Relevant bibliographies by topics / Shock (Mechanics) – Mathematical models

Academic literature on the topic 'Shock (Mechanics) – Mathematical models'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Shock (Mechanics) – Mathematical models"

1

Qu, Zhi Ming. "Investigation of Damage Effect by Shock Wave on Structures in Excavation Roadway." Key Engineering Materials 439-440 (June 2010): 1438–43. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.1438.

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Using the theory of explosion mechanics and gas detonation dynamics and the conservation law of mass, momentum and energy, the physical and mathematical models of damage effect are set up in excavation roadway during gas explosion. In view of gas concentration, accumulation position, volumes and states of spaces, the shock wave damage on structures in the roadway during gas explosion. The damage effects are characterized of heat and mechanic damage. Meanwhile, the high temperature and pressure are formed in different degree. With the action of overpressure and impulse, the damage degree is different with different geometric structures in ventilation system. By means of basic condition, influential factors, procedure features and simulation, some unnecessary structures or barriers should be cleared in order to keep smooth the ventilation system.
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Chang, Juntao, Lei Wang, and Wen Bao. "Mathematical modeling and characteristic analysis of scramjet buzz." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 228, no. 13 (January 29, 2014): 2542–52. http://dx.doi.org/10.1177/0954410014521055.

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Buzz is an important issue for a scramjet engine. A mathematical model of buzz oscillations is necessary for control system design. Control-oriented models of hypersonic vehicle propulsion systems require a reduced-order model that is accurate to some extent but requires less than a few seconds of computational time. To achieve this goal, a reduced-order model of buzz oscillations for a scramjet engine is built by introducing the modeling idea of Moore–Greitzed model for compressors. The introduction of characteristic lines avoids the complex interactions in hypersonic inlet, such as shock–shock interactions and shock–boundary layer interaction. And the inlet characteristics are obtained from the pressure signal of combustor. Based on the established buzz model, we can predict the inlet performance, characterize the stability margin of inlet, reflect the oscillatory characteristics of inlet buzz including the dominant amplitude and frequency and describe the transition process of inlet buzz.
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R., Krupych,, Nishchenko, I., Shevchuk, R., and Krupych, S. "Mathematical model of the system “manual vibration shock shaker – fruit branch”." Mehanization and electrification of agricultural, no. 9(108) (2019): 210–23. http://dx.doi.org/10.37204/0131-2189-2019-9-27.

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Purpose. Development of mathematical model of oscillating system “manual vibration shock shaker – fruit branch” for the purpose of theoretical substantiation of the parameters of the shaker. Methods. The basic positions of mathematics, theoretical mechanics, mathematical modeling, program development and numerical calculations on the PC using methods of constructing mathematical models of functioning of agricultural machines are used. Results. The paper proposes a mathematical system model “manual vibration shock shaker – fruit branch” of six differential equations describing the motion of five separate masses (the mass of branch and four masses of individual shaker strings) and differential equations of the transverse and rotational motion of the system as whole. The mathematical system model determines the regularity of the motion of all masses, as well as the reactions of the viscals of the oscillatory system to the impact and after the impact that is generated in the shock mechanism. The proposed nonlinear, complex system of differential equations solves the numerical Runge-Kutta method of the fourth order of accuracy. On the basis of the calculated data the theoretical regularities of change of movement, speed and acceleration of a branch in the place of capture are received, which confirm that in the case of interaction of the cups of the shock mechanism there is blow that is accompanied by an increase in the acceleration of the branch, which is 4–5 times greater than the acceleration of the vibration mode of operation. Conclusions 1. The mathematical model of oscillating system “manual vibration shock shaker – fruit branch” is proposed in the form of system of six differential equations that allows to theoretically substantiate the basic modes of work of the manual shaker in the vibration shock mode to provide the agrotechnical necessary extraction completeness. 2. The received theoretical regularities of change of displacement, speed and acceleration of branch at the place of capture confirm the effectiveness of the vibration shock mode of the shaker. Due to the vibration-shock mode, the acceleration of the branch at the point of transmission of disturbing forces is 4–5 times higher than the acceleration of the vibrational operation mode. Keywords: manual shakes, vibration shocking process, oscillation oscillators, mathematical model, fruit branch, harvesting.
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Ucar, H., and I. Basdogan. "Dynamic characterization and modeling of rubber shock absorbers: A comprehensive case study." Journal of Low Frequency Noise, Vibration and Active Control 37, no. 3 (August 21, 2017): 509–18. http://dx.doi.org/10.1177/1461348417725954.

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Rubber or elastomeric materials are widely used for shock absorbers having elastic and viscous properties such as high inherent damping, deflection capacity, and energy storage. The dynamic properties of these components are of primary concern in designing rubber absorbers to reduce the shock loading given as well as the structure-borne noise transmissibility. Besides, the dynamic response of the mechanical systems, at where the rubber shock absorbers are used, is directly associated with the properties of the shock absorbers. In order to determine these properties of the rubber, mathematical models are created in terms of hyperelasticity and viscoelasticity. The hyperelastic and viscoelastic material models represent the nonlinear elastic and strain rate dependencies of the overall rubber behavior, respectively. Hyperelastic material model captures the material’s nonlinear elasticity with no-time dependence whereas viscoelastic model describes the material response which contains an elastic and viscous part depending on time, frequency, and temperature. This paper presents the dynamic characterization of rubber shock absorbers, having different shore hardness values, in terms of hyperelastic and viscoelastic constitutive models. The parameters of the constitutive models are determined from the uniaxial tensile and relaxation tests. These parameters are used for the numerical model of the rubber components and the accuracy of the characterization is presented by means of a numerical case study.
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Morozov, Victor A., Vsevolod I. Bogatko, and Andrey B. Yakovlev. "About mathematical simulation of processes for high-speed loading of materials on Department of Physical Mechanics of St. Petersburg State University." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 65, no. 4 (2020): 699–713. http://dx.doi.org/10.21638/spbu01.2020.411.

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The researches of shock-wave processes in the constructional materials are actual, but carrying out of natural experiments is extremely inconvenient and expensive, and sometimes it is even impossible to replicate. Therefore basically all researches of these problems are reduced to various cases of simulation of processes for high-speed loading of materials in the laboratory circumstances. In the paper we consider following directions of mathematical simulation of processes for high-speed loading of materials that were made on department of physical mechanics of St. Petersburg State University: the simulation of shock-loaded media by using of dynamics of dislocations; the simulation of high-speed loading of media with the account of the relaxation phenomena in a near-surface region; the simulation of propagation of the short elastoplastic impulse in medium under the condition of influence of a weak magnetic field; the generation of mathematical models of deformation and destruction of thin metal rings by a magnetic-pulse method; the simulation of crack propagation during the short-term pulse loading.
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Liu, Hongtuo, Fangwei Xie, Kai Zhang, Xinxing Zhang, Jin Zhang, Cuntang Wang, and Hao Li. "Effect of air chamber and oil properties on damping characteristics of single-tube pneumatic shock absorber." International Journal of Structural Integrity 9, no. 1 (February 5, 2018): 27–37. http://dx.doi.org/10.1108/ijsi-03-2017-0017.

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Purpose The shock absorber is an important component of vehicle suspension that attenuates the vehicle vibration. Its running state directly affects the performance of the vehicle suspension. The purpose of this paper is to quantitatively study the relationship between damping characteristics and air chamber and oil properties in single-tube pneumatic shock absorber. Design/methodology/approach Combined with the principle of fluid dynamics and hydraulic transmission technology, the rebound stroke and compression stroke mathematical models, and damping characteristics simulation model are established to investigate the effect of the air chamber and oil property on damping characteristics. Findings Research results show that the initial pressure of the air chamber is the key parameter which influences the damping characteristics of the shock absorber. The change of the initial pressure has more impact on damping force, and less impact on the speed characteristic; the initial volume of the air chamber almost has no effect on the damping characteristics. The density and viscosity of the oil have certain influence on the damping characteristics. Therefore, selecting suitable damping oil is very important. Originality/value Using Matlab/Simulink software to build simulation models, its results are very accurate. The conclusions can provide a theoretical reference for the structure design of a single-tube pneumatic shock absorber.
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Пятакович, В. А., В. Ф. Рычкова, and А. П. Пурденко. "Mathematical models for evaluating the effectiveness of shock-absorbing fasteners of vibro-active mechanisms of marine objects by vibrational power." MORSKIE INTELLEKTUAL`NYE TEHNOLOGII)</msg>, no. 4(54) (December 2, 2021): 13–20. http://dx.doi.org/10.37220/mit.2021.54.4.083.

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Для создания виброакустической защиты судового оборудования необходимо учитывать потоки колебательной энергии, распространяющиеся от источников как через опорные и неопорные связи, так и в виде воздушного шума. В работе представлены математические модели оценки эффективности амортизирующих креплений виброактивных механизмов морских объектов по колебательной мощности, учитываемые при обучении разрабатываемой нейросетевой системы классификации морских целей. Теоретические разработки в области виброзащиты и виброизоляции во многом имеют междисциплинарный характер и опираются на методы теории механизмов и машин, теоретической механики, теории колебаний, теории управления, используются методы инфорьт мационные технологии для оценки, поиска и выбора рациональных проектно-конструкторских решений. Создание амортизирующих устройств, способных защитить объекты от вибраций и ударов и, вместе с тем, обладающих ограниченными размерами, является сложной технической проблемой. В связи с этим первостепенное значение приобретают вопросы теории и расчета адаптивных виброзащитных систем. To create vibro-acoustic protection of ship equipment, it is necessary to take into account the flows of vibrational energy propagating from sources both through support and non-support connections, and in the form of air noise. The paper presents mathematical models for evaluating the effectiveness of shock-absorbing fasteners of vibro-active mechanisms of marine objects by vibrational power, which are taken into account when training the developed neural network system for classifying marine targets. Theoretical developments in the field of vibration protection and vibration isolation are largely interdisciplinary in nature and are based on the methods of the theory of mechanisms and machines, theoretical mechanics, vibration theory, control theory, information technology methods are used to evaluate, search and select rational design solutions. The creation of shock-absorbing devices that can protect objects from vibrations and shocks and, at the same time, have limited dimensions is a complex technical problem. In this regard, the issues of the theory and calculation of adaptive vibration protection systems are of paramount importance.
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Li, Jun, and Zhi Ming Qu. "Application of Much-Touted Stochastic Algorithm in Investigating Active Networks and World Wide Web." Advanced Materials Research 143-144 (October 2010): 62–66. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.62.

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Using the theory of explosion mechanics and gas detonation dynamics and the conservation law of mass, momentum and energy, the physical and mathematical models of damage effect are set up in excavation roadway during gas explosion. In view of gas concentration, accumulation position, volumes and states of spaces, the shock wave damage on structures in the roadway during gas explosion. The damage effects are characterized of heat and mechanic damage. Meanwhile, the high temperature and pressure are formed in different degree. With the action of overpressure and impulse, the damage degree is different with different geometric structures in ventilation system. By means of basic condition, influential factors, procedure features and simulation, some unnecessary structures or barriers should be cleared in order to keep smooth the ventilation system.
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SHPACHUK, Vladimir, Aleksandr CHUPRYNIN, Tatiana SUPRUN, and Andriy KOVALENKO. "MECHANICAL INTERACTION OF THE RAIL TRANSPORT CAR AND JOINT IRREGULARITY." Scientific Journal of Silesian University of Technology. Series Transport 113 (December 1, 2021): 173–89. http://dx.doi.org/10.20858/sjsutst.2021.113.14.

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Mechanical models of a transport system “carriage - track” while crossing a joint irregularity are proposed. An investigation was conducted on the peculiarities of static, shock and dynamic interaction between the four-axle car and the track, considering tram wheelsets motion features over joint irregularity. A method to solve the equations of a mathematical model of static, shock and dynamic interaction is developed. Numerical analysis is used to determine deflections of the facing rail under the first sleeper for each phase of motion depending on motion phases, and car load and speed.
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Kou, Farong, Qiangqiang Jing, Chen Chen, and Jianghao Wu. "Endocrine Composite Skyhook-Groundhook Control of Electromagnetic Linear Hybrid Active Suspension." Shock and Vibration 2020 (February 29, 2020): 1–17. http://dx.doi.org/10.1155/2020/3402168.

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In order to effectively improve vehicle riding comfort, handling stability, and realize vibration energy recovery, a new kind of electromagnetic linear hybrid active suspension (EMLHAS) integrated with linear motor and solenoid valve shock absorber is put forward. Firstly, for the analysis of the suspension performance, a quarter dynamic model of EMLHAS is established. At the same time, the mathematical models of a linear motor, including the active state and energy-regenerative state, are found. The correctness of mathematical models for the linear motor in the active and energy-regenerative states is verified by means of characteristic tests. Moreover, the velocity characteristic tests of solenoid valve shock absorber are carried out to determine its mathematical polynomial model in the semiactive state. Then, a new kind of multimode endocrine composite skyhook-groundhook control strategy is proposed. The suspension motion is divided into four modes according to the driving conditions of the vehicle. An endocrine control with long feedback and short feedback is combined with the skyhook-groundhook control. The control laws of the skyhook-groundhook controller and endocrine controller are, respectively, designed. Finally, the simulation analysis of suspension dynamic performance and energy-regenerative characteristic is done. The results show the control effect of endocrine composite skyhook-groundhook control is better than that of skyhook-groundhook control, which improves vehicle riding comfort and handling stability. Moreover, part of vibration energy is recovered.
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Dissertations / Theses on the topic "Shock (Mechanics) – Mathematical models"

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Handley, Caroline A. "Numerical modelling of two HMX-based plastic-bonded explosives at the mesoscale." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/1709.

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Mesoscale models are needed to predict the effect of changes to the microstructure of plastic-bonded explosives on their shock initiation and detonation behaviour. This thesis describes the considerable progress that has been made towards a mesoscale model for two HMX-based explosives PBX9501 and EDC37. In common with previous work in the literature, the model is implemented in hydrocodes that have been designed for shock physics and detonation modelling. Two relevant physics effects, heat conduction and Arrhenius chemistry, are added to a one-dimensional Lagrangian hydrocode and correction factors are identified to improve total energy conservation. Material models are constructed for the HMX crystals and polymer binders in the explosives, and are validated by comparison to Hugoniot data, Pop-plot data and detonation wave profiles. One and two-dimensional simulations of PBX9501 and EDC37 microstructures are used to investigate the response of the bulk explosive to shock loading. The sensitivity of calculated temperature distributions to uncertainties in the material properties data is determined, and a thermodynamic explanation is given for time-independent features in temperature profiles. Hotspots are widely accepted as being responsible for shock initiation in plastic-bonded explosives. It is demonstrated that, although shock heating of crystals and binder is responsible for temperature localisation, it is not a feasible hotspot mechanism in PBX9501 and EDC37 because the temperatures generated are too low to cause significant chemical reaction in the required timescales. Critical hotspot criteria derived for HMX and the binders compare favourably to earlier studies. The speed of reaction propagation from hotspots into the surrounding explosive is validated by comparison to flame propagation data, and the temperature of the gaseous reaction products is identified as being responsible for negative pressure dependence. Hotspot size, separation and temperature requirements are identified which can be used to eliminate candidate mechanisms in future.
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Rhedin, Kristoffer, and Sjödin Simon Mattsson. "Vätskeslag i rörsystem : Experimentell utvärdering av rörstödens samt rörets utformning och dess inverkan på vätskeslag i rörsystem." Thesis, Linnéuniversitetet, Sjöfartshögskolan (SJÖ), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-74304.

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Studiens syfte är att identifiera en robust ingenjörsmetodik för approximation av sannolikhet och konsekvens (risken) vid vätskeslag i ett specifikt rörsystem. Arbetet har utförts i form av kvalitativa studier med verifierande experiment av analytiska beräkningsresultat.  Studiens resultat, vilka presenteras och diskuteras i slutsatskapitlet, visar på att vätskeslag kan predikteras och därigenom förebyggas med Joukowskys ekvation, vilken formulerades av Johannes von Kries 1883.  I de flesta fall kan ett rörsystems konstruktion optimeras mot oönskade tryckslags-konsekvenser genom omsorgsfullt val av lämpliga rörsystemskomponenter, såsom rördimensioner, ventiler, rörkrökningsradier och rörstödskonstruktioner.
This study’s objective has been to identify and evaluate a robust engineering method for the purpose of approximation and evaluation of a water hammer event in a specific pipe system design.  The study has been conducted in the form of qualitative studies with verifying experiments of the results from various analytical calculations.  The results presented and discussed in the last chapter of the essay, indicates that water hammer can be predicted and prevented by using Joukowsky's equation, formulated Johannes von Kries 1883.  In the most circumstances, pipe systems can be optimized to prevent water hammer consequences by selection of suitable components. Such as tube dimensions, valves, tube bending radius and the tube support design.
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Warren, Paul A. "Mathematical models of 3-D ocular mechanics and control." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312221.

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Lee, M. E. M. "Mathematical models of the carding process." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249543.

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Carding is an essential pre-spinning process whereby masses of dirty tufted fibres are cleaned, disentangled and refined into a smooth coherent web. Research and development in this `low-technology' industry have hitherto depended on empirical evidence. In collaboration with the School of Textile Industries at the University of Leeds, a mathematical theory has been developed that describes the passage of fibres through the carding machine. The fibre dynamics in the carding machine are posed, modelled and simulated by three distinct physical problems: the journey of a single fibre, the extraction of fibres from a tuft or tufts and many interconnecting, entangled fibres. A description of the life of a single fibre is given as it is transported through the carding machine. Many fibres are sparsely distributed across machine surfaces, therefore interactions with other neighbouring fibres, either hydrodynamically or by frictional contact points, can be neglected. The aerodynamic forces overwhelm the fibre's ability to retain its crimp or natural curvature, and so the fibre is treated as an inextensible string. Two machine topologies are studied in detail, thin annular regions with hooked surfaces and the nip region between two rotating drums. The theoretical simulations suggest that fibres do not transfer between carding surfaces in annular machine geometries. In contrast to current carding theories, which are speculative, a novel explanation is developed for fibre transfer between the rotating drums. The mathematical simulations describe two distinct mechanisms: strong transferral forces between the taker-in and cylinder and a weaker mechanism between cylinder and doffer. Most fibres enter the carding machine connected to and entangled with other fibres. Fibres are teased from their neighbours and in the case where their neighbours form a tuft, which is a cohesive and resistive fibre structure, a model has been developed to understand how a tuft is opened and broken down during the carding process. Hook-fibre-tuft competitions are modelled in detail: a single fibre extracted from a tuft by a hook and diverging hook-entrained tufts with many interconnecting fibres. Consequently, for each scenario once fibres have been completely or partially extracted, estimates can be made as to the degree to which a tuft has been opened-up. Finally, a continuum approach is used to simulate many interconnected, entangled fibre-tuft populations, focusing in particular on their deformations. A novel approach describes this medium by density, velocity, directionality, alignment and entanglement. The materials responds to stress as an isotropic or transversely isotropic medium dependent on the degree of alignment. Additionally, the material's response to stress is a function of the degree of entanglement which we describe by using braid theory. Analytical solutions are found for elongational and shearing flows, and these compare very well with experiments for certain parameter regimes.
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Moore, Matthew Richard. "New mathematical models for splash dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:c94ff7f2-296a-4f13-b04b-e9696eda9047.

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In this thesis, we derive, extend and generalise various aspects of impact theory and splash dynamics. Our methods throughout will involve isolating small parameters in our models, which we can utilise using the language of matched asymptotics. In Chapter 1 we briefly motivate the field of impact theory and outline the structure of the thesis. In Chapter 2, we give a detailed review of classical small-deadrise water entry, Wagner theory, in both two and three dimensions, highlighting the key results that we will use in our extensions of the theory. We study oblique water entry in Chapter 3, in which we use a novel transformation to relate an oblique impact with its normal-impact counterpart. This allows us to derive a wide range of solutions to both two- and three-dimensional oblique impacts, as well as discuss the limitations and breakdown of Wagner theory. We return to vertical water-entry in Chapter 4, but introduce the air layer trapped between the impacting body and the liquid it is entering. We extend the classical theory to include this air layer and in the limit in which the density ratio between the air and liquid is sufficiently small, we derive the first-order correction to the Wagner solution due to the presence of the surrounding air. The model is presented in both two dimensions and axisymmetric geometries. In Chapter 5 we move away from Wagner theory and systematically derive a series of splash jet models in order to find possible mechanisms for phenomena seen in droplet impact and droplet spreading experiments. Our canonical model is a thin jet of liquid shot over a substrate with a thin air layer trapped between the jet and the substrate. We consider a variety of parameter regimes and investigate the stability of the jet in each regime. We then use this model as part of a growing-jet problem, in which we attempt to include effects due to the jet tip. In the final chapter we summarise the main results of the thesis and outline directions for future work.
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Huang, Xin, and 黃昕. "Exploring critical-state behaviour using DEM." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206742.

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The critical state soil mechanics (CSSM) framework originally proposed by Schofield & Wroth (1968) has been shown to capture the mechanical behaviour of soils effectively. The particulate implementation of the discrete element method (DEM) can replicate many of the complex mechanical characteristics associated with sand. This research firstly shows that the CSSM framework is useful to assess whether a DEM simulation gives a response that is representative of a real soil. The research then explores the capacity of DEM to extend understanding of soil behaviour within the CSSM framework. The influence of sample size on the critical-state response observed in DEM simulations that use rigid-wall boundaries was examined. The observed sensitivity was shown to be caused by higher void ratios and lower contact densities adjacent to the boundaries. When the void ratio (e) and mean stress (p’) of the homogeneous interior regions were considered, the influence of sample size on the position of the critical state line (CSL) in e-log(p’) space diminished. A parametric study on the influence of the interparticle friction (μ) on the load-deformation response was carried out. The macro-scale stress-deformation characteristics were nonlinearly related to μ and the particle-scale measures (fabric, contact force distribution, etc.) varied systematically with μ. The limited effect of increases in μ on the overall strength at high μ values (μ>0.5) is attributable to transition from sliding-dominant to rolling-dominant contact behaviour. A μ value higher than 0.5 leads to a CSL in e-log(p’) space that does not capture real soil response. True-triaxial simulations with different intermediate stress ratios (b) were performed. The dependency of strength on b agreed with empirical failure criteria for sands and was related to a change of buckling modes of the strong force chains as b increased. DEM simulations showed that the position of the CSL in e-log(p’) space depends on the intermediate stress ratio b. This sensitivity seems to be related to the dependency of the directional fabric anisotropy on b. The link between the state parameter and both soil strength and dilatancy proposed by Jefferies & Been (2006) was reproduced in DEM simulations. A new rotational resistance model was proposed and it was shown that the new model can qualitatively capture the influence of particle shape on the mechanical behaviour of sand. However, it was shown that the effect of rotational resistance is limited and to quantitatively compare the DEM simulation results with laboratory testing data, e.g., the critical-state loci, it is necessary to use non-spherical particles.
published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy
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Beckham, Jon Regan. "Analysis of mathematical models of electrostatically deformed elastic bodies." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 169 p, 2008. http://proquest.umi.com/pqdweb?did=1475178561&sid=27&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Morland, Lawrence Christopher. "Mathematical models for a fluid flow arising in turbine blade cooling passages." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330029.

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Beylin, Andrey V. "Supersymmetric Landau Models." Scholarly Repository, 2011. http://scholarlyrepository.miami.edu/oa_dissertations/624.

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This work is focused on the different supersymmetric extensions of the Landau model. We aim to fully solve each model and describe its energy levels, wavefunctions, Hilbert space and define a norm on it, as well as find symmetry generators and transformations with respect to them. Several possible generalizations were considered before. It was found for Landau model on the so called Superflag manifold as well as planar Superflag and Superplane Landau models that standard norm on the Hilbert space is not positive definite. Later for planar cases it was found that it is possible to fix this by introducing a new norm which will be invariant and positive definite. Surprisingly this procedure brings up "hidden" symmetries for the known super Landau models. In the dissertation we apply the same procedure for Landau model on superpshere and Superflag manifolds. It turns out that superpsherical Landau model is equivalent to the Superflag model with one of the parameters fixed. Because the model on superpshere can be recovered from the Superflag we will do calculations of corrected norm only for the Superflag. After this we develop a different generalization of the Superplane Landau model. Starting with Lagrangian in a superfield form we introduce two arbitrary functions of superfields K(Φ) and V(Φ) into the Lagrangian. We follow with the component form of Lagrangian. The quantization of the model is possible, and we will show that there is a reparametrization which turn equation of motion of the first scheme into the second set. Standard metric is again non-positive definite and we apply already known procedure to correct it. It will not be possible to solve Schrodinger equations in general with undefined K and V, so we consider one specific case which give us Landau model on a sphere with N = 2 supersymmetry, which put it apart from the superspherical Landau model, which have a superpshere for a target space but do not possess supersymmetry.
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Zhao, Qian, and 赵倩. "A thermomechanical approach to constitutive modeling of geomaterials." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B47166836.

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Modeling of the mechanical behavior of geomaterials is a fundamental yet very difficult problem in geotechnical engineering. The difficulty lies in that the engineering behavior of geomaterials is strongly nonlinear and anisotropic, depending on confining pressure, void ratio, stress history, and drainage conditions. A traditional approach to the modeling of geomaterials is to formulate empirical equations to fit experimental data. Generally, this approach is not able to provide physical insights into the diverse responses observed in the soil mechanics laboratories. Another conventional approach is to make use of the classical plasticity theory, established mainly for metals, to develop constitutive models for geomaterials. While this approach is capable of shedding light on the mechanisms involved, it has been recognized that such models may violate the basic laws of physics. The objective of this thesis is to apply a new approach to constructing constitutive models for geomaterials, by making use of thermomechanical principles. The essence of the new approach is that the constitutive behavior of geomaterials can be completely determined once two thermomechanical potentials, i.e. the free energy and dissipation rate functions, are specified. The yield function and flow rule in the classical plasticity theory can be established from the two potentials, and the models so derived satisfy the basic laws of physics automatically. In this thesis, the theoretical framework for constructing thermomechanical models is introduced. Several concepts in relation to plastic work, dissipated and stored energy are discussed. Both the isotropic and anisotropic models are formulated and realized in this framework and the generated predictions are compared with the test data of a series of triaxial compression tests on sand. To address the important density- and pressure-dependent behaviors of sand in the framework, a state-dependent thermomechanical model is developed, by introducing the state parameter into the dissipation rate function such that a unique set of model parameters is able to predict the behaviors of sand for a wide variation of densities and pressures. Finally, a thermomechanical model for predicting the complex unloading and reloading behaviors of sand is developed by modifying the hardening laws, and the performance of this model is investigated.
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Civil Engineering
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Master of Philosophy
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Books on the topic "Shock (Mechanics) – Mathematical models"

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Osher, Stanley. Essentially non-oscillatory shock capturing methods applied to turbulence amplification in shock wave calculations. [Washington, DC]: National Aeronautics and Space Administration, 1989.

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Szuladzinski, Gregory. Formulas for mechanical and structural shock and impact. Boca Raton: Taylor & Francis, 2010.

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Berger, Rutherford C. A finite element scheme for shock capturing. Vicksburg, Miss: U.S. Army Corps of Engineers, Waterways Experiment Station, 1993.

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Subbotin, S. G. Dinamika udarostoĭkikh konstrukt︠s︡iĭ. Snezhinsk: RFI︠A︡T︠S︡--VNIITF, 2003.

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W, Davison L., and Shahinpoor Mohsen, eds. High-pressure shock compression of solids III. New York: Springer, 1998.

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Morozov, Nikita Fedorovich. Dynamics of fracture. Berlin: Springer, 2000.

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Rosenberg, Zvi. Terminal Ballistics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Rosenberg, Zvi. Terminal ballistics. Heidelberg: Springer, 2012.

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Arthur, Rizzi, and Hirschel Ernst-Heinrich, eds. Numerical solutions of the Euler equations for steady flow problems. Braunschweig; Wiesbaden: Vieweg, 1991.

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Andaluzia, Matei, ed. Mathematical models in contact mechanics. New York: Cambridge University Press, 2012.

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Book chapters on the topic "Shock (Mechanics) – Mathematical models"

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Fey, R. H. B., and G. J. Meijer. "Tuning Shock Test Results and Mathematical Models Using an Optimal State Estimation Method." In Topics in Applied Mechanics, 39–55. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2090-6_4.

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Polishchuck, Mikhail N., Arkadii N. Popov, and Dmitrii V. Reshetov. "Mathematical Model of Shock Machine." In Advances in Mechanical Engineering, 86–96. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-91553-7_10.

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Grishchenko, V. I., M. S. Kilina, and G. A. Dolgov. "Mathematical Model of Hydraulic Shock Absorber with Feedback." In Lecture Notes in Mechanical Engineering, 1262–70. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-54817-9_147.

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Chapelle, Dominique, and Klaus-Jürgen Bathe. "Shell Mathematical Models." In Computational Fluid and Solid Mechanics, 95–134. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16408-8_4.

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Chapelle, Dominique, and Klaus-Jürgen Bathe. "Shell Mathematical Models." In Computational Fluid and Solid Mechanics, 81–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05229-7_4.

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Matsumoto, Y., M. Kameda, F. Takemura, H. Ohashi, and A. Ivandaev. "Wave dynamics of bubbly liquids mathematical models and numerical simulation." In Shock Waves, 535–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77648-9_84.

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Miara, Bernadette. "Mathematical Justifications of Plate Models." In Encyclopedia of Continuum Mechanics, 1–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53605-6_138-1.

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Miara, Bernadette. "Mathematical Justifications of Plate Models." In Encyclopedia of Continuum Mechanics, 1514–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_138.

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Zin, W. A., and R. F. M. Gomes. "Mathematical Models in Respiratory Mechanics." In Anaesthesia, Pain, Intensive Care and Emergency Medicine — A.P.I.C.E., 391–400. Milano: Springer Milan, 1996. http://dx.doi.org/10.1007/978-88-470-2203-4_34.

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Serovajsky, Simon. "Mathematical models of fluid and gas mechanics." In Mathematical Modelling, 261–78. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003035602-14.

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Conference papers on the topic "Shock (Mechanics) – Mathematical models"

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Altuhov, Vladimir, Aleksey Boldyrev, and Pavel Zhirov. "INFLUENCE OF DYNAMIC LOADING ON THE CHARACTERISTICS OF POLYMER IMPACT DAMPERS." In PROBLEMS OF APPLIED MECHANICS. Bryansk State Technical University, 2020. http://dx.doi.org/10.30987/conferencearticle_5fd1ed035dbc84.89285592.

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The article is devoted to the study of the influence of dynamic loading on the characteristics of polymer elements of shock absorbers of the rolling stock of railways and to the description of the creation of a mathematical model of their work. The results of mathematical modeling are further used to solve problems of the longitudinal dynamics of rolling stock. In the study, the initial loading rate varied, the ambient temperature and the influence of the wear factor remained unchanged. For the operating speeds of a freight car, a mathematical model of the PMKP-110 draft gear was determined.
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Peshkov, Ilya, Miroslav Grmela, and Evgeniy Romenski. "Two-Phase Solid-Fluid Mathematical Model of Yield Stress Fluids." In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/smasis2012-7913.

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In this work, we present results on mathematical modelling of polymeric yield stress fluids which have the properties of both elastic solids and fluids. Our research is based on the approach of multiphase continuum mechanics. A two-phase solid-fluid model is developed. This model is thermodynamically compatible and its governing differential equations can be written in a conservative form. Such a model is convenient for application of advanced high-accuracy numerical methods and modelling of discontinuous solutions such as shock waves and contacts.
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Laksari, Kaveh, Mehdi Shafieian, Kurosh Darvish, and Keyanoush Sadeghipour. "Shock Wave Propagation as a Mechanism of Injury in Nonlinear Viscoelastic Soft Tissues." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64717.

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This study investigates the propagation of shock waves and self-preserving waves in soft tissues such as brain as a mechanism of injury in high rate loading conditions as seen in blast-induced neurotrauma (BINT). The derived mathematical models indicate that whereas linear viscoelastic models predict only decaying waves, instances of such phenomena as shock can be achieved in nonlinear media. In this study, a nonlinear viscoelastic material model for brain tissue was developed in compression. Furthermore, nonlinear viscoelastic wave propagation in brain tissue was studied and a criterion for the development of shock waves was formulated. It was shown that discontinuities in the acceleration that happen in blast loading conditions may evolve to shock waves, resulting in large discontinuities in strain and stress at the wave front leading to tissue injuries.
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Tan, X. G., Andrzej J. Przekwas, and Joseph B. Long. "Validations of Virtual Animal Model for Investigation of Shock/Blast Wave TBI." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64587.

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Complementary to animal testing and analysis of clinical data, a validated anatomy and physiology based mathematical models can provide capabilities for a better understanding of blast wave brain injury mechanisms, animal-human injury scaling, assessing and improving protective armor. We developed the 3D “virtual” animal models for multi-scale computational simulations of blast induced injury. A multi-scale modeling tool, CoBi, has been adopted for the analysis of blast wave primary TBI mechanisms and coupled biomechanics events. The shock wave over a rat in a shock tube was modeled by the CFD method. The primary biomechanics FEM study uses anatomic based animal geometry with a high resolution brain model. The virtual rat model has been validated against recently collected data from shock tube tests on rodents, including pressure time history in the free-stream and inside the rat brain. The model has been used to conduct parametric simulations to study the effect of animal placement location in the shock tube, and different loading orientations on the rat response. We also compared the rat brain biomechanical response between simulations of a free-to-move and a protected or constrained rat under the same shock tube loading to identify the role of body protection and head movement and on the rat TBI. The implications of these results suggest that virtual animal model could be used to predict the biomechanical response in the blast TBI event, and help design the protection against the blast TBI.
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Bhalla, Kenneth, Lixin Gong, and George McKown. "Implementation of a Bottom-Hole Assembly Program." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29467.

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A state of the art windows graphical user interface (GUI) program has been developed to predict and design the bottom-hole assembly (BHA) performance for drilling. The techniques and algorithms developed in the program are based upon those developed by Lubinski and Williamson. The BHA program facilitates in conducting parametric studies, and in making field decisions for optimal performance. The input parameters may include: formation class, dip angle, hole size, drill collar size, number of stabilizers, stabilizer spacing. The program takes into consideration bit-formation characteristics and interaction, drill collar sizes, square collars, shock absorbers, MWD tools, reamer tools, directional tools, rotary steerable systems etc. The output may consist of hole curvature (build up or drop rate), hole angle, weight on bit and is presented in drilling semantics. Additionally, the program can perform mechanical analyses and solve for the bending moments and reactions forces. Moreover, the program has the capability to predict the wellpath using a drill ahead algorithm. The program consists of a mathematical model which makes assumptions of 2-D, static, constant hole curvature resulting in a robust computationally efficient tool that produces rapid reliable results in the field.
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Ajaj, M. A., A. M. Sharaf, S. A. Hegazy, and Y. H. Hossamel-deen. "Investigation of Control Algorithms for Semi-Active Suspension Systems Based on a Full Vehicle Model." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63090.

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This paper presents a comprehensive investigation of automotive semi-active suspension control algorithms and compares their characteristics in terms of ride comfort and tire-road holding ability. Particular attention has been paid to the semi-active suspension systems fitted with a shock absorber of dual damping characteristics. Different mathematical models are presented to investigate the ride response considering both simplified and complex vehicle models. Numerical simulation has been carried out through the MATLAB/SIMULINK environment which aids the future development of controllable suspension systems to improve vehicle ride comfort. The results show a considerable improvement of the vehicle ride response using different schemes of semi-active suspension system in particular the modified groundhook control algorithm.
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LOPATO, A. I., and A. G. EREMENKO. "PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS." In 9th International Symposium on Nonequilibrium Processes, Plasma, Combustion, and Atmospheric Phenomena. TORUS PRESS, 2020. http://dx.doi.org/10.30826/nepcap9b-17.

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The paper is devoted to the numerical modeling of detonation initiation in the flat channel with the profiled end-wall of the elliptic form. Mathematical model is based on two-dimensional Euler equations supplemented by the chemical kinetics model to describe the combustion of a hydrogen-oxygen mixture under the low pressure. Both the global kinetic model and the detailed Petersen—Hanson (PH) model are applied. The computations are performed on unstructured triangular grids using numerical method of second approximation order. For the calculation of time reduction, the computational algorithm was parallelized using the open source library ParMETIS to divide the computational domain. The mechanism of detonation initiation by the incident shock wave (SW) with the Mach number~2.7 is described. The results of initiation of the detonation wave (DW) for two models of chemical kinetics are compared with the identification of similarities and differences in the process.
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Culp, David B., and Xia Ma. "Modeling Fragmentation within Pagosa Using Particle Methods." In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-085.

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Abstract The mechanics involved in shock physics often involves materials undergoing large deformations being subjected to high strain rates and temperature variations. When considering high-velocity impacts and explosions, metals experience plastic flow, dynamic failures and fragmentation that are often too complex for a Lagrangian method, such as the finite element method, to properly resolve. Conversely, Eulerian methods are simple to setup, but often result in numerical diffusion errors [1]. These unpleasantries can be skirted by using an alternative technique that incorporates a blend of these aforementioned methods. FLIP+MPM (FLuid Implicit Particle + Material Point Method) employs Lagrangian points to track state quantities associated with materials as strength, as well as conserved quantities, such as mass. Concurrently, an Eulerian grid is used to calculate gradient fields and incorporate an algorithm that carries out the hydrodynamics [2]. By incorporating the FLIP+MPM method into Los Alamos National Laboratory’s Pagosa hydrodynamics code, massively parallel architectures may be employed to solve such problems as those including fragmentation, plastic flow and fluid-structure interaction. This paper will begin with a mathematical description of the FLIP+MPM technique and describe how it fits into Pagosa. After a description of the implementation, the capabilities of this numerical technique are highlighted by simulating fragmentation as a result of high velocity impacts and explosions. Several strength and damage models will be exercised to demonstrate the code’s flexibility. Comparison of the different models’ fragment size distributions are given and discussed.
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Seifert, C. "Almost sure purely singular continuous spectrum for quasicrystal models." In QMath12 – Mathematical Results in Quantum Mechanics. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814618144_0030.

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Santos Belle, Vilson Wenis, and RICARDO TEIXEIRA DA COSTA NETO. "VTR4 X 4 THREE-DIMENSIONAL MATHEMATICAL MODEL WITH INDEPENDENT SUSPENSIONS AND MAGNETORREOLOGICAL SHOCK ABSORBERS." In 26th International Congress of Mechanical Engineering. ABCM, 2021. http://dx.doi.org/10.26678/abcm.cobem2021.cob2021-0017.

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Reports on the topic "Shock (Mechanics) – Mathematical models"

1

Modlo, Yevhenii O., Serhiy O. Semerikov, Stanislav L. Bondarevskyi, Stanislav T. Tolmachev, Oksana M. Markova, and Pavlo P. Nechypurenko. Methods of using mobile Internet devices in the formation of the general scientific component of bachelor in electromechanics competency in modeling of technical objects. [б. в.], February 2020. http://dx.doi.org/10.31812/123456789/3677.

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An analysis of the experience of professional training bachelors of electromechanics in Ukraine and abroad made it possible to determine that one of the leading trends in its modernization is the synergistic integration of various engineering branches (mechanical, electrical, electronic engineering and automation) in mechatronics for the purpose of design, manufacture, operation and maintenance electromechanical equipment. Teaching mechatronics provides for the meaningful integration of various disciplines of professional and practical training bachelors of electromechanics based on the concept of modeling and technological integration of various organizational forms and teaching methods based on the concept of mobility. Within this approach, the leading learning tools of bachelors of electromechanics are mobile Internet devices (MID) – a multimedia mobile devices that provide wireless access to information and communication Internet services for collecting, organizing, storing, processing, transmitting, presenting all kinds of messages and data. The authors reveals the main possibilities of using MID in learning to ensure equal access to education, personalized learning, instant feedback and evaluating learning outcomes, mobile learning, productive use of time spent in classrooms, creating mobile learning communities, support situated learning, development of continuous seamless learning, ensuring the gap between formal and informal learning, minimize educational disruption in conflict and disaster areas, assist learners with disabilities, improve the quality of the communication and the management of institution, and maximize the cost-efficiency. Bachelor of electromechanics competency in modeling of technical objects is a personal and vocational ability, which includes a system of knowledge, skills, experience in learning and research activities on modeling mechatronic systems and a positive value attitude towards it; bachelor of electromechanics should be ready and able to use methods and software/hardware modeling tools for processes analyzes, systems synthesis, evaluating their reliability and effectiveness for solving practical problems in professional field. The competency structure of the bachelor of electromechanics in the modeling of technical objects is reflected in three groups of competencies: general scientific, general professional and specialized professional. The implementation of the technique of using MID in learning bachelors of electromechanics in modeling of technical objects is the appropriate methodic of using, the component of which is partial methods for using MID in the formation of the general scientific component of the bachelor of electromechanics competency in modeling of technical objects, are disclosed by example academic disciplines “Higher mathematics”, “Computers and programming”, “Engineering mechanics”, “Electrical machines”. The leading tools of formation of the general scientific component of bachelor in electromechanics competency in modeling of technical objects are augmented reality mobile tools (to visualize the objects’ structure and modeling results), mobile computer mathematical systems (universal tools used at all stages of modeling learning), cloud based spreadsheets (as modeling tools) and text editors (to make the program description of model), mobile computer-aided design systems (to create and view the physical properties of models of technical objects) and mobile communication tools (to organize a joint activity in modeling).
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