Advanced Vibration Analysis of Euler-Bernoulli Beams

This course covers the comprehensive study of the Euler-Bernoulli beam's force vibration analysis, a model extensively utilized in diverse engineering applications. The course starts with the general formulation of forced vibration problems and their derivation for the Euler-Bernoulli beam. It further explores the application of these formulations in various scenarios, such as a bridge girder. The course also delves into the principle of mode superposition, the concept of natural frequencies and mode shapes, and the application of Duhamel's integral in solving forced vibration problems. The course concludes with a detailed analysis of examples like a simply supported beam subjected to harmonic excitation and a fixed-fixed beam subjected to a uniformly distributed load. Additionally, the course covers the dynamic analysis of Euler-Bernoulli beams subjected to moving loads and support excitation, the impact of moving load speed on the impact factor, and the calculation of mid-span deflection, bending moment, and shear force. Special topics like the vibration of a beam on an elastic foundation, the effect of axial force on beam vibration, and the vibration of an infinitely long beam are also included.