NOC:Vibrations of Plates and Shells

Lecture 1 - Introduction to differential geometry

Lecture 2 - Properties of surfaces: First fundamental form

Lecture 3 - Properties of surfaces: Second fundamental form

Lecture 4 - Surfaces of revolution

Lecture 5 - Gauss Codazzi relations

Lecture 6 - Gauss Codazzi (Continued...)

Lecture 7 - Differential element length in a thin shell

Lecture 8 - Strain of a differential element

Lecture 9 - Explicit strain expressions

Lecture 10 - Love simplifications and inconsistencies Of the theory

Lecture 11 - Euler Bernoulli Beam equation using the Hamilton's Law

Lecture 12 - Euler Bernoulli Beam and Hamilton's Law (Continued...)

Lecture 13 - Beta definition, force and moment resultants

Lecture 14 - Hamilton's Law for a general shell

Lecture 15 - The Hamilton's law (Continued...)

Lecture 16 - Final Dynamical Equations and boundary conditions

Lecture 17 - Physics of each term in the dynamic equations

Lecture 18 - Physics of each term (Continued...)

Lecture 19 - The sixth equation of motion

Lecture 20 - The sixth equation of motion (Continued...)

Lecture 21 - Equations of motion for a rectangular plate using Hamilton's law

Lecture 22 - Equations of motion for a rectangular Plate (Continued...)

Lecture 23 - Rectangular plate boundary conditions

Lecture 24 - Rectangular plate equation using force balance

Lecture 25 - Modeshapes and resonances of a vibrating beam

Lecture 26 - Modeshapes and resonances of a vibrating Rectangular plate

Lecture 27 - Modeshapes and resonances of a vibrating Circular plate

Lecture 28 - Vibrating circular plate (Continued...)

Lecture 29 - Modeshapes and resonances of a vibrating Circular ring

Lecture 30 - Details of vibrating rings

Lecture 31 - Insights into vibrations of ring

Lecture 32 - Cylindrical shell equations of motion using Force balance

Lecture 33 - Cylindrical shell: Transverse equation of motion

Lecture 34 - Orthogonality of modeshapes

Lecture 35 - Orthogonality of Modes (Continued...)

Lecture 36 - The Rayleigh Quotient

Lecture 37 - Rayleigh Quotient Example: Simply-supported beam

Lecture 38 - The Rayleigh Ritz method

Lecture 39 - The Rayleigh Ritz method applied to a Complicated system

Lecture 40 - The Lagrange Multiplier method

Lecture 41 - The penalty method

Lecture 42 - Orthogonal polynomials of RB Bhat

Lecture 43 - Rayleigh Ritz paper by RB Bhat

Lecture 44 - Numerical examples of the Rayleigh Ritz method

Lecture 45 - Numerical examples of Rayleigh Ritz method And animations

Lecture 46 - Raylegh Ritz applied to curved structures

Lecture 47 - Forced response of plates and shells

Lecture 48 - Forced response (Continued...)

Lecture 49 - Simply-supported plate response to various forces

Lecture 50 - Simply-supported plate response to various Forces (Continued...)

Lecture 51 - Simply-supported cylindrical shell response to a Point harmonic force

Lecture 52 - Cylindrical shell response (Continued...)

Lecture 53 - Cylindrical shell response (Continued...)

Lecture 54 - Cylindrical shell response to a traveling load using Only transverse modes

Lecture 55 - The Receptance method

Lecture 56 - The receptance method (Continued...)

Lecture 57 - Stiffening a cylindrical shell using rings

Lecture 58 - Stiffening of a cylindrical shell (Continued...)

Lecture 59 - Damping in structures

Lecture 60 - Loss factor and Complex Young modulus