Hamiltonian's Principle in Aero Elasticity Contd. — Lesson 5

This lesson covers the application of Hamiltonian's principle in aeroelasticity. It explains how to formulate equations for a beam-like structure under bending deformation and torsion problem. The lesson also discusses the kinetic energy, potential energy, and the distributed load of the beam. It further elaborates on the Hamiltonian principle and how to evaluate each quantity term by term. The lesson also explains how to derive the kinetic energy expression, the variation of strain energy expression, and the variation of external work. Towards the end, the lesson discusses the boundary conditions for different problems and how to solve them.

Video Highlights

01:22 - Discussion on the representation of the wing by a beam and the definition of coordinates.
06:51 - Application of Hamiltonian principle to evaluate each quantity term by term.
19:48 - Explanation of the boundary conditions for different types of beams.
45:15 - Discussion on the solution methods for the equations derived from Hamiltonian’s principle.
71:28 - Discussion on the boundary conditions of the free vibration problem.

Key Takeaways

- Hamiltonian's principle can be applied in aeroelasticity to formulate equations for a beam-like structure under bending deformation and torsion problem.
- The kinetic energy, potential energy, and the distributed load of the beam can be derived using the Hamiltonian principle.
- The Hamiltonian principle allows us to evaluate each quantity term by term, which simplifies the process of deriving the kinetic energy expression, the variation of strain energy expression, and the variation of external work.
- Understanding the boundary conditions for different problems is crucial in solving them.