Dynamics of structures

Teacher(s)

Saraiva Esteves Pacheco De Almeida João;

Language

English

Prerequisites

Background on strength of materials, structural mechanics and structural analysis (e.g. courses LGCIV1031, LGCIV1022 and LGCIV1023).

Main themes

See "content"

Aims

At the end of this learning unit, the student is able to :
1	Contribution of the course to the program objectives: AA 1.1, AA 1.2, et AA 1.3 At the end of this learning unit, the student is 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. - Model and solve practical problems of different structures affected by vibrations (induced by earthquakes, machines, people, wind, traffic and construction activities) for serviceability and safety limit states

Content

• Linear single­-degree­-of-­freedom (SDoF) systems: free vibration, damping values in structures, harmonic loading, evaluation of viscous damping and frequency, response to unit impulse and other forces, methods of solution, force transmission, response to ground motion, and vibration isolation.
• Nonlinear SDoF systems: numerical time-domain integration (central difference, constant average acceleration and linear acceleration, Newmark), classification, stability, computational error, algorithmic damping, inelastic response (bilinear system).
• Linear multi­degree­of­freedom (MDoF) systems: free vibration of undamped systems (natural vibration frequencies and modes, modal and spectral matrices, orthogonality of mode shapes, normalisation, modal expansion), free vibration of damped systems, damping and energy dissipation in linear (and nonlinear) analyses, damping models, modal analysis, displacement response and element forces, restated form, modal contribution factors, modal responses and required number of modes, influence of dynamic response factor, applications (including ground motion).
• Nonlinear multi­degree­of­freedom (MDoF) systems: numerical time-domain integration, applications.
• Frequency-domain method of response analysis.

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Lectures based on course slides and exercise solving with student participation. Project.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Assignments (35%), project (40%), and written evaluation (25%).
NOTE: These instructions take into account a “green” or "yellow" Covid scenario at UCLouvain. Modifications can be made in case of “orange” or “red” scenario, or restrictions in classroom capacities.

Other information

• Use of Matlab / Python scripts and structural analysis program.

Online resources

Available in Moodle.

Bibliography

• « Dynamics of structures: Theory and Applications to Earthquake Engineering », Anil K. Chopra, Prentice Hall, 2012.
• « Dynamics of structures », Ray W. Clough and Joseph Penzien, Computers & Structures, 2003.
• « Vibration problems in structures: Practical guidelines », Hugo Bachmann et al., Birkhauser Verlag, 1995.

Faculty or entity

GC