1. Dynamic loading of structures. Differences between dynamic and static loading.
2. Dynamic analysis of single-degree-of-freedom (SDOF) systems. Equation of motion of SDOF systems subjected to dynamic loads and seismic excitations. Stiffness and damping of SDOF systems. Free vibration of SDOF systems. Forced vibration of SDOF systems. Generalized single-degree-of-freedom systems. Computer-based dynamic analysis of SDOF systems.
3. Dynamic analysis of multi-degree-of-freedom (MDOF) systems (structures). Equation of motion of MDOF systems (structures) subjected to dynamic loads and seismic excitations. Free vibration of MDOF systems. Eigenvalue problem. Natural frequencies and mode shapes. Methods for computing eigenvalues and mode shapes. Forced vibration of MDOF systems. Dynamic analysis of MDOF systems (structures) using either the mode superposition method or the step-by-step time integration method. Computer-based dynamic analysis of structures.

Learning Outcomes

The course aims to provide the necessary knowledge for understanding and computing the dynamic response of structures. This competence is critical for Civil Engineers involved in the analysis and design of structures subjected to dynamic loading, such as those induced by earthquakes, wind, or other time-varying actions.

Upon successful completion of the course, the student will be able to:

• Distinguish between static and dynamic loading.
• Identify the essential characteristics of a structural dynamics problem (dynamic loads, structural modeling, mass, damping, stiffness, and response).
• Interpret the modeling of damping in structures using viscous damping formulations.
• Formulate the equations of motion of a single-degree-of-freedom system subjected to dynamic loads and seismic excitations.
• Analyze the free vibration response of a single-degree-of-freedom system (undamped and damped).
• Determine the dynamic response of a single-degree-of-freedom system subjected to harmonic or general dynamic loading, taking into account the effects of viscous damping.
• Use free and open-source software for the computer-based dynamic analysis of single-degree-of-freedom systems.
• Interpret the formulation of equations of motion for simple and complex structural models (single-degree-of-freedom, generalized, and multi-degree-of-freedom systems) subjected to dynamic loads and seismic excitations, and apply appropriate solution methods.
• Formulate the equations of motion of a multi-degree-of-freedom system (structure) subjected to dynamic loads and seismic excitations by first computing the corresponding mass, damping, and stiffness matrices.
• Compute the natural frequencies and mode shapes of a multi-degree-of-freedom system (structure).
• Determine the dynamic response of multi-degree-of-freedom systems (structures) using either the mode superposition method or step-by-step time integration of the equations of motion.
• Use free and open-source software for the computer-based dynamic analysis of structures.
• Analyze the dynamic response of structures subjected to various types of excitation, such as seismic loading, wind loading, and impact loading associated with natural hazards.