# Vibrations of Plates and Shells - Institution: IISc Bangalore - Department: Mechanical Engineering - Teacher: Prof. Venkata R. Sonti - Level: Graduate - Language: English - Subjects: Engineering - Source: [NPTEL](https://nptel.ac.in/courses/112108312) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/112108312) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) The course presents theory of vibrations of continuous systems such as rods, plates and shells. Many engineering applications like automobiles, aircraft structures, ship hulls, submarine hulls, pipes carrying water and all such applications where high speed moving parts are used, require knowledge of this topic as high vibrations will be a problem. Intended audience: Masters and PhD students Prerequisites: Bachelors in engineering or science. A basic course in lumped vibrations is required. ## Lectures 1. [Introduction to differential geometry.](https://invisiblenetwork.ai/learn/nptel/112108312/cba167caf913) (YouTube) 2. [Properties of surfaces:First fundamental form.](https://invisiblenetwork.ai/learn/nptel/112108312/b5a876bd9a0f) (YouTube) 3. [Properties of surfaces: Second fundamental form.](https://invisiblenetwork.ai/learn/nptel/112108312/698ed9b5dab0) (YouTube) 4. [Surfaces of revolution.](https://invisiblenetwork.ai/learn/nptel/112108312/fb5cee1a49d1) (YouTube) 5. [Gauss Codazzi relations.](https://invisiblenetwork.ai/learn/nptel/112108312/ac2dd57bca6a) (YouTube) 6. [Gauss Codazzi contd.](https://invisiblenetwork.ai/learn/nptel/112108312/e5f8ca96baa4) (YouTube) 7. [Differential element length in a thin shell.](https://invisiblenetwork.ai/learn/nptel/112108312/d134835cfd5d) (YouTube) 8. [Strain of a differential element.](https://invisiblenetwork.ai/learn/nptel/112108312/4e4f8259eb39) (YouTube) 9. [Explicit strain expressions.](https://invisiblenetwork.ai/learn/nptel/112108312/d304668e3738) (YouTube) 10. [Love simplifications and inconsistencies Of the theory.](https://invisiblenetwork.ai/learn/nptel/112108312/f342a66e512d) (YouTube) 11. [Euler Bernoulli Beam equation using the Hamilton’s Law.](https://invisiblenetwork.ai/learn/nptel/112108312/818fca3de232) (YouTube) 12. [Euler Bernoulli Beam and Hamilton’s Law contd.](https://invisiblenetwork.ai/learn/nptel/112108312/e6a1518517d6) (YouTube) 13. [Beta definition, force and moment resultants.](https://invisiblenetwork.ai/learn/nptel/112108312/41b8d002bc75) (YouTube) 14. [Hamilton’s Law for a general shell.](https://invisiblenetwork.ai/learn/nptel/112108312/e6ae0624de2e) (YouTube) 15. [The Hamilton’s law continued.](https://invisiblenetwork.ai/learn/nptel/112108312/9cf5a5b16084) (YouTube) 16. [Final Dynamical Equations and boundary conditions.](https://invisiblenetwork.ai/learn/nptel/112108312/292750210c1c) (YouTube) 17. [Physics of each term in the dynamic equations.](https://invisiblenetwork.ai/learn/nptel/112108312/b84ee813f318) (YouTube) 18. [Physics of each term continued.](https://invisiblenetwork.ai/learn/nptel/112108312/75ef18db17ba) (YouTube) 19. [The sixth equation of motion.](https://invisiblenetwork.ai/learn/nptel/112108312/a35fcad71f04) (YouTube) 20. [The sixth equation of motion contd.](https://invisiblenetwork.ai/learn/nptel/112108312/1c58955248e1) (YouTube) 21. [Equations of motion for a rectangular plate using Hamilton’s law.](https://invisiblenetwork.ai/learn/nptel/112108312/891a3cda6e7a) (YouTube) 22. [Equations of motion for a rectangular Plate continued.](https://invisiblenetwork.ai/learn/nptel/112108312/152764880b60) (YouTube) 23. [Rectangular plate boundary conditions.](https://invisiblenetwork.ai/learn/nptel/112108312/6730d7c7ab51) (YouTube) 24. [Rectangular plate equation using force balance.](https://invisiblenetwork.ai/learn/nptel/112108312/3bc3a9287518) (YouTube) 25. [Modeshapes and resonances of a vibrating beam.](https://invisiblenetwork.ai/learn/nptel/112108312/031bc33c1a39) (YouTube) 26. [Modeshapes and resonances of a vibrating Rectangular plate.](https://invisiblenetwork.ai/learn/nptel/112108312/02b76f059482) (YouTube) 27. [Modeshapes and resonances of a vibrating Circular plate.](https://invisiblenetwork.ai/learn/nptel/112108312/b8c550294218) (YouTube) 28. [Vibrating circular plate continued.](https://invisiblenetwork.ai/learn/nptel/112108312/c8abf8dac123) (YouTube) 29. [Modeshapes and resonances of a vibrating Circular ring.](https://invisiblenetwork.ai/learn/nptel/112108312/6fadc202b286) (YouTube) 30. [Details of vibrating rings.](https://invisiblenetwork.ai/learn/nptel/112108312/40cf3063f0e4) (YouTube) 31. [Insights into vibrations of rings](https://invisiblenetwork.ai/learn/nptel/112108312/aca5fbfdd22b) (YouTube) 32. [Cylindrical shell equations of motion using Force balance.](https://invisiblenetwork.ai/learn/nptel/112108312/bd6d2198b23e) (YouTube) 33. [Cylindrical shell: Transverse equation of motion.](https://invisiblenetwork.ai/learn/nptel/112108312/6f6508d33bb4) (YouTube) 34. [Orthogonality of modeshapes.](https://invisiblenetwork.ai/learn/nptel/112108312/abd8df15e3e6) (YouTube) 35. [Orthogonality of Modes continued.](https://invisiblenetwork.ai/learn/nptel/112108312/4cd7ef71c38b) (YouTube) 36. [The Rayleigh Quotient.](https://invisiblenetwork.ai/learn/nptel/112108312/f639267246e4) (YouTube) 37. [Rayleigh Quotient Example: Simply-supported beam.](https://invisiblenetwork.ai/learn/nptel/112108312/2492e8f521ae) (YouTube) 38. [The Rayleigh Ritz method.](https://invisiblenetwork.ai/learn/nptel/112108312/7a87db97e3cd) (YouTube) 39. [The Rayleigh Ritz method applied to a Complicated system.](https://invisiblenetwork.ai/learn/nptel/112108312/7598b6a9d698) (YouTube) 40. [The Lagrange Multiplier method.](https://invisiblenetwork.ai/learn/nptel/112108312/ea7c357d74b6) (YouTube) 41. [The penalty method.](https://invisiblenetwork.ai/learn/nptel/112108312/5907cdc37b7e) (YouTube) 42. [Orthogonal polynomials of RB Bhat.](https://invisiblenetwork.ai/learn/nptel/112108312/71cc806b9556) (YouTube) 43. [Rayleigh Ritz paper by RB Bhat.](https://invisiblenetwork.ai/learn/nptel/112108312/bd14fc589884) (YouTube) 44. [Numerical examples of the Rayleigh Ritz method.](https://invisiblenetwork.ai/learn/nptel/112108312/0952880e2f14) (YouTube) 45. [Numerical examples of Rayleigh Ritz method And animations.](https://invisiblenetwork.ai/learn/nptel/112108312/5c77f87ae688) (YouTube) 46. [Raylegh Ritz applied to curved structures.](https://invisiblenetwork.ai/learn/nptel/112108312/66ca71fc4b22) (YouTube) 47. [Forced response of plates and shells.](https://invisiblenetwork.ai/learn/nptel/112108312/df65225d60ac) (YouTube) 48. [Forced response continued.](https://invisiblenetwork.ai/learn/nptel/112108312/f637ab9f513c) (YouTube) 49. [Simply-supported plate response to various forces.](https://invisiblenetwork.ai/learn/nptel/112108312/1069ef448063) (YouTube) 50. [Simply-supported plate response to various Forces continued.](https://invisiblenetwork.ai/learn/nptel/112108312/c47ab7228fe3) (YouTube) 51. [Simply-supported cylindrical shell response to a Point harmonic force.](https://invisiblenetwork.ai/learn/nptel/112108312/a5c5abef1d7c) (YouTube) 52. [Cylindrical shell response continued.](https://invisiblenetwork.ai/learn/nptel/112108312/478f34aa1f53) (YouTube) 53. [Cylindrical shell response continued.](https://invisiblenetwork.ai/learn/nptel/112108312/54d1ca7eb6ed) (YouTube) 54. [Cylindrical shell response to a traveling load using Only transverse modes.](https://invisiblenetwork.ai/learn/nptel/112108312/598485ae49a8) (YouTube) 55. [The Receptance method.](https://invisiblenetwork.ai/learn/nptel/112108312/0ed19546633c) (YouTube) 56. [The receptance method continued.](https://invisiblenetwork.ai/learn/nptel/112108312/f98640d2b607) (YouTube) 57. [Stiffening a cylindrical shell using rings.](https://invisiblenetwork.ai/learn/nptel/112108312/3efb0af39784) (YouTube) 58. [Stiffening of a cylindrical shell continued.](https://invisiblenetwork.ai/learn/nptel/112108312/60a7330f0d56) (YouTube) 59. [Damping in structures.](https://invisiblenetwork.ai/learn/nptel/112108312/e0b173007bd9) (YouTube) 60. [Loss factor and complex Young modulus.](https://invisiblenetwork.ai/learn/nptel/112108312/1752d3642fad) (YouTube)