It is common for Departments of Mathematics to offer a junior-senior level course on Linear Algebra. This book represents one possible course. It evolved from my teaching a junior level course at Texas A&M University during the several years I taught after I served as President. I am deeply grateful to the A&M Department of Mathematics for allowing this Mechanical Engineer to teach their students.
This book is influenced by my earlier textbook with C.-C Wang, Introductions to Vectors and Tensors, Linear and Multilinear Algebra. This book is more elementary and is more applied than the earlier book. However, my impression is that this book presents linear algebra in a form that is somewhat more advanced than one finds in contemporary undergraduate linear algebra courses. In any case, my classroom experience with this book is that it was well received by most students. As usual with the development of a textbook, the students that endured its evolution are due a statement of gratitude for their help.
Painter, John H.; Tachita, R.; Ikeda, K.; Teranishi, A.; Noe, P.S.(IEEE, November 29, 1988)
[more]
[less]
Abstract:
An investigation was conducted on compact, multichannel GPS (global positioning system) receivers. The code generator and correlation equipment were simplified, attempting to avoid downgrading the properties possessed by multichannel receivers as much as possible, and the error-increasing factors caused by such modification were examined. As a means of simplifying the receiver hardware, phases with a unit of 1/8 chip were established in the code generator. Each channel was provided with a circuit for determining correlation, and the phase differences of the carrier and the code were measured by time division. It was confirmed that sufficient accuracy of measurement can be obtained even if such simplification is carried out.
The basic laws of friction. Fluid Film Bearings. Basic Operational Principles. Hydrodynamic and Hydrostatic Bearing Configurations. Example of rotordynamic study. Performance objectives.
Introduction to motion in mechanical systems. Definition of design, analysis, and testing. Steps in Modeling. Continuous and lumped parameter systems. Second Order Systems and differential equations of motion. Definitions of Free and Forced Responses. The purpose of analysis and the relevant issues to resolve.
Fundamental elements in mechanical systems: inertias, stiffness and damping elements. Equivalent spring coefficients and associated potential energy. Equivalent mass or inertia coefficients and associated kinetic energy. Equations of motion of a rigid body in a plane. Equivalent damping coefficients and associated dissipation energy. Types of damping models (linear or viscous and nonlinear).
The fundamental assumption in Lubrication Theory. Derivation of thin film flow equations from Navier-Stokes equations. Importance of fluid inertia effects in thin film flows. Some fluid physical properties
Reynolds equation for cylindrical journal bearings. Kinematics of motion and film thickness. Distinction between fixed and rotating coordinates. The pure squeeze velocity vector. Examples of journal motion.
Work and Energy – Single particle. Constraints – degrees of freedom. Principle of virtual work. D’Alembert Principle. Hamilton Principle. Lagrange’s equations of motion.
The long and short bearing models. Pressure field and fluid film forces on short length journal bearings. Equilibrium condition, load capacity and the Sommerfeld number.
Equations of motion of a rigid rotor. The concept of force coefficients. Derivation of stiffness and damping coefficients for the short bearing. Stability analysis and the effect of cross-coupled stiffness. Effect of rotor flexibility on stability and imbalance response.
Evaluation of dynamic force coefficients in finite length bearings using a perturbation of the flow equations. Finite Element models: basic equations and their solution.
Free & Force Vibrations of undamped MDOF systems. Orthogonality properties of natural modes. Rayleigh energy methods. Mode superposition (displacement and acceleration methods)
The nature of turbulence. Turbulence equations in thin film flows. Turbulence flow models. The bulk-flow model of turbulence, Hirs’ and Moody’s friction factors.
When fluid inertia effects are important. Bulk-flow model for inertial flows. Turbulence and inertia in short length journal bearings and open end dampers.
Browse
