Passive and Active Inertia Forces in Flexible Body Dynamics

1992 ◽  
Vol 114 (4) ◽  
pp. 571-579 ◽  
Author(s):  
W. C. Hsu ◽  
A. A. Shabana
Keyword(s):  
Mathematical Model ◽  
Initial Conditions ◽  
Flexible Body ◽  
Beam Model ◽  
Axial Deformation ◽  
Passive System ◽  
Active System ◽  
Passive Systems ◽  
Modes Of Vibration ◽  
Inertia Forces

This investigation is devoted to a discussion on the effect of the coupling between the longitudinal and transverse displacements of kinematically driven rotating beams. To this end, the inertia forces that act on a flexible body as the result of the finite rotation are categorized into two classes. These are the passive and active inertia forces. While the effect of the active inertia forces of kinematically driven systems is recognized in the absence of external disturbances and nonzero initial conditions, the passive inertia forces of such systems are not recognized in the case of zero initial conditions and in the absence of external excitations. Depending on the assumed displacement field, three classes of mechanical systems are defined in this paper. These are the active, partially active, and passive systems. The active system has a mathematical model in which both passive and active inertia forces are fully presented. In a partially active system, a part of the passive inertia forces and the active inertia forces appear in the mathematical model. The vibration of the kinematically driven passive system is governed by homogeneous equations which contain only the passive inertia forces. In the case of zero initial conditions and in the absence of external excitation, the response of the passive kinematically driven system is zero regardless of the value of the angular velocity. The effect of the inertia forces of the passive system appear as a time varying modification of the system parameters. It is shown in this investigation that a rotating beam model in which the axial deformation is neglected is a partially active or passive system. It is also demonstrated that the neglect of the effect of the longitudinal displacement has two significant effects. It decouples the modes of vibration and makes the form of the complementary solution independent of the sense of rotation. The behavior of the active, partially active, and passive systems when they are subjected to driving constraints (specified motion) is examined and it is shown that the response of the passive system converges to the partially active system if the effect of the initial conditions becomes dominant as compared to the effect of the active inertia forces of the partially active system.

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

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
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.

The REPAS Study: Reliability Evaluation of Passive Safety Systems

2002 ◽  
Author(s):  
M. E. Ricotti ◽  
F. Bianchi ◽  
L. Burgazzi ◽  
F. D’Auria ◽  
G. Galassi
Keyword(s):  
Initial Conditions ◽  
Natural Circulation ◽  
Quantitative Information ◽  
External Input ◽  
Passive System ◽  
Two Phase ◽  
Passive Safety Systems ◽  
Safety Systems ◽  
Physical Laws ◽  
Physical Phenomena

The strategy of approach to the problem moves from the consideration that a passive system should be theoretically more reliable than an active one. In fact it does not need any external input or energy to operate and it relies only upon natural physical laws (e.g. gravity, natural circulation, internally stored energy, etc.) and/or “intelligent” use of the energy inherently available in the system (e.g. chemical reaction, decay heat, etc.). Nevertheless the passive system may fail its mission not only as a consequence of classical mechanical failure of components, but also for deviation from the expected behaviour, due to physical phenomena mainly related to thermalhydraulics or due to different boundary and initial conditions. The main sources of physical failure are identified and a probability of occurrence is assigned. The reliability analysis is performed on a passive system which operates in two-phase, natural circulation. The selected system is a loop including a heat source and a heat sink where the condensation occurs. The system behavior under different configurations has been simulated via best-estimate code (Relap5 mod3.2). The results are shown and can be treated in such a way to give qualitative and quantitative information on the system reliability. Main routes of development of the methodology are also depicted.

scholarly journals AGV Brake System Simulation

2019 ◽  
Vol 10 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Daniel Varecha ◽  
Robert Kohar ◽  
Frantisek Brumercik
Keyword(s):  
Mathematical Model ◽  
Input Data ◽  
Initial Conditions ◽  
Brake System ◽  
Disc Brake ◽  
Hydraulic Control ◽  
Stopping Distance ◽  
Braking Force ◽  
Braking Process ◽  
The Mathematical Model

Abstract The article is focused on braking simulation of automated guided vehicle (AGV). The brake system is used with a disc brake and with hydraulic control. In the first step, the formula necessary for braking force at the start of braking is derived. The stopping distance is 1.5 meters. Subsequently, a mathematical model of braking is created into which the formula of the necessary braking force is applied. The mathematical model represents a motion equation that is solved in the software Matlab by an approximation method. Next a simulation is created using Matlab software and the data of simulation are displayed in the graph. The transport speed of the vehicle is 1 〖m.s〗^(-1) and the weight of the vehicle is 6000 kg including load. The aim of this article is to determine the braking time of the device depending from the input data entered, which represent the initial conditions of the braking process.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Severe Accident Analysis for BWR With Containment Outer Pool

2012 ◽  
Author(s):  
Koki Yoshimura ◽  
Kohei Hisamochi
Keyword(s):  
Cooling System ◽  
Water Injection ◽  
Heat Removal ◽  
Severe Accident ◽  
Gas Temperature ◽  
Passive System ◽  
Active Components ◽  
Active System ◽  
Station Blackout ◽  
Materials Used

Newly designed plants, e.g., next-generation light water reactor or ESBWR, employ a passive containment cooling system and have an enhanced safety with RHRs (Residual Heat Removal system) including active components. Passive containment cooling systems have the advantage of a simple mechanism, while materials used for the systems are too large to employ these systems to existing plants. Combination of passive system and active system is considered to decrease amount of material for existing plants. In this study, alternatives of applying containment outer pool as a passive system have been developed for existing BWRs, and effects of outer pool on BDBA (Beyond Design Basis Accident) have been evaluated. For the evaluation of containment outer pool, it is assumed that there would be no on-site power at the loss of off-site power event, so called “SBO (Station BlackOut)”. Then, the core of this plant would be uncovered, heated up, and damaged. Finally, the reactor pressure vessel would be breached. Containment gas temperature reached the containment failure temperature criteria without water injection. With water injection, containment pressure reached the failure pressure criteria. With this situation, using outer pool is one of the candidates to mitigate the accident. Several case studies for the outer pool have been carried out considering several parts of containment surface area, which are PCV (Pressure Containment vessel) head, W/W (Wet Well), and PCV shell. As a result of these studies, the characteristics of each containment outer pool strategies have become clear. Cooling PCV head can protect it from over-temperature, although its effect is limited and W/W venting can not be delayed. Cooling suppression pool has an effect of pressure suppressing effect when RPV is intact. Cooling PCV shell has both effect of decreasing gas temperature and suppressing pressure.

From Soft Mooring System to Active Positioning in Laboratory Experiments

2020 ◽  
Author(s):  
Thomas Sauder ◽  
Galin Tahchiev
Keyword(s):  
Laboratory Experiments ◽  
Low Frequency ◽  
Positioning System ◽  
Mooring System ◽  
Passive System ◽  
Active System ◽  
Floating Structures ◽  
Main Components

Abstract This paper presents an active positioning system aimed at replacing the classical “passive” soft horizontal mooring system used in seakeeping tests of floating structures. We discuss the limitations of the passive approach, present the main components of the active system, and demonstrate its ability to reproduce results obtained with the passive system. We then show how the active system allow controlling the low-frequency damping applied to the floater. We conclude on the possibilities offered by this apparatus.

scholarly journals Mathematical model of a drive mechanism with a crank device of a crank press

2020 ◽  
Vol 164 ◽  
pp. 03051 ◽  
Author(s):  
Kirill Kobzev
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Structural Element ◽  
Kinematic Excitation ◽  
Drive Mechanism ◽  
Dynamic Errors ◽  
Partial Systems ◽  
The Stability ◽  
Inertia Forces ◽  
Crank Mechanism

The most important link in the forging equipment is a crank mechanism. Their significant drawback is the unbalanced inertia forces of the moving masses of the crank mechanism, which cause vibration. The analysis of the phenomena occurring in the mechanism and the assessment of the technological process are based on the theory of chains, which allows analytically analyzing the dynamic characteristics of systems with a large number of degrees of freedom, based on the analysis of one structural element. The study of the process of force interaction inevitably comes down to the construction of a mathematical model of mechanisms, the formative movement of which leads to its formation. One of the partial systems makes an irregular programmed motion, meaning the crank drive mechanism. In addition, unwanted vibrations caused by kinematic excitation are superimposed on this drive. According to numerous papers on this topic, significant dynamic errors arise due to vibration accelerations. One of the main tasks in reducing the vibration activity and, accordingly, the level of acoustic emission of the process under study is to ensure the required law of motion of the instrument. On this basis, the study of the stability of formative movements is of particular importance. This question is complicated by the fact that in the processing, there is a change in the process parameters and, consequently, in the characteristics of the friction coupling. The latter circumstance presupposes the evolution of the system under study, and therefore the need for process control.

Zero-Energy Active Suspension System for Automobiles With Adaptive Sky-Hook Damping

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Kalpesh Singal ◽  
Rajesh Rajamani
Keyword(s):  
Active Suspension ◽  
Suspension System ◽  
Energy Management System ◽  
Zero Energy ◽  
Passive System ◽  
Active System ◽  
Active Suspensions ◽  
Resonant Frequencies ◽  
Active Systems ◽  
Automotive Suspension

Previous research has shown that a semiactive automotive suspension system can provide significant benefits compared to a passive suspension but cannot quite match the performance of a fully active system. The advantage of the semiactive system over an active system is that it consumes almost zero energy by utilizing a variable damper whose damping coefficient is changed in real time, while a fully active suspension consumes significant power for its operation. This paper explores a new zero-energy active suspension system that combines the advantages of semiactive and active suspensions by providing the performance of the active system at zero energy cost. Unlike a semiactive system in which the energy is always dissipated, the proposed system harvests and recycles energy to achieve active operation. An electrical motor-generator is used as the zero-energy actuator and a controller and energy management system are developed. An energy adaptive sky-hook gain is proposed to prevent the system from running out of energy, thereby eliminating the need to switch between passive and active systems. The results show that the system performs at least as well as a passive system for all frequencies, and is equivalent to an active system for a broad range of frequencies including both resonant frequencies.

A MATHEMATICAL MODEL FOR THE REPRODUCTION DYNAMICS OF TOXOPLASMA GONDII

2015 ◽  
Vol 23 (supp01) ◽  
pp. S91-S100
Author(s):  
JOHN ALEXANDER LEÓN MARÍN ◽  
IRENE DUARTE GANDICA
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Toxoplasma Gondii ◽  
Epithelial Cells ◽  
Sexual Reproduction ◽  
Numerical Solution ◽  
Definitive Host ◽  
Initial Conditions ◽  
Felis Catus ◽  
One Dimensional

This paper presents a mathematical model describing the reproduction dynamics of the Toxoplasma gondii parasite in the definitive host Felis catus (cat). The dynamics is described by a system of partial differential equations defined in a one-dimensional region, with boundary and initial conditions. The model considers both asexual and sexual reproduction processes of the T. gondii parasite starting from the consumption of T. gondii oocysts from the environment, by the definitive host, and describing the reproduction dynamics until the cat expels infectious oocysts to the environment through its feces. The numerical solution of the system is obtained, and some simulations are made, leaving constant of transition and loss rates, since its variation does not produce significant changes in the reproduction, propagation and creation of new populations; and varying the initial consumption of oocysts from the environment by the cat. It is concluded that, either low or high, the involved populations are always reproduced; they spread by all over epithelial cells and subsequently are expelled to the environment through the cat feces. It is corroborated that the cats are potential multipliers of the oocysts and therefore, the main disseminators of the infection.

scholarly journals A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

2015 ◽  
Vol 12 (108) ◽  
pp. 20150276 ◽  
Author(s):  
María Fuentes-Garí ◽  
Ruth Misener ◽  
David García-Munzer ◽  
Eirini Velliou ◽  
Michael C. Georgiadis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Cell Lines ◽  
Phase Distribution ◽  
Initial Conditions ◽  
Cellular Heterogeneity ◽  
Cycle Phase ◽  
Biologically Relevant ◽  
Future Outcomes ◽  
Unique Cell

Acute myeloid leukaemia is characterized by marked inter- and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics.

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