Vibration of Continuous Systems

This learning track covers a comprehensive understanding of vibration problems in dynamic systems, starting with the fundamentals of vibration analysis and the difference between discrete and continuous systems. It delves into the characteristics of dynamic systems, the modeling of undamped and damp systems, and the effects of vibration, such as resonance, fatigue, and serviceability. The track further explores the mathematical properties of periodic functions, the concept of degrees of freedom, and the response of a system subjected to arbitrary excitation. It also discusses the application of transform techniques in solving dynamic systems, and the use of integral transform, particularly Laplace and Fourier transforms, in vibration analysis of linear systems. The learning track then moves on to the study of one-dimensional wave equations, axial and torsional vibrations, transverse vibration in beams, and the force vibration analysis of the Euler-Bernoulli beam. It also covers the vibration in continuous systems, the vibration of membranes and rectangular plates, and advanced vibration analysis techniques. The track concludes with lessons on support excitation in structures, the application of numerical methods in solving dynamic equations, and the spectral method of analysis for structures subjected to random excitation.