By the end of this course, students will be able to:

• Understand the principles of analytical dynamics and their application to continuous structural systems.
• Apply Hamilton’s principle to derive partial differential equations of motion.
• Formulate and solve boundary-value and eigenvalue problems for vibration analysis.
• Determine the natural vibration modes of strings, rods, beams, and membranes using analytical methods.
• Apply computational methods such as Rayleigh’s method, Rayleigh–Ritz, assumed modes, and weighted residual techniques.
• Compare exact and approximate solution methods for the response of undamped continuous systems.
• Integrate theoretical and computational approaches to model and simulate structural and mechanical systems.