There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Numerical Initial Value Problems in Ordinary Differential Equations

Semiactive control devices have received significant attention in recent years because they offer the adaptability of active control devices without requiring the associated large power sources. Magnetorheological (MR) dampers are semiactive control devices that use MR fluids to produce controllable dampers. They potentially offer highly reliable operation and can be viewed as fail-safe in that they become passive dampers should the control hardware malfunction. To develop control algorithms that take full advantage of the unique features of the MR damper, models must be developed that can adequately characterize the damper's intrinsic nonlinear behavior. Following a review of several idealized mechanical models for controllable fluid dampers, a new model is proposed that can effectively portray the behavior of a typical MR damper. Comparison with experimental results for a prototype damper indicates that the model is accurate over a wide range of operating conditions and is adequate for control design an...

Phenomenological model for magnetorheological dampers

A scheme for understanding the organization of human postural movements is developed in the format of a position paper. The structural characteristics of the body and the geometry of muscular actions are incorporated into a three-dimensional graphical representation of human movement mechanics in the sagittal plane. A series of neural organizational hypotheses limit a theoretically infinite number of combinations of muscle contractions and associated movement trajectories for performing postural corrections: (1) Controls are organized to use the minimum number of muscles; (2) frequently performed movements are organized to require a minimum of neural decision-making.These hypotheses lead to the prediction that postural movements are composed of muscle contractile strategies derived from a limited set of distinct contractile patterns. The imposition of two mechanical constraints related to the configuration of support and to requirements for body stability with respect to gravity predict the conditions under which individual movement strategies will be deployed.A complementary organizational scheme for the senses is developed. We show that organization of postural movements into combinations of distinct strategies simplifies the interpretation of sensory inputs. The fine-tuning of movement strategies can be accomplished by breaking down the complex array of feedback information into a series of scalar quantities related to the parameters of the movement strategies. For example, the magnitude, aim, and curvature of the movement trajectory generated by an individual strategy can be adjusted independently.The second half of the report compares theoretical predictions with a series of actual experimental observations on normal subjects and patients with known sensory and motor disorders. Actual postural movements conform to theoretical predictions about the composition of individual movement strategies and the conditions under which each strategy is used. Observations on patients suggest how breakdowns in individual steps within the logical process of organization can lead to specific movement abnormalities.Discussion focuses on the areas needing further experimentation and on the implications of the proposed organizational scheme. We conclude that although our organizational scheme is not new in demonstrating the need for simplifying the neural control of movement, it is perhaps original in imposing discrete logical control upon a continuous mechanical system. The attraction of the scheme is that it provides a framework compatible with both mechanical and physiological information and amenable to experimental testing.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X00020008

The organization of human postural movements: A formal basis and experimental synthesis

In recent years, considerable attention has been paid to research and development of structural control devices, with particular emphasis on alleviation of wind and seismic response of buildings and bridges. In both areas, serious efforts have been undertaken in the last two decades to develop the structural control concept into a workable technology. Full-scale implementation of active control systems have been accomplished in several structures, mainly in Japan; however, cost effectiveness and reliability considerations have limited their wide spread acceptance. Because of their mechanical simplicity, low power requirements, and large, controllable force capacity, semiactive systems provide an attractive alternative to active and hybrid control systems for structural vibration reduction. In this paper we review the recent and rapid developments in semiactive structural control and its implementation in full-scale structures.

/pdf/state-of-the-art-of-structural-control-20ojs9jpb9.pdf

State of the art of structural control

An automotive suspension strut is proposed that utilizes compressible magnetorheological (CMR) fluid. A CMR strut consists of a double ended rod in a hydraulic cylinder and a bypass comprising tubing and an MR valve. The diameter on each side of the piston rods are set to be different in order to develop spring force by compromising the MR fluid hydrostatically. The MR bypass valve is adopted to develop controllable damping force. A hydro-mechanical model of the CMR strut is derived, and the spring force due to fluid compressibility and the pressure drop in the MR bypass valve are analytically investigated on the basis of the model. Finally, a CMR strut, filled with silicone oil based MR fluid, is fabricated and tested. The spring force and variable damping force of the CMR strut are clearly observed in the measured data, and compares favorably with the analytical model.

An automotive suspension strut using compressible magnetorheological fluids

Controllable Electrorheological and Magnetorheological Materials

Hot isostatic pressing using the intelligent processing of materials approach

A comparison study is conducted to evaluate the performance of shear and flow mode magnetorheological energy absorbers (MREAs) for a semi-active seat suspension system. The design methodologies for both flow mode and shear mode MREAs are presented. To validate the analytical results, both flow-mode and shear-mode MREAs are developed and their performance such as yield force and viscous damping as a function of the velocity, is experimentally evaluated. It is shown that the off-state force (viscous force) of the shear mode MREA is only a linear function of the damper velocity and, in comparison, the viscous force of typical flow mode damper increases sharply as the damper velocity increases. Using the validated design methodologies, flow-mode and shear-mode MREAs are designed for a crashworthy helicopter crew seat, and resulting metrics such as the size and weight of the flowand shear-mode MREAs are developed as a function of damper performance requirements, i.e. maximum yield force, viscous damping and maximum stroke.

Performance Evaluation of Shear Mode and Flow Mode Magnetorheological (MR) Energy Absorbers for Adaptive Seat Suspension Systems

Magnetorheological (MR) based semi-active dampers for the protection of sensitive devices against high shock and impact is examined from design considerations to characterization testing. Shock and impact dampers should be able to produce a high damping force at high velocities. However, a specification requiring high damping force generally causes an increase in the size of shock and impact dampers, which motivates the study of MR dampers to retrofit existing or conventional passive shock and impact dampers. A novel MR damper design was developed in this study for achieving both design goals: high force and compactness. The novel MR damper design increases the number of magnetically active volumes through which fluid to passes while minimizing damper length. Through FEM (Finite Element Method) analysis, the magnetic properties of the proposed design are investigated prior to actual fabrication. In addition to the unique magnetic circuit, other considerations stemming from the high pressures and velocities expected in this device are addressed. Characterization testing was performed up to 12 Hz with 1 inch sinusoidal stroke on a servo-hydraulic testing machine. These tests demonstrate that the MR damper is able to provide a high damping force at high velocity.

Design and testing of a compact magnetorheological damper for high impulsive loads

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