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Seminar

Seminar. Reporter ： Chine-Feng Wu Advisor ： Jeng-Tzong Chen Date ： October 22, 2019 Space ： HR1 104. Outline. Continuous system Discrete system SDOF MDOF. Question ：.

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Seminar

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  1. Seminar Reporter：Chine-Feng Wu Advisor：Jeng-Tzong Chen Date：October 22, 2019 Space：HR1 104 Department of Harbor and River Engineering

  2. Outline • Continuous system • Discrete system • SDOF • MDOF Department of Harbor and River Engineering

  3. Question ： Consider a straight bar for which the axial stiffness EA and mass per unit length vary along its length as indicated in Fig. Department of Harbor and River Engineering

  4. Notation • : Displacement in the axial direction • : Mass per unit length • : Modulus of elasticity • : Area • : Length • : Wave number • : Mass • : Spring constant • : Eigenvalues • : Eigenvetors Department of Harbor and River Engineering

  5. The governing equation Department of Harbor and River Engineering

  6. Dynamic equilibrium relationship • Where • The governing equations , Department of Harbor and River Engineering

  7. The method of separation of variables The wave equation The boundary condition Department of Harbor and River Engineering

  8. trivial trivial Department of Harbor and River Engineering

  9. Department of Harbor and River Engineering

  10. Department of Harbor and River Engineering

  11. Eigenvalue & Eigenvector Department of Harbor and River Engineering

  12. Eigenvalue Continuous system Department of Harbor and River Engineering

  13. Eigenvetors Department of Harbor and River Engineering

  14. Mode one of continuous system n=1 • Mode one of discrete System (詹雅馨) • Mode one of continuous system Department of Harbor and River Engineering

  15. Mode two of continuous system n=2 • Mode two of discrete system (詹雅馨) • Mode two of continuous system Department of Harbor and River Engineering

  16. Mode three of continuous system (n=3) • Mode threeof discrete system (詹雅馨) • Mode 3 of continuous system Department of Harbor and River Engineering

  17. Discrete system Department of Harbor and River Engineering

  18. Department of Harbor and River Engineering

  19. Department of Harbor and River Engineering

  20. Department of Harbor and River Engineering

  21. Department of Harbor and River Engineering

  22. Eigenvalue Department of Harbor and River Engineering

  23. Eigenvetors Department of Harbor and River Engineering

  24. Continuous system Department of Harbor and River Engineering

  25. x t=10 t=0 y SDOF Department of Harbor and River Engineering

  26. Department of Harbor and River Engineering

  27. t=0 t=10 Department of Harbor and River Engineering

  28. Department of Harbor and River Engineering

  29. Department of Harbor and River Engineering

  30. Department of Harbor and River Engineering

  31. Rigid body G Example (1) Motorcycle frame Department of Harbor and River Engineering

  32. G = Department of Harbor and River Engineering

  33. Department of Harbor and River Engineering

  34. G Example (2) Motorcycle frame Department of Harbor and River Engineering

  35. Department of Harbor and River Engineering

  36. Transform back to obtain the physical response. Solve the free vibration problem (eigenvalue problem) to obtain the natural frequencies and modal vectors. Solve the uncoupled equations to obtain the modal response. Evaluate the transformed mass, stiffness and force matrices. Form the modal matrix. Identify the generalized coordinates that will be used to describe the motion of the system. Derive the equations of motion for the system. Department of Harbor and River Engineering

  37. where Department of Harbor and River Engineering

  38. Department of Harbor and River Engineering

  39. Department of Harbor and River Engineering

  40. Thanks for your kind attentions You can get more information from our website. http://msvlab.hre.ntou.edu.tw/ Department of Harbor and River Engineering

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