Critical Plate Thickness for Energy Dissipation During Sphere–Plate Elastoplastic Impact Involving Flexural Vibrations

Solid processing storage and conveying units (e.g., hoppers, silos, tumblers, etc.) often involve the collision of granular media with relatively thin walls. Therefore, the impact of a sphere with a thin plate is a problem with both fundamental and practical importance. In the present work, the normal elastoplastic impact between a sphere and a thin plate is analyzed using an explicit finite element method (FEM). The impact involves plastic deformation and flexural vibrations, which when combined results in significant energy dissipation. One way to quantify the energy dissipation is to employ the coefficient of restitution (COR), which is also a key input parameter needed in various granular flow models. The results were validated against the available experimental data. It is observed that, in addition to material properties and impact parameters, the energy dissipation is strongly dependent on the ratio of plate thickness to sphere diameter. A comprehensive parametric study is conducted to evaluate the effect of material properties, geometry, and impact parameters on the energy dissipation. For the impact velocities commonly observed in granular systems (V = 5 m/s or less), it was determined that the energy lost to flexural vibrations can be neglected if the plate thickness is more than twice the sphere diameter, i.e., tcr > 2d. In this scenario, the mode of energy dissipated is primarily due to the plasticity effects.

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Experimental Investigations on the Coefficient of Restitution for Sphere–Thin Plate Elastoplastic Impact

Journal of Tribology ◽

10.1115/1.4037212 ◽

2017 ◽

Vol 140 (1) ◽

Cited By ~ 1

Author(s):

Deepak Patil ◽

C. Fred Higgs

Keyword(s):

Energy Dissipation ◽

Thin Plate ◽

Wall Thickness ◽

Input Parameter ◽

Contact Process ◽

Infinite Plate ◽

Coefficient Of Restitution ◽

Experimental Investigations ◽

Sphere Diameter ◽

The Impact

In multiparticle simulations of industrial granular systems such as hoppers, tumblers, and mixers, the particle energy dissipation is governed by an important input parameter called the coefficient of restitution (COR). Oftentimes, the wall thickness in these systems is on the order of a particles diameter or less. However, the COR value implemented in event-driven simulations is either constant or a monotonically decreasing function of the impact velocity. The present work experimentally investigates the effect of wall thickness on the COR through sphere–thin plate elastoplastic impacts and elucidates the underlying impact phenomena. Experiments were performed on 0.635 cm and 0.476 cm diameter (d) spheres of various materials impacting aluminum 6061 plates of different thicknesses (t) with the low impact velocities up to 3.1 m/s. Besides COR, indentation measurements and numerical simulations are performed to gain a detailed understanding of the contact process and energy dissipation mechanism. As the “t/d” ratio decreases, a considerable amount of energy is dissipated into flexural vibrations leading to a significantly lower COR value. Based on the results, it can be concluded that using a constant COR input value in particle simulations may not always be an appropriate choice, especially, in the case of thin plates. However, these new COR results validate that when the wall thickness is more than twice the sphere diameter (i.e., t/d > 2), a constant COR value obtained for an impact with semi-infinite plate can be reasonably used.

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Experimental cyclic loading of concentric HSS braces

Canadian Journal of Civil Engineering ◽

10.1139/l10-113 ◽

2011 ◽

Vol 38 (1) ◽

pp. 110-123 ◽

Cited By ~ 14

Author(s):

Madhar Haddad ◽

Tom Brown ◽

Nigel Shrive

Keyword(s):

Energy Dissipation ◽

Material Properties ◽

Slenderness Ratio ◽

Plate Thickness ◽

Earthquake Ground Motion ◽

Braced Frames ◽

Gusset Plate ◽

Plate Size ◽

Tension And Compression ◽

Hysteresis Behaviour

During earthquake ground motion, diagonal braces in braced frames are subject to a series of cyclic loadings, alternately tension and compression. The brace can buckle and deform plastically, dissipating energy with damage accumulating in the steel. Eventually a crack may form and the brace fractures. To optimize energy dissipation, the effects of brace and gusset plate dimensions (thickness and length of the gusset plate, size of the brace, length of the brace), and material properties, on brace behaviour, need to be understood. Ten concentric bracing members, designed according to the weak brace – strong gusset concept, were tested. The objective was to investigate the effects of displacement history, brace effective slenderness ratio, and brace width/thickness ratio, on the hysteresis behaviour of bracing members. Displacement history was found to affect energy dissipation and fracture life. The effects of increasing the gusset plate thickness on the energy dissipation and the fracture life is not the same as reducing the effective slenderness ratio of the bracing member resulted from reducing the length of the HSS. New fracture life and energy life equations are proposed.

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Effect of replacement strike-face material on the ballistic performance of multi-ply soft armor targets

Textile Research Journal ◽

10.1177/0040517517753641 ◽

2018 ◽

Vol 89 (5) ◽

pp. 711-725 ◽

Cited By ~ 7

Author(s):

Zherui Guo ◽

Weinong Chen ◽

James Zheng

Keyword(s):

Stainless Steel ◽

Energy Dissipation ◽

Material Properties ◽

High Performance ◽

Ballistic Limit ◽

Stainless Steel Mesh ◽

Ballistic Performance ◽

Gas Gun ◽

The Impact ◽

Armor System

In this study, the impact-face material of a multi-ply soft armor system was varied to different ratios and tested for the effects on the ballistic performance. It is known that the first few layers of multi-ply soft armor material typically fail inelastically near the system ballistic limit and can be replaced with a “sacrificial” material with other more desirable properties. Previous studies have determined that the ballistic performance of these hybrid systems is largely dependent on the amount of high-performance backing material. However, the extent to which the high-performance fabric can be replaced has yet to be fully quantified and examined. Materials of different properties, namely stainless steel mesh, Makrolon® polycarbonate sheets, and cotton, were used as replacement frontal material for 840 d Twaron® panels, and the hybrid panels were impacted by O1 tool steel right-circular cylinder projectiles fired using a single-stage smooth-bore gas gun. Results show that the ballistic performance is maintained up to a frontal material ratio of about 40%, and off-axis material properties play a role in energy dissipation.

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Influence of the plate thickness and material properties on the violin top plate modes

INTER-NOISE and NOISE-CON Congress and Conference Proceedings ◽

10.3397/in-2021-2387 ◽

2021 ◽

Vol 263 (3) ◽

pp. 3369-3377

Author(s):

Evaggelos Kaselouris ◽

Yannis Orphanos ◽

Makis Bakarezos ◽

Michael Tatarakis ◽

Nektarios A. Papadogiannis ◽

...

Keyword(s):

Material Properties ◽

Plate Thickness ◽

Fem Analysis ◽

Wood Formation ◽

String Instruments ◽

Vibrational Behavior ◽

Vibrational Response ◽

Optimization And Control ◽

And Control ◽

The Impact

In this paper we analyze the vibrational behavior of the violin top plate, for varying plate thickness and material properties via finite element method (FEM) numerical simulations. It is well known that the vibrational properties of the top plates of string instruments influence their sound emission characteristics. Due to the impact of global warming on wood formation and due to their configurability, many manufacturers investigate the use of composite materials to produce musical instruments. Therefore, composite, carbon fiber reinforced epoxy (CFRE) prepreg along with traditional wooden material, such as spruce, are adopted in this study. FEM modal analysis along with a frequency response function (FRF) FEM analysis are performed. The vibrational variations of the plate's response are computed under free conditions. The main vibrational modes and the natural frequencies obtained by the simulations show the influence of the different mechanical and geometric properties on the top plate's vibrational response. The resulting eigenmode frequencies and shapes of the plate in relation to the varying thickness and the material properties used, are discussed. The results of this study offer valuable information on the evaluation of the acoustical characteristics of violins and may be further used on their vibrational behavior optimization and control.

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Experimental Investigation on the Anticollision Performance of Corrugated Steel-Reinforced Composites for Bridge Piers

Shock and Vibration ◽

10.1155/2021/5847559 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Guicheng Chen ◽

Haidong Huang ◽

Zhongfu Xiang

Keyword(s):

Energy Dissipation ◽

Natural Frequency ◽

Lateral Displacement ◽

Plate Thickness ◽

Steel Plates ◽

Extreme Value Analysis ◽

Value Analysis ◽

Dissipation Effect ◽

The Impact ◽

Peak Value

To reduce the loss of life and property caused by the collision of a ship against a bridge pier, this study proposes a new type of anticollision facility. The facility uses corrugated steel plates and corrugated steel pipes (CSPs), or ordinary steel plates and corrugated steel pipes (OSPs), as structural elements to form a honeycomb structure, which can greatly improve the impact resistance of bridge piers and reduce any damage to ships. To evaluate the anticollision performance of the proposed anticollision facility, this work uses the CSPs and OSPs as study objects in the impact test research. A pendulum impact test system was utilized to compare and analyze the column with CSP and OSP specimens and the column without any anticollision facilities. Test results show that the CSP and OSP specimens have a relatively high energy dissipation effect. When the impact energy is small, the energy dissipation effect of the OSPs with the same plate thickness is stronger than that of the CSPs. When the impact energy is large, the energy dissipation effect of the CSPs with the same plate thickness is stronger than that of the OSPs. In addition, the extreme value analysis method is used to analyze the relationship curve between the peak value of the D1 lateral displacement and the specimen’s plate thickness, weight, and natural frequency; the optimal thickness, weight, and natural frequency values of the CSP and OSP specimens are also deduced. Taking the optimal value of the specimen’s natural frequency as a target, the structure of the CSP and OSP specimens is optimized. When the optimized plate thickness is 2.50 mm, the ratios of the optimal value of the specimen plate thickness, weight, and natural frequency to the optimal calculation value are all in the range of [0.80, 1.12]. OSP and CSP specimens are found to have the best energy dissipation effect. The peak value of the D1 lateral displacement of the top of the column equipped with the CSPs is at least 88.37% lower than that of the column without any anticollision facilities. For the top of the column equipped with the OSPs, the peak value of the D1 lateral displacement is at least 80.37% lower than that of the column without any anticollision facilities. Optimization results show that the extreme value analysis method is suitable for the optimal design of anticollision facilities for piers.

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Selected Issues on Material Properties of Objects in Computer Simulations of Floodlighting

Energies ◽

10.3390/en14175448 ◽

2021 ◽

Vol 14 (17) ◽

pp. 5448

Author(s):

Rafał Krupiński ◽

Henryk Wachta ◽

Wojciech Maciej Stabryła ◽

Cedric Büchner

Keyword(s):

Computer Simulation ◽

Material Properties ◽

Input Parameter ◽

Lighting Design ◽

Complete Analysis ◽

Lighting System ◽

Utilization Factor ◽

Object A ◽

Architectural Structures ◽

The Impact

This paper addresses issues with computer simulation involved in designing illumination for architectural structures. In particular, the reflectance and transmittance of materials were studied with respect to their influence on luminance values, thus directly the power levels for luminaires applied under particular projects. Raster images derived from digitally processed daytime pictures were used to precisely define material properties. Bitmaps were tested with regard to measuring and editing materials with a widely used graphic application. A real architectural object, the Basilica of the Dormition in Jerusalem, served as the test object. A floodlighting design was performed following a complete analysis of all electrical and photometric parameters. Luminance distributions were analysed comprehensively. Hence, the data allowed for an assessment of the lighting design compliance with guidance given by International Commission on Illumination (CIE) for floodlighting objects and its required standards. The floodlighting utilization factor of the lighting solution developed was also verified, as it is the input parameter for evaluating not only the energy efficiency for the installed lighting system, but also the impact it has on the surroundings, in this case, the project that is to be implemented.

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On Kaufmann's theory of the impact of the pianoforte hammer

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1920.0016 ◽

1920 ◽

Vol 97 (682) ◽

pp. 99-110 ◽

Cited By ~ 12

Keyword(s):

Initial Conditions ◽

Practical Importance ◽

Prima Facie ◽

Point Of View ◽

Infinite Length ◽

Modes Of Vibration ◽

Rigorous Treatment ◽

The Subject ◽

Set Up ◽

The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

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Droplet impact onto a spring-supported plate: analysis and simulations

Journal of Engineering Mathematics ◽

10.1007/s10665-021-10107-5 ◽

2021 ◽

Vol 128 (1) ◽

Author(s):

Michael J. Negus ◽

Matthew R. Moore ◽

James M. Oliver ◽

Radu Cimpeanu

Keyword(s):

High Speed ◽

Flexible Substrate ◽

Practical Importance ◽

Hybrid Approach ◽

Hydrodynamic Pressure ◽

Analytical Framework ◽

Canonical System ◽

Linear Process ◽

Plate Motion ◽

The Impact

AbstractThe high-speed impact of a droplet onto a flexible substrate is a highly non-linear process of practical importance, which poses formidable modelling challenges in the context of fluid–structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed analytical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot, and stiffness of the spring have on the motion of the solid, which undergo forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length and time scales.

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Exoplanet mass estimation for a sample of targets for the Ariel mission

Experimental Astronomy ◽

10.1007/s10686-021-09758-0 ◽

2021 ◽

Author(s):

J. R. Barnes ◽

C. A. Haswell

Keyword(s):

Radial Velocity ◽

Input Parameter ◽

Noise Sources ◽

Time Commitment ◽

Low Mass ◽

Time Required ◽

Fixed Input ◽

The Impact ◽

Quadrature Sampling

AbstractAriel’s ambitious goal to survey a quarter of known exoplanets will transform our knowledge of planetary atmospheres. Masses measured directly with the radial velocity technique are essential for well determined planetary bulk properties. Radial velocity masses will provide important checks of masses derived from atmospheric fits or alternatively can be treated as a fixed input parameter to reduce possible degeneracies in atmospheric retrievals. We quantify the impact of stellar activity on planet mass recovery for the Ariel mission sample using Sun-like spot models scaled for active stars combined with other noise sources. Planets with necessarily well-determined ephemerides will be selected for characterisation with Ariel. With this prior requirement, we simulate the derived planet mass precision as a function of the number of observations for a prospective sample of Ariel targets. We find that quadrature sampling can significantly reduce the time commitment required for follow-up RVs, and is most effective when the planetary RV signature is larger than the RV noise. For a typical radial velocity instrument operating on a 4 m class telescope and achieving 1 m s−1 precision, between ~17% and ~ 37% of the time commitment is spent on the 7% of planets with mass Mp < 10 M⊕. In many low activity cases, the time required is limited by asteroseismic and photon noise. For low mass or faint systems, we can recover masses with the same precision up to ~3 times more quickly with an instrumental precision of ~10 cm s−1.

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