Dynamics of structures

At the end of this learning unit, the student is able to :

Contribution of the course to the program objectives:

AA1.1, AA1.2, AA1.3, AA2.1, AA2.2, AA2.3, AA2.4, AA3.1, AA3.2, AA4.2, AA4.4

Specific learning outcomes of the course :

• At the end of the course, the student will be able to:
• Understand the field of application of different models: single-degree-of-freedom (SDoF) systems versus multi-degree of freedom (MDoF) systems, material and geometric linearity versus nonlinearity, static versus dynamic problems.
• Write the equations of motion and understand solution methods for SDoF and MDoF systems, both for linear and nonlinear problems.
• Characterize the dynamic properties of a SDoF system and compute its response under various loadings.
• Characterize the dynamic properties of a MDoF system and compute its response under various loadings.
• Characterize dynamically a system by the frequency response function, represent loading as a summation of harmonic components (Fourier transform), compute response to harmonic components (convolution in the frequency domain), transform sum of harmonic responses to time domain (inverse Fourier transform), understand consequences of sampling and aliasing errors.
• Understand principles of seismic modelling and analysis of frame structures accounting for material and geometric nonlinearity.
• Solve practical problems of different structures affected by critical vibrations (induced by people, machines, wind, traffic and construction activities, earthquakes) for serviceability and safety limit states.