigated. The robustness of the presented method to handle noisy measured data is investigated too.

Theoretical and numerical studies of cryogenic fracturing induced by thermal shock for reservoir stimulation

The phenomenon of cryogenic fracturing in rock via thermal shock is approached theoretically and numerically. This study first proposes a theoretical solution of the temperature and stress distribution in a finite plate based on the thermoelastic theory and then discusses the effect of several parameters, including the heat transfer coefficient, the thermal conductivity and the size of the specimen, on the temperature distribution and the associated thermal stress evolution in the plate-shaped model. In addition to predicting the stress and temperature distribution based on the theoretical solution, numerical modeling of the initiation and propagation of cryogenic fractures in a finite plate is used to further explain the effect of the heat transfer coefficient on the density of the newly formed fractures and the length of the fracture growth. The initiation and propagation of cryogenic fractures around a borehole filled with cold liquid and the effect of anisotropic stress on cryogenic fracturing are also studied via numerical modeling. The fracture mechanics are based on the time-dependent thermal loading (thermal shock) and on the concept of stress release and redistribution, with single- and multiple-fracture propagation starting from quenching-generated flaws at the surface at the beginning of thermal shock. Analysis of the best method for increasing the heat transfer coefficient further indicates that it is feasible to stimulate reservoirs with the cryogenic fracturing technique to create a strong thermal gradient that generates a considerable local tensile stress in the rocks surrounding the pre-existing main fractures or the borehole.

A feasible approach to predicting time-dependent bearing performance of jacked piles from CPTu measurements

In this paper, a simple but feasible approach is proposed to predict the time-dependent load carrying behaviours of jacked piles from CPTu measurements. The corrected cone resistance, which considers the unequal area of the cone rod and the cone, is used to determine the soil parameters used in the proposed approach. The pile installation effects on the changes in the stress state of the surrounding soil are assessed by an analytical solution to undrained expansion of a cylindrical cavity in K0-consolidated anisotropic clayey soil. Considering the similarity and scale effects between the piezocone and the pile, the CPTu measurements are properly incorporated in the shaft and end resistance factors as well as in the load-transfer curves to predict the time-dependent load carrying behaviours of the pile. Centrifuge model tests are conducted and the measured load carrying behaviours of the model piles are compared with the predictions to validate the proposed approach. The proposed approach not only greatly saves the time of conducting time-consuming pile load tests, but also effectively avoids solving the complex partial differential equations involved in the consolidation analysis, and hence is feasible enough to determine the time-dependent load carrying behaviours of jacked piles in clay.

Piecewise-linear large-strain model for radial consolidation with non-Darcian flow and general constitutive relationships

A piecewise-linear large-strain radial consolidation model, called VRCS1, is developed for soft soil stabilized by prefabricated vertical drain (PVD) assisted by vacuum-surcharge combined preloading incorporating non-Darcian flow and nonlinear compressibility and permeability relationships. VRCS1 accounts for large strain, soil self-weight, smear effect, partial drain penetration, time-dependent surcharge loading, time- and depth-dependent vacuum pressure, unload/reload effects, radial and vertical flows, hydraulic conductivity anisotropy, non-Darcian flow and nonlinearly varying relationships of compressibility and permeability. The compressibility and permeability constitutive relationships are specified using discrete data points and, as a result, VRCS1 is more flexible than other existing models in terms of considering a variety of different constitutive relationships. VRCS1 shows excellent agreement with other exiting solutions and field measurements involving Darcian flow and non-Darcian flow, surcharge loading and surcharge-vacuum combined loading, and small and large strains. A series of numeric examples indicates that compressibility and permeability relationships can have significant effect on the rate of radial consolidation. Results also indicate that solutions based on small-strain theory can be in significant error for large strain conditions, especially when non-Darcian flow and nonlinear constitutive relationships are encountered.

The reconstruction of a solely time-dependent load in a simply supported non-homogeneous Euler–Bernoulli beam

In this paper, the theoretical and numerical determination of a solely time-dependent load distribution is investigated for a simply supported non-homogeneous Euler–Bernoulli beam. The missing source is recovered from an additional “local” integral measurement. The existence and uniqueness of a solution to the corresponding variational problem is proved by employing Rothe’s method. This method also reveals a time-discrete numerical scheme based on the backward Euler method to approximate the solution. Corresponding error estimates are proved and assessed by two numerical experiments.

Synthesis and Electrochemical Characterization of Silk Fibroin Micro/Nano Particles

In this study, the dynamic instability of three-layered cylindrical shells containing a functionally graded (FG) interlayer subjected to static and time dependent periodic axial compressive loads are investigated. The governing relations, modified Donnell type dynamic stability and deformation compatibility equations are derived. The governing equations are reduced Mathieu–Hill equation by using Galerkin׳s method and the expressions for boundaries of unstable regions of three-layered cylindrical shell with an FG interlayer are found. Finally, the effects of variations of volume fractions of FG interlayer and shell characteristics on the magnitudes of boundaries of unstable regions are studied numerically.

FRP fibre-cementitious matrix interfacial bond under time-dependent loading

This paper presents the behavior of the interfacial bond between an innovative FRP fibre and cement mortar under time-dependent loading. Two types of FRP fibres—GFRP and CFRP were investigated. Particularly, the fibre pullout response under quasi-static loading is compared with the response under dynamic loading. To gauge the long term behavior of cracked fibre reinforced composites, fibre relaxation tests were conducted in which initial strain was imparted and sustained, and the relaxation of the composite in terms of drop in load over time period was monitored at room temperature as well as at 50 °C. FRP fibres were found to be to some extent sensitive to loading rate, with an increase in the range of 30–50% in the peak load under dynamic loading. The GFRP fibres itself depicted higher strengths under dynamic loading rate. Under a sustained fibre slip, FRP fibres showed a lower relaxation at both room temperature and at 50 °C compared to commercially available steel and polypropylene fibres. There was also no conclusive change in pullout response in specimen subjected to sustained strains compared to reference.

A dynamic quantitative microbial risk assessment for norovirus in potable reuse systems

This study describes the results of a dynamic quantitative microbial risk assessment (QMRA) for norovirus (NoV) that was used to evaluate the relative significance of foodborne, person-to-person, and person-to-sewage-to-person transmission pathways. This last pathway was incorporated into simulated potable reuse systems to evaluate the adequacy of typical treatment trains, operational conditions, and regulatory frameworks. The results confirm that secondary and foodborne transmission dominate the overall risk calculation and that waterborne NoV likely contributes no appreciable public health risk, at least in the scenarios modeled in this study. De facto reuse with an environmental buffer storage time of at least 30 days was comparable or even superior to direct potable reuse (DPR) when compound failures during advanced treatment were considered in the model. Except during these low-probability failure events, DPR generally remained below the 10−4 annual risk benchmark for drinking water. Based on system feedback and the time-dependent pathogen load to the community's raw sewage, this model estimated median raw wastewater NoV concentrations of 107–108 genome copies per liter (gc/L), which is consistent with high-end estimates in recent literature.