Vibration Analysis and Dynamic Systems Principles

This course covers the fundamental principles of vibration analysis and dynamic systems. It starts with the basics of vibration analysis, including the formulation of differential equations for discrete and continuous systems, and the application of Newton's law and D'Alembert's principle. The course then delves into the concepts of holonomic and non-holonomic systems, equilibrium approach, and free body diagrams, using examples like a simple pendulum and a unicyclist moving along a curve. The course also explores the work energy principle, kinetic energy, potential energy, and the conservation of energy. It further discusses the method of formulating vibration problems using Hamilton's principle and Lagrange's equation, providing examples of a bar undergoing axial vibration and single degree freedom systems. The course concludes with the solution of numerical problems related to natural frequencies and the discussion of phase plane diagrams.