Free & Force Vibrations of undamped MDOF systems. Orthogonality properties of natural modes. Rayleigh energy methods. Mode superposition (displacement and acceleration methods)
Work and Energy – Single particle. Constraints – degrees of freedom. Principle of virtual work. D’Alembert Principle. Hamilton Principle. Lagrange’s equations of motion.
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).
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.
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.
When fluid inertia effects are important. Bulk-flow model for inertial flows. Turbulence and inertia in short length journal bearings and open end dampers.
Evaluation of dynamic force coefficients in finite length bearings using a perturbation of the flow equations. Finite Element models: basic equations and their solution.
The mechanism of centering stiffness in seals. Force coefficients for short-length pressure seals. Design of annular seals: swirl brakes, impact on rotordynamics. Hydrostatic bearings in modern applications. The principle of hydrostatic lubrication. Effects of recess volume-fluid compressibility on force coefficients for operation at low and high frequencies. Applications of hydrostatic bearings
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