Inertial Effects Research Articles

Energy absorption and in-plane mechanical behavior of honeycomb structures with reinforced strut

Negative Poisson's ratio honeycombs have been extensively studied due to their unique mechanical properties. In this paper, a novel negative Poisson's ratio honeycomb (NPH) is proposed by introducing a reinforced strut into the negative Poisson's ratio honeycomb (NPR). A finite element numerical model was constructed using Abaqus/Explicit, and the accuracy of the model was verified, and a series of researches were carried out. First, the mechanical properties of NPH at different angles were analyzed under different loading conditions, and the results showed that under the loading conditions of y-direction and x-direction, NPH-120 and NPH-105 had the best mechanical properties respectively. Subsequently, the mechanical properties of NPH at different velocities were studied. The research showed that the NPR effect of NPH was the most obvious under low-velocity impact, and as the velocity increased, the inertia effect increased, and NPH's deformation mode has changed. And the dynamic Poisson's ratio of NPH at medium-velocity is analyzed, and its energy absorption mechanism is analyzed through the deformation of subunits. Finally, the mechanical properties of NPH under different wall thicknesses were studied, and the mechanical properties of several typical reinforced supports and NPH-120 were compared.

Critical velocities of a two-layer composite tube incorporating the effects of transverse shear, rotary inertia and material anisotropy

Critical velocities of a two-layer composite tube subjected to a uniform internal pressure moving at a constant velocity are analytically derived by using a first-order shear deformation shell theory incorporating the transverse shear, rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar materials, which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form expressions for four critical velocities are first derived for the general case by including the effects of transverse shear, rotary inertia, material orthotropy and radial stress. The formulas for composite tubes without the transverse shear, rotary inertia or radial stress effect and with simpler anisotropy are then obtained as special cases. In addition, it is shown that the model for a single-layer, homogeneous tube is included in the current model as a special case. To illustrate the newly derived closed-form formulas, a composite tube with an isotropic inner layer and an orthotropic outer layer is analyzed as an example. The numerical values of the lowest critical velocity of the two-layer composite tube predicted by the new formulas compare well with existing data.

Flow past a sphere translating along the axis of a rotating fluid: revisiting numerically Maxworthy's experiments

We compute the flow induced by the steady translation of a rigid sphere along the axis of a large cylindrical container filled with a low-viscosity fluid set in rigid-body rotation, the sphere being constrained to spin at the same rate as the undisturbed fluid. The parameter range covered by the simulations is similar to that explored experimentally by Maxworthy (J. Fluid Mech., vol. 40, 1970, pp. 453–479). We describe the salient features of the flow, especially the internal characteristics of the Taylor columns that form ahead of and behind the body and the inertial wave pattern, and determine the drag and torque acting on the sphere. Torque variations are found to obey two markedly different laws under rapid- and slow-rotation conditions. The corresponding scaling laws are predicted by examining the dominant balances governing the axial vorticity distribution in the body vicinity. Results for the drag agree well with the semi-empirical law proposed for inertialess regimes by Tanzosh & Stone (J. Fluid Mech., vol. 275, 1994, pp. 225–256). This law is found to apply even in regimes where inertial effects are large, provided that rotation effects are also large enough. Influence of axial confinement is shown to increase dramatically the drag in rapidly rotating configurations, and the container length has to be approximately a thousand times larger than the sphere for this influence to become negligibly small. The reported simulations establish that this confinement effect is at the origin of the long-standing discrepancy existing between Maxworthy's results and theoretical predictions.

Propagation characteristics of guided waves in CNTRCs plates resting on elastic foundations in a thermal environment

This paper investigates the wave propagation behavior of carbon nanotube-reinforced composites (CNTRCs) plates resting on elastic foundations in a thermal environment. The first-order shear deformation plate theory is applied to establish the mathematical model for the CNTRC plates. The effective material properties are calculated using the rule of mixture. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the CNTRC plates are derived using Hamilton’s principle. Then, the equations of motion are discretized by the Galerkin method and solved analytically by the eigenvalue method. Finally, the effects of various parameters including the temperature variations, the volume fraction of carbon nanotubes (CNTs), elastic foundations and the CNTs’ distribution patterns on the dispersion relations are investigated, it can be found that these parameters have significant effects on the wave propagation of CNTRCs plates.

Local gradient theory of dielectrics incorporating polarization inertia and flexodynamic effect

A higher-grade theory of non-ferromagnetic thermo-elastic dielectrics which incorporates the local mass displacement, the heat flux gradient, polarization inertia, and flexodynamic effects is developed. The process of local mass displacement is associated with changes in material microstructure. Using the fundamental principles of continuum mechanics, electrodynamics, and non-equilibrium thermodynamics, the gradient-type constitutive equations are derived. Due to accounting for the polarization inertia, the rheological constitutive equation for the polarization vector is obtained. In the balance equation of linear momentum, an additional term with the second time derivative of the polarization vector appears in comparison with the classical theory. This term controls the influence of the dynamic flexoelectric effect on the mechanical motion of dielectric solids. The propagation of a plane harmonic wave is analyzed within the context of the developed theory. It is shown that the theory allows for capturing the experimentally observed phenomenon of high-frequency dispersion of a longitudinal elastic wave. The theory may be useful for modeling coupled processes in nanodielectrics and heterogeneous polarized systems.

Nonlinear inertia and its effect within an X-shaped mechanism – Part II: Nonlinear influences and experimental validations

In this study, the effects of nonlinear inertia are further investigated and verified with prototyping and experimental validation. The new inertia unit integrated within a well-designed X-shaped mechanism can produce 3 different typical nonlinear inertia forms which have different nonlinear influence on dynamic response. A critical parametric indicator (Ratio of Inertia) is thus proposed to identify and indicate different types of nonlinearities and a new performance assessment indicator (F-stability) is proposed to assess the performance improvement compared to different nonlinearity with respect to linear counterparts in a dynamic excitation sense. A method for testing different nonlinear inertia is also proposed. It is uniquely revealed that (a) the Ratio of Inertia can be well used to tune different types of inertia nonlinearities; (b) the symmetrical nonlinear inertia (HCHE-type) is generally better in vibration isolation with smaller peak/anti-peak values, peak/anti-peak frequencies (∼ 1 Hz and 3∼4Hz in our prototype), and faster decay rate (∼ -50dB/Dec with our prototype) but higher high-frequency transmissibility compared to the two asymmetric nonlinearities; (c) the nonlinear inertia contributes significantly to tune the interactive force between vibration source and object in the low frequency range (<10Hz in our prototype) and obviously helpful and robust to stronger excitations. All the theoretical analysis results are verified with our developed prototype. These results should for the first time provide a comprehensive and in-depth understanding of nonlinear inertia and its effects in different cases and thus definitely shed light on various engineering applications.

Longitudinal Seismic Response of a Pipe Pile Embedded in Saturated Thermoelastic Ground Subjected to Rayleigh Waves

This work investigates the longitudinal vibration characteristics of the pipe pile in the liquid-saturated ground due to Rayleigh waves propagation with considering the influence of the nonisothermal condition on the wave motion. Firstly, the Rayleigh wavefield in the liquid-saturated thermoelastic ground is deduced theoretically with taking advantage of the Biot theory and the non-Fourier law of heat conduction. Secondly, the longitudinal frequency domain solution of the pipe pile under Rayleigh waves is derived analytically. Finally, the dependence of the pipe pile response on the physical parameter is illustrated by utilizing several numerical examples. The result reveals that increase in the thermal expansion coefficient of saturated soil significantly augments the longitudinal displacement and side friction of pile body. Increase in the permeability of saturated soil will reduce the pile head displacement. When the pile length is less than its effective length, the rise of the pile length will reduce the pile head displacement. Augment of both the outer radius and wall thickness of the pipe pile will help to reduce the pile head displacement. However, the lateral inertia effect of the pipe pile has slight influence on its longitudinal behavior under Rayleigh waves.

Improvements in Drilling Fluid Rheology Predictions Using Rotational Viscometer

Summary The success of an oilwell drilling operation is directly associated with the correct formulation of drilling fluids and their rheological measurements. The goal of this study is to investigate the usage of a Fann 35A viscometer and the methodology for rheological characterization of drilling fluids by comparison with the use of a rotational rheometer. Flow curves and gel strength tests were performed considering classic measurement artifacts such as apparent wall slip, secondary flows, steady-state (SS) regime, and inertial effects, among others. In addition, a study of the relationship between pressure drop and flow rate in a tube and in an annular space was carried out to investigate the influence of the viscosity function and of the rheological properties on the design of pipelines and the correct sizing of pumps. Use of American Petroleum Institute (API) equations and curve fitting were explored as potential choices for viscosity functions. The results indicate that the use of API equation predictions can compromise the effectiveness of the drilling process, while the choice of an adequate viscosity function is essential for the correct sizing of pumps. The gel strength was evaluated in the viscometer and presented divergent results from those obtained in the rheometer. Furthermore, a grooved geometry was developed for the viscometer to avoid the effects of apparent slip at low shear rates. Some recommendations are made based on the results obtained, which lead to better accuracy in the rheological results of drilling fluids and, consequently, better performance of some functions assigned to it. The proposed improvements and methodologies proved to be promising, although in some cases the cost-benefit remained unchanged.

Direct Numerical Simulation and Large Eddy Simulation of a 67-Pebble-Bed Experiment

An in-depth understanding of the flow physics in packed beds is critical for developing simulation tools for pebble bed reactors. Advances in computing power have now made the full-core pebble-resolved computational fluid dynamics simulation of these systems possible. This work presents validation of the velocity and pressure predictions made by the spectral element code NekRS followed by a study of the turbulent kinetic energy and turbulent heat flux budgets. Two cases with corresponding experiments are considered: a bed of 67 pebbles with Re = 1460 and a bed of 789 pebbles with 324 < Re < 1024. Velocity and pressure drop comparisons are performed with the two cases, respectively. Good agreement is found between the experiments and their respective NekRS simulations. The 67-pebble case was then used to perform a direct numerical simulation to extract the turbulent kinetic energy and turbulent heat flux budget terms. Analysis of the turbulent kinetic energy production revealed large areas of negative production near the bottom surfaces of the pebbles. Further investigation revealed a trend between the average amount of negative turbulent kinetic energy production and the local porosity. These results continue to suggest that inertial effects play a large role in differentiating near-wall flow from bed-interior flow.

Role of Flow Inertia in Aggregate Restructuring and Breakage at Finite Reynolds Numbers.

Forces acting on aggregates depend on their properties, such as size and structure. Breakage rate, stable size, and structure of fractal aggregates in multiphase flows are strongly related to the imposed hydrodynamic forces. While these forces are prevalently viscous for finite Reynolds number conditions, flow inertia cannot be ignored, thereby requiring one to fully resolve the Navier-Stokes equations. To highlight the effect of flow inertia on aggregate evolution, numerical investigation of aggregate evolution in simple shear flow at the finite Reynolds number is conducted. The evolution of aggregates exposed to shear flow is tracked over time. Particle coupling with the flow is resolved with an immersed boundary method, and flow dynamics are solved using a lattice Boltzmann method. Particle dynamics are tracked by a discrete element method, accounting for interactions between primary particles composing the aggregates. Over the range of aggregate-scale Reynolds numbers tested, the breakage rate appears to be governed by the combined effect of momentum diffusion and the ratio of particle interaction forces to the hydrodynamic forces. For higher shear stresses, even when no stable size exists, breakage is not instantaneous because of momentum diffusion kinetics. Simulations with particle interaction forces scaled with the viscous drag, to isolate the effect of finite Reynolds hydrodynamics on aggregate evolution, show that flow inertia at such moderate aggregate Reynolds numbers has no impact on the morphology of nonbreaking aggregates but significantly favors breakage probability. This is a first-of-its-kind study that establishes the role of flow inertia in aggregate evolution. The findings present a novel perspective into breakage kinetics for systems in low but finite Reynolds number conditions.

A discrete-based multi-scale modeling approach for the propagation of seismic waves in soils

A three-dimensional multi-scale discrete–continuum model (Finite Volume Method × Discrete Element Method, FVM × DEM) is developed for a discrete-based description of the mechanical behavior of granular soils in boundary value problems (BVPs). In such a scheme, the constitutive response of the material is derived through direct DEM computations on a representative volume element attached to each mesh element. The developed multi-scale approach includes the inertial effect in the stress homogenization formulation and serves to study the mechanism of propagation of seismic waves, in comparison with a more classical BVP simulation that adopts an advanced bounding surface plasticity model “P2PSand”. We start with a detailed and fair calibration and validation of these two models against laboratory tests for Toyoura sand under monotonic and cyclic loading. Then, the performance of the two approaches is compared for the case of a seismic wave loading passing through a saturated soil column with different relative densities, revealing several differences between the results of the two models.

Ultrasound treated asphaltene laden W/O Interface: Insights into emulsion destabilization mechanism using a Microrheology approach

In this study, the effect of different levels of ultrasonic fields on the microrheology of an asphaltene laden flat interface and on the behavior of asphaltene-stabilized emulsions was evaluated. Experiments were performed at frequencies of 20, 40, 50, 80, 120, and 150 kHz, and voltages of 20, 30, 40, and 50 V. In the flat interface experiments, four distinct microrheology regimes were observed: I. no movement, II. slow streaming, III. strong streaming and interfacial cavitation, IV. bulk cavitation and mixing. The regime encountered depended on the inertial effect of ultrasound on the subphase (Reynolds number) as well as the thermodynamic impact of ultrasonic fields. Treating the emulsions with the same ultrasonic fields resulted in three categories of behavior: I. no coalescence, II. coalescence, III. emulsification. There was a strong correlation between emulsion behavior with the microrheology regime. Below the threshold of interfacial cavitation (Microrheology Regimes I and II), no change in the emulsions was detected. When interfacial cavitation occurred (Microrheology Regime II), the emulsions coalesced significantly. This behavior was attributed to the ability of the cavitation process in breaking the asphaltene barrier between the droplets. However, increasing the frequency and the voltage of the field increased the mechanical effects of the ultrasonic field (Microrheology Regime IV) and caused secondary emulsification in the system.

Practice Changes Induced by a Traveling Fellowship.

The John N. Insall Knee Society Traveling Fellowship selects four international arthroplasty or sports fellowship-trained orthopaedic surgeons to spend 1 month traveling to various Knee Society members' joint replacement and knee surgery centers in North America. The fellowship aims to foster research and education and shares ideas among fellows and Knee Society members. The role of such traveling fellowships on surgeon preferences has yet to be investigated. A 59-question survey encompassing patient selection, preoperative planning, intraoperative techniques, and postoperative protocols was completed by the four 2018 Insall Traveling Fellows before and immediately after the completion of traveling fellowship to assess anticipated practice changes (e.g., initial excitement) related to their participation in a traveling fellowship. The same survey was completed 4 years after the completion of the traveling fellowship to assess the implementation of the anticipated practice changes. Survey questions were divided into two groups based on levels of evidence in the literature. Immediately after fellowship, there was a median of 6.5 (range: 3-12) anticipated changes in consensus topics and a median of 14.5 (range: 5-17) anticipated changes in controversial topics. There was no statistical difference in the excitement to change consensus or controversial topics (p = 0.921). Four years after completing a traveling fellowship, a median of 2.5 (range: 0-3) consensus topics and 4 (range: 2-6) controversial topics were implemented. There was no statistical difference in the implementation of consensus or controversial topics (p = 0.709). There was a statistically significant decline in the implementation of changes in consensus and controversial preferences compared with the initial level of excitement (p = 0.038 and 0.031, respectively). After the John N. Insall Knee Society Traveling Fellowship, there is excitement for practice change in consensus and controversial topics related to total knee arthroplasty. However, few practice changes that had initial excitement were implemented after 4-year follow-up. Ultimately, the effects of time, practice inertia, and institutional friction overcome most of the anticipated changes induced by a traveling fellowship.

Liquid entrainment of the toroidal bubble crossing the interface between two immiscible liquids

We experimentally investigate the transport of liquid by a toroidal bubble that rises vertically and penetrates a horizontal interface between two immiscible liquids. Experiments are conducted with various strengths of vortex circulation in the bubble, and with different liquid densities and viscosities. In contrast to a spherical bubble, a rising toroidal bubble carries a great amount of the lower liquid by virtue of the self-induction of circulating flow. The lower liquid is entrained by the toroidal bubble and forms an ellipsoidal body enclosing the bubble after it penetrates the interface. The downward net force acting on the ellipsoidal body results in the radial contraction of the bubble, reducing the volume of the entrained lower liquid. As the entrained volume decreases, the nearby upper liquid eventually pierces the ellipsoidal body, making the bubble unstable. At this instant, the net force acting on the ellipsoidal body approaches zero, and the volume ratio of the entrained lower liquid and bubble converges to a specific value. For smaller vortex circulation and larger density difference between the liquids, the volume of the entrained lower liquid within the ellipsoidal body becomes smaller and the travel distance of the bubble from the initial interface until it becomes unstable decreases. The effective Froude number, which accounts for both the inertial effect of vortex circulation and the gravitational effect of liquid density difference, is found to characterise the temporal changes in the ring radius, propagation speed and entrained volume.

Investigations on the quasi-static/dynamic mechanical properties of 3D printed random honeycombs under in-plane compression

The aim of this study was to reveal the effects of inertia and base material strain rate on the mechanical properties of 3D-printed random honeycombs. First, random honeycombs were established with various meso-structural parameters based on the Voronoi technique and then manufactured by 3D printing. Quasi-static compression tests were performed using a universal test machine. The results indicated that the random honeycombs exhibited a more uniform deformation mode which led to a gentle stress–strain curve when compared with the regular honeycombs. Furthermore, the strain rate effect of the base material was determined by Split Hopkinson Pressure Bar (SHPB) tests. Finite element models considering the base material strain rate were verified by the quasi-static compression and drop weight impact tests. Dynamic simulations were carried out to determine the critical velocity between the deformation mode and clarify its mechanisms. The second critical velocities increase as the cell size and cell wall thickness increased or as the strain rate effect of the base material is considered. The effects of inertia and base material strain rate on the mechanical properties were discussed. The dynamic stress enhancement is dominated by the strain rate effect of the base material and the inertia effect in the random and shock modes, respectively. Finally, an empirical model that includes the inertia effect and strain rate effect of the base material was proposed based on the 1D shock wave theory and the Johnson–Cook material model.

Variable viscous flow resistance based on rotational inertia

Viscous flow resistance is dominated by viscous friction between fluid and wall. The flow resistance characteristic curve (i.e., the relationship curve between pressure drop and flow rates, represented as the Δp–Q curve) depends on some inherent characteristic variables, such as structural size, fluid viscosity, density, and temperature. Usually, to change the Δp–Q curve, these inherent characteristic variables must be changed. This paper proposes a new design of variable viscous flow resistance. The new design uses two disks to construct a slit flow channel, and rotate one of the disks to drive the fluid in the slit flow channel to form a rotational inertia effect. Therefore, by changing the rotating speed of the disk, the rotational inertia effect can be changed, thereby achieving the purpose of changing the Δp–Q curve. This paper derives a theoretical model for the pressure distribution of the rotating slit flow field and conducted experimental verification. It was found that the rotational inertia gradient and viscous gradient terms play major roles in governing the radial pressure gradient. The sum of the other two inertial gradient terms accounts for a maximum of about 1.58% of the total pressure gradient. There is a coupling relationship between circumferential velocity, radial velocity, and flow rates. An increase in Q can increase the rotational inertial gradient term by up to 24.9%. The rotating disk causes additional radial velocity and thus weakens the viscous gradient term by at least 16.41%.

Dynamic response of a thin-walled curved beam with a mono-symmetric cross-section under a moving mass

This paper presents analytical solutions for the dynamic response of thin-walled curved beams induced by moving vehicles. The solutions encompass vertical, torsional, radial, and axial motions. A comprehensive set of governing equations for the dynamic response of thin-walled curved beams is established by considering the mass inertia of moving vehicles, rotary inertia, and warping resistance. The solutions are obtained for the four-directional response of curved beams, involving vertical, torsional, radial, and axial motions, based on the Fourier finite integral transformation, the Laplace–Carson transformation, their inverse transformations, and the Galerkin approach. A comparison of the results calculated by the analytical solutions in this study are compared with those calculated by the moving-force solutions using the Galerkin approach reported in a related literature, demonstrates the reliability and superiority of the analytical solutions. Hence, an extensive parametric study is carried out to investigate the effect of the mass inertia of moving vehicles, velocities, higher-order modes of vibrations, and radii of curvature on the dynamic responses of beams. As per the results, the mass and velocity of the moving vehicles play important roles in the dynamic response of curved beams. Furthermore, the dynamic response for thin-walled curved beams increases significantly with heavier vehicles and higher velocities, confirming that it is necessary to consider the mass inertia effect to study the dynamic response of curved beams.

Deviation of Frequency and Inertia with penetration of Renewable

Inertia response is a function of bulky synchronous generators with large rotating rotor masses that cover the instantaneous difference between supply and grid demand, typically in power grids. The rotor rotation frequency helps speed up or slow down the rotor rotation due to the lack of adequate gap between the power supply and the electrical power demand. When demand increases or a fault occurs, or load fluctuations exceed the balance of supply and demand, grid inertia is always induced at this stage. This helps the automatic grid operator rebalance the system to avoid speed drifts, resulting in a relatively small change in AC frequency over the system's frequency range. But the system consists of a system with low or zero inertia, like the wind, it lacks the effect of inertia and could not gain equilibrium. So, to balance and to reach the target frequency; the frequency deviation of the system due to the lack of inertia of the wind turbine is improved by the droop control technique in this research because the wind system reduced the total inertia of the system. Droop rate control mode for AC generator techniques was used to control the frequency fluctuations due to the lack of inertia of the renewable energy system. A synchronous generator connected to the mains was used as the governor control mode. It works by controlling power generation using the mains frequency of the prime mover. This mode allows synchronous generators to run in parallel and share the loads with the same drooping technique in proportion to their rated output. Injected grid inertia increased generator inertia on large power grids.

A comparative study on dynamic compression response of multi-cell thin-walled structures with filling foams and connecting ribs

In order to comparatively study effect of foam filling and connecting ribs on dynamic response of multi-cell thin-walled structure (MTS), high velocity (30–70 m/s) mass block impact tests were performed on empty MTS, polyurethane foam (PUR) filled MTS (FMTS) and 2nd order MTS (MTS-2nd) with connecting ribs between sub-cells. The dynamic enhancement mechanism of energy absorption of three kinds of thin-walled structures was discussed based on experimental and numerical results. The results indicate that the dynamic enhancement coefficient (DEC) of the mean crushing force (MCF) is 1.07–1.23 and 1.08–1.33 for empty MTS and FMTS, respectively. The dynamic enhancement of total energy absorption (EA) is 11.4–26.32% for MTS, 13.83–32.52% for FMTS and 4.3–9.68% for MTS-2nd, compared to the quasi-static compression. The multi-cellularization tends to degenerate the crushing force sensitivity of MTS to the loading rate, while the foam filling increases the sensitivity. The inertia effect is the main reason for the dynamic enhancement of crushing force of thin-walled structures. The coupling effect of FMTS is related to the dimensions of sub-cells, the impact velocity and the foam strength. The folding pattern and deformation stability of MTS can be improved by filling foams and increasing impact velocity. The multi-cellularization by using connecting ribs is still the most effective method to improve the specific energy absorption of thin-walled structures, although it causes a size effect and reduces the robustness of deformation modes.

Bearing capacity of shallow foundations accounting for seismic excess pore pressures

The method of characteristics has been used to develop a rigorous solution for the evaluation of seismic bearing capacity of shallow foundations resting on homogenous fully submerged soil accounting for the effect of earthquake-induced pore water pressures. The solution, derived with reference to both the Hill and Prandtl plastic mechanisms, is essentially referred to the bearing capacity factor Nγ, is of general validity and has been checked against finite element analysis results. An original empirical expression providing the corrective coefficient to be introduced in the usual trinomial bearing capacity formula has been proposed, accounting for the reduction in bearing capacity due to combined effect of soil inertia and earthquake-induced pore water pressures. It has also been demonstrated that, even considering earthquake-induced excess pore pressures, the soil and superstructure inertial effects are still decoupled. This allowed introducing an overall corrective coefficient accounting for both the inertial (soil and superstructure) and excess pore pressure effects, computed as the product of the corresponding corrective coefficients. Finally, original simple equations were derived giving a threshold value of the excess pore pressure ratio required to trigger a bearing capacity failure in the static post-seismic conditions because of the soil shear strength reduction.