Learn · Vibrations of Plates and Shells
Lecture 46 of 60Week 10 Forced response of plates and shells using modal Summation
Raylegh Ritz applied to curved structures.
Prof. Venkata R. Sonti · IISc Bangalore
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All the lectures
- Introduction to differential geometry.
- Properties of surfaces:First fundamental form.
- Properties of surfaces: Second fundamental form.
- Surfaces of revolution.
- Gauss Codazzi relations.
- Gauss Codazzi contd.
- Differential element length in a thin shell.
- Strain of a differential element.
- Explicit strain expressions.
- Love simplifications and inconsistencies Of the theory.
- Euler Bernoulli Beam equation using the Hamilton’s Law.
- Euler Bernoulli Beam and Hamilton’s Law contd.
- Beta definition, force and moment resultants.
- Hamilton’s Law for a general shell.
- The Hamilton’s law continued.
- Final Dynamical Equations and boundary conditions.
- Physics of each term in the dynamic equations.
- Physics of each term continued.
- The sixth equation of motion.
- The sixth equation of motion contd.
- Equations of motion for a rectangular plate using Hamilton’s law.
- Equations of motion for a rectangular Plate continued.
- Rectangular plate boundary conditions.
- Rectangular plate equation using force balance.
- Modeshapes and resonances of a vibrating beam.
- Modeshapes and resonances of a vibrating Rectangular plate.
- Modeshapes and resonances of a vibrating Circular plate.
- Vibrating circular plate continued.
- Modeshapes and resonances of a vibrating Circular ring.
- Details of vibrating rings.
- Insights into vibrations of rings
- Cylindrical shell equations of motion using Force balance.
- Cylindrical shell: Transverse equation of motion.
- Orthogonality of modeshapes.
- Orthogonality of Modes continued.
- The Rayleigh Quotient.
- Rayleigh Quotient Example: Simply-supported beam.
- The Rayleigh Ritz method.
- The Rayleigh Ritz method applied to a Complicated system.
- The Lagrange Multiplier method.
- The penalty method.
- Orthogonal polynomials of RB Bhat.
- Rayleigh Ritz paper by RB Bhat.
- Numerical examples of the Rayleigh Ritz method.
- Numerical examples of Rayleigh Ritz method And animations.
- Raylegh Ritz applied to curved structures.
- Forced response of plates and shells.
- Forced response continued.
- Simply-supported plate response to various forces.
- Simply-supported plate response to various Forces continued.
- Simply-supported cylindrical shell response to a Point harmonic force.
- Cylindrical shell response continued.
- Cylindrical shell response continued.
- Cylindrical shell response to a traveling load using Only transverse modes.
- The Receptance method.
- The receptance method continued.
- Stiffening a cylindrical shell using rings.
- Stiffening of a cylindrical shell continued.
- Damping in structures.
- Loss factor and complex Young modulus.