1. Formulation of the equation of motion for viscously damped SDOF systems for (a) externally applied loads and (b) support excitation (e.g. earthquake problem).
2. Free vibrations of viscously damped SDOF systems; effects of damping: underdamped, critically damped and overdamped systems.
3. Free vibrations of SDOF systems with COULOMB friction.
4. Forced vibration response of viscously damped SDOF systems to harmonic loading; analytic solution. Applications: (a) measurement of damping of structures; (b) vibration isolation; (c) vibration measurement instruments.
5. Response of SDOF systems to periodic loadings.
6. Energy dissipated by damping: viscous damping; equivalent viscous damping; rate independent damping; complex stiffness.
7. Forced vibration response of SDOF systems to pulse type loadings; analytic solutions. Introduction of the concept of shock spectrum.
8. Forced vibration response of SDOF systems to general type of loading: DUHAMEL’s (convolution) integral.
9. Numerical evaluation of the dynamic response of a SDOF system; time-stepping methods.
10. Response & design spectra for seismic excitation.
11. Discrete parameter MDOF systems: Formulation of the equations of motion [reduction of (static) Degrees of Freedom (DOF); static & dynamic condensation]; system matrices [mass, stiffness, and damping matrices, influence vector (for support excitation problems)].
12. MDOF systems: Free vibrations of undamped MDOF systems: the generalized eigenvalue problem: natural frequencies and natural modes of vibration. Fundamental properties of the eigenvalues and eigenvectors. Methods for obtaining estimates of natural frequencies (e.g. RAYLEIGH quotient). Free vibrations of MDOF systems with classical damping (RAYLEIGH damping & extended RAYLEIGH damping).
MDOF systems: Forced vibrations. Modal response analysis; modal contributions (modal contribution factor; dynamic response factor).
|LANGUAGE OF INSTRUCTION and EXAMINATIONS||
By the end of the course students should have mastered the course content described below and, in particular, the following points:
1. The students should be able to setup the equations of motion for simple or complex mechanical models of structures.
2. The students must be able to proceed to solve analytically (wherever this is feasible) or numerically the equations of motion and thus compute the response of the structural models.
3. The students must have acquired a basic understanding of the concept of response spectrum and its usefulness in evaluating the response of MDOF systems, in particular for seismic excitation.