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

Dynamics of structures

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

Although the concepts of Jacobian matrix, manipulability, and condition number have existed since the very early beginning of robotics their real significance is not always well understood. In this paper we revisit these concepts for parallel robots as accuracy indices in view of optimal design. We first show that the usual Jacobian matrix derived from the input-output velocities equations may not be sufficient to analyze the positioning errors of the platform. We then examine the concept of manipulability and show that its classical interpretation is erroneous. We then consider various common local dexterity indices, most of which are based on the condition number of the Jacobian matrix. It is emphasized that even for a given robot in a particular pose there are a variety of condition numbers and that their values are not coherent between themselves but also with what we may expect from an accuracy index. Global conditioning indices are then examined. Apart from the problem of being based on the local accuracy indices that are questionable, there is a computational problem in their calculation that is neglected most of the time. Finally, we examine what other indices may be used for optimal design and show that their calculation is most challenging.

/pdf/jacobian-manipulability-condition-number-and-accuracy-of-5ecm213mgd.pdf

Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

Artificial intelligence for the modeling and control of combustion processes: a review

A finite element vibration analysis of thin-watled cylindrical shells conveying fluid with uniform velocity is presented The dynamic behavior of thin-walled shell is based on the Sanders’ theory and the fluid in cyhndrical shell is considered as inviscid and incompressible so that it satisfies the Laplace’s equation A beam-like shell element is used to reduce the number of degrees-of-freedom by restricting to the circumferential modes of cylindrical shell An estimation of frequency response function of the pipe considering of the coupled effects of the internal fluid is presented A dynamic coupling condition of the interface between the fluid and the structure is used The effective thickness of fluid according to circumferential modes is also discussed The influence of fluid velocity on the frequency response function is illustrated and discussed The results by this method are compared with published lesults and those by commercial tools

Frequency response analysis of cylindrical shells conveying fluid using finite element method

Improvement of impulse response spectrum and its application

This paper presents a tire–road friction coefficient estimation method based on the six-degrees-of-freedom (6-DoF) vehicle body acceleration. The key principle of the proposed method is to estimate the tire–road friction coefficient from the accelerations at the tire. A vehicle model is applied to the 6-DoF vehicle body acceleration to derive longitudinal, lateral, and normal accelerations at each tire. Then, the recursive least squares (RLS) method is applied to the accelerations thus derived to estimate the tire–road friction coefficient. The main advantage of the proposed method is that it can be implemented with a 6-DoF accelerometer, which may be available in today's passenger vehicles equipped with accelerometers and gyroscopes. The method was validated with experiments in a passenger sedan, which demonstrates that the method is able to estimate tire–road friction coefficients accurately in real time during longitudinal emergency braking.

Estimation of Tire–Road Friction Based on Onboard 6-DoF Acceleration Measurement

Spring Operating Mechanism (SOM) is a dynamic system to open and close the circuit breaker in a voltage controlling system. For a high-speed action of opening and closing within a few mili-seconds, a SOM consists of many links, joints, chains, and cams. Thus, various dynamic characteristics are occurred, especially large contact forces between the cam and the roller, the shaft and the stopper. To save time and money for a new design of SOM system, analysis of the mechanism is necessary. In this paper, a multibody dynamic analysis and test technique was applied for a SOM to predict, estimate and validate forces occurring during the operation. For the multibody dynamic analysis, the ADAMS program was employed for 145kV circuit breaker with a SOM. For an accurate modeling, several components were sequentially added and the reliability of modeling was validated through the comparison with test data of opening and closing.

Dynamic analysis and design of a high voltage circuit breaker with spring operating mechanism

Virtual simulation is an economical and efficient method in mechanical system design. Numerical modeling of a spar platform, tethered by a mooring cable with a spherical joint is developed for the dynamic simulation of the floating structure in ocean. The geometry modeling of the spar is created using finite element methods. The submerged part of the spar bears the buoyancy, hydrodynamic drag force, and effect of the added mass and Froude-Krylov force. Strip theory is used to sum up the forces acting on the elements. The geometry modeling of the cable is established based on the lumped-mass-and-spring modeling through which the cable is divided into 10 elements. A new element-fixed local frame is used, which is created by the element orientation vector and relative velocity of the fluid, to express the loads acting on the cable. The bottom of the cable is fixed on the seabed by spring forces, while the top of the cable is connected to the bottom of the spar platform by a modified spherical joint. This system suffers the propagating wave and current in the X-direction and the linear wave theory is applied for setting of the propagating wave. Based on the numerical modeling, the displacement-load relationships are analyzed, and the simulation results of the numerical modeling are compared with those by the commercial simulation code, ProteusDS. The comparison indicates that the numerical modeling of the spar platform tethered by a mooring cable is well developed, which provides an instruction for the optimization of a floating structure tethered by a mooring cable system.

Wan-Suk Yoo

Papers

Frequency response analysis of cylindrical shells conveying fluid using finite element method

Improvement of impulse response spectrum and its application

Estimation of Tire–Road Friction Based on Onboard 6-DoF Acceleration Measurement

Dynamic analysis and design of a high voltage circuit breaker with spring operating mechanism

Numerical modeling of a spar platform tethered by a mooring cable