Velocity Exponent Research Articles

Lunar Secondary Craters and Estimated Ejecta Block Sizes Reveal a Scale‐Dependent Fragmentation Trend

AbstractPlanetary impact events eject large volumes of surface material. Crater excavation processes are difficult to study, and in particular the details of individual ejecta fragments are not well understood. A related, enduring issue in planetary mapping is whether a given crater resulted from a primary impact (asteroid or comet) or instead is a secondary crater created by an ejecta fragment. With mapping and statistical analyses of six lunar secondary crater fields (including Orientale, Copernicus, and Kepler) we provide three new constraints on these issues: (1) estimation of the maximum secondary crater size as a function of distance from a primary crater on the Moon, (2) estimation of the size and velocity of ejecta fragments that formed these secondaries, and (3) estimation of the fragment size ejected at escape velocity. Through this analysis, we confirmed and extended a suspected scale‐dependent trend in ejecta size‐velocity distributions. Maximum ejecta fragment sizes fall off much more steeply with increasing ejection velocity for larger primary impacts (compared to smaller primary impacts). Specifically, we characterize the maximum ejecta sizes for a given ejection velocity with a power law and find that the velocity exponent varies between approximately −0.3 and −3 for the range of primary craters investigated here (0.83–660 km in diameter). Data for the Jovian moons Europa and Ganymede confirm similar trends for icy surfaces. This result is not predicted by analytical theories of formation of Grady‐Kipp fragments or spalls during impacts and suggests that further modeling investigations are warranted to explain this scale‐dependent effect.

Dynamic variability of at-a-station hydraulic-geometry for mountain rivers in the southeast Qinghai-Tibet Plateau: The cases of Yalong River and upper Jinsha River

To be able to precisely estimate discharges in un-gaged streams and reconstruct hydrological features in river systems, the temporal and spatial variations of at-a-station hydraulic geometry (AHG) and their impacting factors need to be detected. To this end, the Yalong River and Upper Jinsha River, which located in southeast Qinghai-Tibet Plateau, are selected as case study. This investigation explores quantitative data on the magnitude of spatial and temporal variations in AHGs over a period of 10 years for 38 mountain reaches with drainage areas ranging from 0.53 × 103 to 259.18 × 103 km2. Effects of ice regime and drainage area on AHG were discussed and the stability of AHG was analyzed. 42.1% of the reaches have flow velocity exponents that are greater than the river width and flow depth exponents combined. No significant spatial variation tendency is observed for AHG exponents while significant temporal variations are reported. Larger fluctuations are found for AHG exponents in annual variations compared with those in inter-annual variations. Ice regimes significantly contribute to the seasonal changes of AHGs. The relative differences of AHG coefficients (a, c, k) and exponents (b, f, m) with and without ice vary between −49.4 to 80.8% and −70.1% to 22.6%, respectively. Compared with no ice regime, the reaches with border ice and slush ice run have smaller exponents m and Froude Number and larger coefficients c and exponents f. Besides, coefficients a and exponents m increase while coefficients k and exponents b decrease with the increase of drainage area. However, coefficients c and exponents f exhibit no tendency with drainage area changes. AHG stabilities increase with the increased stream order and drainage area. Results of this study can enrich the AHG database for mountain rivers and provide a preliminary understanding of ice effects on AHG variations.

Nonlinear vibrations of fluid-conveying FG cylindrical shells with piezoelectric actuator layer and subjected to external and piezoelectric parametric excitations

Nonlinear vibrations of a fluid-conveying functionally graded (FG) cylindrical shell with piezoelectric actuator layer and subjected to external excitation and piezoelectric parametric excitation are analyzed theoretically. Considering the electric-thermo-fluid-structure interaction effect, a nonlinear dynamic model of fluid-conveying FG cylindrical shell with piezoelectric actuator layer is developed based on Hamilton’s principle and von-Karman geometrical nonlinearity. The inviscid, incompressible, isentropic and irrotational fluid is coupled into governing equations using the linearized potential theory. The nonlinear coupled differential governing equations of system are obtained by using Galerkin’s method with two modes. The developed coupled model is validated by comparing with the prior data and good agreements are observed. Multiple scales method is used to obtain nonlinear dynamic behaviors of the coupled system in case of 1:2 internal resonance, primary parametric resonance and 1/2 subharmonic resonance. The effects of three coupling cases between two modes on the dynamic behaviors of system are explored. Considering strongly coupled effect between two modes, the effect of external excitation, damping coefficient, piezoelectric harmonic voltage, fluid flow velocity, temperature and volume fraction exponent of FG cylindrical shell on the frequency-response curves are investigated. The influence of detuning parameters on force-amplitude response and voltage-amplitude response of system are also discussed.

A Design Method for Viscous Dampers Connecting Adjacent Structures

This paper investigates the seismic design of fluid viscous dampers connecting adjacent structural systems. A simplified dampers design strategy is proposed, which relies on a linearized reduced order model of the coupled system. A stochastic linearization technique is adopted with the aim of extending the design method to nonlinear viscous dampers. The effectiveness of the design method and of the coupling strategy are assessed via numerical analysis of two adjacent buildings with shear-type behaviour connected by linear or nonlinear viscous dampers and subjected to Gaussian stochastic base acceleration. Different dampers locations are analysed. The accuracy of the reduced order model is assessed, by comparing the relevant response statistics to those provided by a refined multi degree of freedoms model. Finally, a parametric study is performed to assess the effectiveness of dissipative connection for different values of seismic intensity and dampers parameters (i.e., viscous coefficients and velocity exponents).

Temperature and fluid velocity on the freeze-out surface from π , K , and p spectra in pp , p -Pb, and Pb-Pb collisions

We present a new approach to take into account resonance decays in the blast-wave model fits of identified hadron spectra. Thanks to pre-calculated decayed particle spectra, we are able to extract, in a matter of seconds, the multiplicity dependence of the single freeze-out temperature $T_{\rm fo}$, average fluid velocity $\left<\beta_{\rm T}\right>$, velocity exponent $n$, and the volume $dV/dy$ of an expanding fireball. In contrast to blast-wave fits without resonance feed-down, our approach results in a freeze-out temperature of $T_{\rm fo}\approx 150\,\text{MeV}$, which has only weak dependence on multiplicity and collision system. Finally, we discuss separate chemical and kinetic freeze-outs separated by partial chemical equilibrium.

Influence of Fluid Viscous Damper on the Dynamic Response of Suspension Bridge under Random Traffic Load

Fluid viscous dampers (FVDs) are widely used in long‐span suspension bridges for earthquake resistance. To analyze efficiently the influences of FVDs on the dynamic response of a suspension bridge under high‐intensity traffic flow, a bridge‐vehicle coupling method optimized by isoparametric mapping and improved binary search in this work was first developed and validated. Afterwards, the traffic flow was simulated on the basis of monitored weigh‐in‐motion data. The dynamic responses of bridge were analyzed by the proposed method under different FVD parameters. Results showed that FVDs could positively affect bridge dynamic response under traffic flow. The maximum accumulative longitudinal girder displacement, longitudinal girder displacement, and longitudinal pylon acceleration decreased substantially, whereas the midspan girder bending moment, pylon bending moment, longitudinal pylon displacement, and suspender force were less affected. The control efficiency of maximum longitudinal girder displacement and accumulative girder displacement reached 33.67% and 57.71%, longitudinal pylon acceleration and girder bending moment reached 31.51% and 7.14%, and the pylon longitudinal displacement, pylon bending moment, and suspender force were less than 3%. The increased damping coefficient and decreased velocity exponent can reduce the bridge dynamic response. However, when the velocity exponent was 0.1, an excessive damping coefficient brought little improvement and may lead to high‐intensity work under traffic flow, which will adversely affect component durability. The benefits of low velocity exponent also reduced when the damping coefficient was high enough, so if the velocity exponent has to be increased, the damping coefficient can be enlarged to fit with the velocity exponent. The installation of FVDs influences dynamic responses of bridge structures in daily operations and this issue warrants investigation. Thus, traffic load should be considered in FVD design because structural responses are perceptibly influenced by FVD parameters.

Propagation of non-planar weak and strong shocks in a non-ideal relaxing gas

In this article, the kinematics of one-dimensional motion have been applied to construct evolution equations for non-planar weak and strong shocks propagating into a non-ideal relaxing gas. The approximate value of exponent of shock velocity, at the instant of shock collapse, obtained from systematic approximation method is compared with those obtained from characteristic rule and Guderley’s scheme. Computation of exponent is carried out for different values of van der Waals excluded volume. Effects of non-ideal and relaxation parameters on the wave evolution, governed by the evolution equations, are analyzed.

Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification

We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the functional renormalization group and scaling relations involving two independent exponents, roughness ζ, and dynamics z, are confronted to high-precision numerical simulations of an elastic line with short-range elasticity, i.e., of internal dimension d = 1. The latter are based on a novel stochastic algorithm which generates its disorder on the fly. Its precision grows linearly in the time discretization step, and it is parallelizable. Our results show good agreement between theory and numerics, both for the critical exponents as for the scaling functions. In particular, the prediction for the velocity exponent is confirmed with good accuracy.

Dynamic Mechanical Property Experiment of Viscous Material for Viscous Damping Wall

Viscous damping wall (VDW) is an effective velocity-dependent damper, which can dissipate earthquake energy by shear strain of viscous material. The damping force equation of VDW can only be obtained from regression of VDW dynamic test results, as velocity exponent of power-law material can not be obtained from rheometers. This study designed a Dynamic Sandwich-Type Shear (DSTS) test which matches the engineering working condition of VDW, and conducted a series of experiments with different frequencies and strain amplitudes. Simple data procession methods were proposed to calculate velocity exponent and storage/loss modulus of polymer from experimental data. Comparison with methods adapted from those for VDW formula validated that radial linear regression method was proper to separate stress components and pivotal point method was accurate to evaluate velocity exponent. The velocity exponents obtained varied from 0.8 to 1, with various loading frequency and strain amplitude. Finally, the differences between the results of storage/loss modulus in DSTS test and ARES test were compared. Due to the extrusion effect caused by engineering working condition, the storage and loss modulus obtained by DSTS test was larger than the modulus obtained by ARES test.

Evaluation on sediment erosion of Pelton turbine flow passage component

A rotating disc with jet nozzle experiment system is applied to study the anti-erosion performance of flow passage component matrix materials for Pelton turbine. The test condition such as sediment characteristics(concentration, hardness, mineral content), and flow velocity are designed to simulate the actual operating condition of prototype Pelton turbine. The resultant velocity in test is high to 107 ms−1. The anti-erosion performance of materials (ADB610, ZG25, 04Cr13Ni5Mo), which are used to fabricate needle and nozzle and bucket of Pelton turbine, was studied in detail on this experiment system. The experimental studies were carried on different resultant velocities and different sediment concentrations. Multiple linear regression analysis was applied to get the exponents of velocity and sediment concentration. The exponents for different materials are different. Basing on velocity exponents and concentration exponents acquired in tests, the sediment erosion prediction models for different materials were derived. Sediment erosion for different flow passage components, such as needle tip and nozzle ring and bucket of Pelton turbine in one China hydraulic power station, were evaluated on actual operating condition for different flow passage components.

Design of finger gestures for locomotion in virtual reality

Background Within a virtual environment (VE) the control of locomotion (e.g., self-travel) is critical for creating a realistic and functional experience. Usually the direction of locomotion, while using a head-mounted display (HMD), is determined by the direction the head is pointing and the forward or backward motion is controlled with a hand held controllers. However, hand held devices can be difficult to use while the eyes are covered with a HMD. Free hand gestures, that are tracked with a camera or a hand data glove, have an advantage of eliminating the need to look at the hand controller but the design of hand or finger gestures for this purpose has not been well developed. Methods This study used a depth-sensing camera to track fingertip location (curling and straightening the fingers), which was converted to forward or backward self-travel in the VE. Fingertip position was converted to self-travel velocity using a mapping function with three parameters: a region of zero velocity (dead zone) around the relaxed hand position, a linear relationship of fingertip position to velocity (slope or/J) beginning at the edge of the dead zone, and an exponential relationship rather than a linear one mapping fingertip position to velocity (exponent). Using a HMD, participants moved forward along a virtual road and stopped at a target on the road by controlling self-travel velocity with finger flexion and extension. Each of the 3 mapping function parameters was tested at 3 levels. Outcomes measured included usability ratings, fatigue, nausea, and time to complete the tasks. Results Twenty subjects participated but five did not complete the study due to nausea. The size of the dead zone had little effect on performance or usability. Subjects preferred lower β values which were associated with better subjective ratings of control and reduced time to complete the task, especially for large targets. Exponent values of 1.0 or greater were preferred and reduced the time to complete the task, especially for small targets. Conclusions Small finger movements can be used to control velocity of self-travel in VE. The functions used for converting fingertip position to movement velocity influence usability and performance.

Study of vertical seismic isolation technique with nonlinear viscous dampers for lateral response reduction

In a vertical seismic isolation (VSI) system, an individual structure is partitioned in a vertical isolation plane into two dynamically different substructures interconnected by a mechanism. In this way, response reduction is expected in each substructure when compared to the original non-partitioned structure. In this study, the features of an SDOF with nonlinear viscous dampers (NVDs) subjected to harmonic loading have first been investigated, and a criterion has been proposed for evaluating their seismic behavior by comparing to that of linear viscous damper (LVD) based on damper force capacity. Then, by using a set of earthquakes with a wide range of dominant periods, and conducting a series of nonlinear time history analyses, the application of NVDs in the VSI has been thoroughly studied in regard to substructure displacement and acceleration response reduction. In these analyses, the interaction effect of isolation ratios and link parameters on response control of the VSI system was explored. The investigation of NVDs was carried out equating the viscous damper force in different velocity exponents with the corresponding LVD. Results did not indicate a preferable performance of NVDs over an LVD. Yet, employing appropriate link parameters proportional to mass and stiffness ratios could lead to satisfactory levels of seismic response reduction in cases of both types of dampers.

Optimisation of Longitudinal Seismic Energy Dissipation System for Straddle‐type Monorail‐Cum‐Road Long‐Span Cable‐Stayed Bridge

To investigate the optimal longitudinal seismic energy dissipation system of straddle‐type monorail‐cum‐road long‐span cable‐stayed bridges, the Niutianyang Bridge was selected as the engineering background, and the explicit time‐domain dimension‐reduced iteration method was adopted to carry out nonlinear time‐history analysis. To consider the dynamic characteristics of longitudinal movable supports, the static and dynamic responses of four kinds of energy dissipation systems were studied, including longitudinal unconstrained, elastic cable, viscous damper, and speed lock‐up devices. The damping effect of four types of schemes in which viscous dampers were installed at piers or towers was analysed, and the parameters of the viscous dampers were optimised. The influences of the straddle‐type monorail train braking force and the running vibration of the straddle‐type monorail traffic on the parameters of the viscous dampers were analysed. This study shows that the viscous damper system had the lowest bending moment at the bottom of the tower and a smaller displacement response, and the energy dissipation was the best. Each viscous damper had the highest energy dissipation efficiency when they are installed only at the main tower. The damping effect was better when the damping coefficient c ranged from 3500 to 5000 kN · (m/s)−α and the velocity exponent α ranged from 0.35 to 0.5. The static friction of the straddle‐type monorail‐cum‐road long‐span cable‐stayed bridge support can resist the trains’ braking force, and the parameters of the viscous damper can be selected regardless of train braking. A suitably large value of velocity exponent α may be required to increase the working velocity of the viscous damper to reduce the damper’s participation in the process of the train crossing the bridge.

Low Velocity Normal Impact Performance of Functionally Graded Conical Shell with Simple Power Law

The current study deals with the problem of functionally graded untwisted and pretwisted conical shells under to low-velocity normal impact by a spherical mass striker. A numerical solution technique is developed to solve and predict the impact performance in terms of contact force, impactor displacement, impactor velocity and target displacement of the FG conical shells with different simple power law exponent. A modified Hertzian contact theory considering permanent depression is used to calculate the contact force along with other impact performance parameters. Using the Newmark’s time integration scheme the dynamic equations are solved. Isoparametric shell element with eight nodes is considered for the current finite element model. Parametric observations are performed to see the effects of prime parameters like impactor initial velocity, twist angle and different power law exponent for Ti–6Al–4V-ZrO2 functionally graded conical shell under low velocity normal impact condition. The effects of impactor initial velocity, twist angle of conical shell and the constituent volume fraction of FGM configuration through power law index on the transient impact performance of the conical shell are examined and analyzed.

Experimental Investigations on Laminar Burning Velocity Variation of Methyl Formate–Air Mixtures at Elevated Temperatures

In the present work, measured laminar burning velocities of methyl formate (MF)–air mixtures at atmospheric pressure are presented for high mixture temperatures (up to 500 K) using an externally heated mesoscale diverging channel method. The experiments were performed for equivalence ratios ranging from Φ = 0.6 to Φ = 1.4 with an unburnt mixture temperature range from 350 to 500 K. The results reported in the literature and mechanism predictions of Aramco 2.0 (2016), Dievart (2013), and Dooley (2010) using PREMIX code are then compared with the data obtained from the existing experimental setup. The progressive change of temperature exponent and laminar burning velocity with equivalence ratios is akin to the other gaseous and liquid fuels outlined in the literature. The maxima and minima associated with the laminar burning velocity and temperature exponent (α) respectively is observed at Φ ≈ 1.1 or a slightly richer side. The mechanism predictions of the Aramco 2.0 (2016) detailed kinetic model is used fo...

Effect of cenosphere filler surface treatment on the erosion behavior of epoxy matrix syntactic foams

Influence of cenosphere surface modification and volume fraction on the solid particle erosion of cenosphere/epoxy syntactic foams is investigated. Fly ash cenospheres are used as filler in both as received and silane surface modified configurations. Erosion behavior is studied at room temperature for different impact angles (30, 45, 60, and 90°) and velocities (30, 45, and 60 m/s). Neat epoxy shows the highest erosion rate compared with that of the syntactic foams. Results show a strong dependence of impact angle and velocity on erosion rate of syntactic foams. With increasing cenosphere content erosion rate decreases for all impact angles. Erosion rate decreases with increasing impact angle and with decreasing velocity. Good interfacial bonding of treated cenospheres enhances the erosion resistance. All the samples exhibit ductile erosive behavior, with maximum erosion at 30°. The velocity exponent and erosion efficiency parameters confirm the ductile behavior of syntactic foams. POLYM. COMPOS., 40:2109–2118, 2019. © 2018 Society of Plastics Engineers

Seismic protection of the benchmark highway bridge with passive hybrid control system

The present paper deals with the optimum performance of the passive hybrid control system for the benchmark highway bridge under the six earthquakes ground motion. The investigation is carried out on a simplified finite element model of the 91/5 highway overcrossing located in Southern California. A viscous fluid damper (known as VFD) or non-linear fluid viscous spring damper has been used as a passive supplement device associated with polynomial friction pendulum isolator (known as PFPI) to form a passive hybrid control system. A parametric study is considered to find out the optimum parameters of the PFPI system for the optimal response of the bridge. The effect of the velocity exponent of the VFD and non-linear FV spring damper on the response of the bridge is carried out by considering different values of velocity exponent. Further, the influences of damping coefficient and vibration period of the dampers are also examined on the response of the bridge. To study the effectiveness of the passive hybrid system on the response of the isolated bridge, it is compared with the corresponding PFPI isolated bridges. The investigation showed that passive supplement damper such as VFD or non-linear FV spring damper associated with PFPI system is significantly reducing the seismic response of the benchmark highway bridge. Further, it is also observed that non-linear FV spring damper hybrid system is a more promising strategy in reducing the response of the bridge compared to the VFD associated hybrid system.

Adaptive numerical method algorithms for nonlinear viscous and bilinear oil damper models subjected to dynamic loading

Adaptive numerical method algorithms are presented for the numerical simulation of the hysteretic behaviour of nonlinear viscous and bilinear oil dampers within a finite element program for nonlinear dynamic analysis of frame structures under earthquake excitations. The adaptive algorithms are applicable for computing high-precision solutions for nonlinear viscous and bilinear oil dampers with valve relief that are typically represented mathematically with a nonlinear Maxwell model. The algorithms presented possess excellent convergence characteristics for viscous dampers with a wide range of velocity exponents and axial stiffness properties. The algorithms are implemented in an open source finite element software, and their applicability and computational efficiency is demonstrated through a number of validation examples with data that involve component experimentation as well as the utilization of full-scale shake table tests of a 5-story steel building equipped with nonlinear viscous and bilinear oil dampers.

Analytical solution of convective heat transfer of a quiescent fluid over a nonlinearly stretching surface using Homotopy Analysis Method

Abstract In this article, an analytical solution of the boundary layer fluid flow and heat transfer of a quiescent viscous fluid over a non-linearly stretching surface is presented. The thermal radiation effects are included in the energy governing equation. Surface velocity and temperature conditions are assumed to be of the power-law form with an exponent of 1/3 for velocity and arbitrary exponent m for surface temperature or heat flux conditions. The system of nonlinear differential equations is solved by Homotopy Analysis Method (HAM) for two cases of Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF). The results of this method appear in the form of series expansions, the convergence of which is analyzed carefully. Graphical results are finally presented in order to investigate the influence of Prandtl number (Pr) and thermal radiation on heat transfer phenomena.

Measurement of laminar burning velocity of ethanol-air mixtures at elevated temperatures

The present work focuses on new measurement of laminar burning velocities of ethanol-air mixtures at 1 atm pressure and elevated mixture temperatures using an externally heated meso-scale diverging channel technique. The burning velocity measurements were carried out for a temperature range of 350–620 K and equivalence ratio range of 0.7–1.3. Various detailed kinetic models available in literature were used for assessment and comparison with experimental results. The experimental results show a good match at lower mixture temperatures across all equivalence ratios. However, at higher temperatures, the difference between the measurements and predictions of different kinetic models is considerably higher, particularly for rich mixture regime. The effect of mixture temperature on laminar burning velocity was assessed using power law correlation, Su=Su,0(Tu/Tu,0)α. The variation of temperature exponent, α with equivalence ratio, Φ showed a minimum value for slightly rich mixtures. This variation of the measured laminar burning velocity and temperature exponent at elevated mixture temperatures and predictions using various kinetic mechanisms shows a good match for lean mixtures.