Free vibration of two and three degrees of freedom systems. Analytical solution of natural frequencies and normal modes. Forced vibration of two degrees of freedom systems. Steady-state amplitudes. Effects of damping on amplitudes and phase angles
Coupling of modes e.g. between translation and rotation.
Vibration Suppression and control, use of transmissibilty equations
Undamped vibration absorber. Basic principle of operation. Isolated frequencies; system frequencies; applications to machines and structures.
Use of Lagrange’s Equations in the derivation of the equations of motion of dynamic systems.
Rayleigh’s Method. Evaluation of strain energy and kinetic energy. Choice of shape function. Accuracy of solution.
Iterative Methods. Matrix methods; Flexibility and Stiffness matrices, choice of initial mode shape, convergence of the iteration.
Continuous Systems. Derivations of equations of motion for axial vibration of a heavy bar or rod; torsional vibration of a heavy shaft; transverse vibration of a heavy beam. Boundary conditions, free and forced vibration, normal modes.
Modal Analysis: Modal analysis of multi-degree of freedom undamped systems. Modal matrices; mass and stiffness. Mode participation factor in the overall system response.
Flow induced vibration. Free and forced vibration response of a one degree of freedom model. Galloping oscillations and vortex induced oscillations. Strouhal Number.
Motion in 3-dimensions. Moments and products of inertia. Principal moments of inertia; principal axis.
Derivation of Euler's Equations of motion of a rigid body. Application to rotors, discs, etc. Evaluation of the dynamic moment exerted by a rotor on its bearings.
