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).
Work and Energy – Single particle. Constraints – degrees of freedom. Principle of virtual work. D’Alembert Principle. Hamilton Principle. Lagrange’s equations of motion.
Free & Force Vibrations of undamped MDOF systems. Orthogonality properties of natural modes. Rayleigh energy methods. Mode superposition (displacement and acceleration methods)
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