Introduction to Structural Dynamics
- Continuous systems vs. discrete systems
- Lumped parameter systems (notions of mass, stiffness and damping)
- Mathematical models of single degree of freedom systems
- Derivation of the equations of motion by the Newton’s law and D’Alembert principle
- Derivation of the equations of motion by the of the Principle of virtual displacements
Single Degree of Freedom (Sdof) Systems
Free vibrations
- Undamped vibrations
- Viscous damped vibrations
- Stability of motion
- Notions of frequency, period, amplitude and phase of the motion
Harmonic excitation
- Response of undamped Sdof systems to harmonic excitations
- Response of viscous damped Sdof systems to harmonic excitations
- Steady state response, resonance and beat phenomenon
- Equivalent viscous damping
Periodic excitation and harmonic analysis
- Periodic functions and Fourier series
- Fundamental frequency and Fourier coefficients
- Spectrum of a periodic function
- Evaluation of the steady state response of dynamic systems
General excitations
- Impulse, momentum and impulse response function
- Convolution integral method (Duhamel integral)
- Response of a viscous damped system to rectangular pulses and ramp loadings
Elements of numerical integration of the equations of motion
- Central difference method
- Newmark’s method
- Stability and accuracy of the numerical solution
Vibrations isolation: Force Transmissibility and Base motion
Elements of experimental dynamics
- Dynamic excitation devices
- Vibration measuring instruments: accelerometer
- Identification of natural frequency and damping factor

Multiple Degrees of Freedom (Mdof) Systems
2-dof systems
- Mathematical models of 2dof systems
- Matrix form of the equations of motion
- Free and forced (harmonic) vibrations
- Natural frequencies and mode shapes
- Principal coordinates and Modal analysis
- Vibration absorber
M-dof systems
- Generalization of 2-dof systems solutions
- Orthogonality of mode shapes and method of modes superpostion
- Participation coefficient, modal mass and modal stiffness
- Forced vibrations and base motion
- Rayleigh damping
Elements of vibration of continuous systems
- Derivation of the equations of motion by the Newton’s laws
- Axial, shear and torsional vibrations of beams
- Transverse vibrations of beams