## Structural Dynamics

### Module aims

• To provide students with a general grounding in the basic concepts and principles of dynamics as applied to structural engineering problems.
• To introduce the students to the most common dynamic phenomena in structural engineering and train them in the application of appropriate idealization approaches, their analytical formulation and their mathematical solution.

### Learning outcomes

On successfully completing this course unit, students will be able to:

• Analyse and interpret the dynamic response of conventional structural systems and gain insight into their time-dependent nature.
• Formulate appropriate models of simple structural systems under dynamic conditions and apply them to the solution of engineering problems.
• Estimate the natural frequencies and vibration modes of elastic and multiple degree of freedom systems.
• Evaluate maximum values of significant structural response parameters for systems subjected to the most usual forms of dynamic excitation.
• Appreciate the phenomena involved in the loss of linearity in the dynamic response of simple structures as well as the engineering approaches employed to model them appreciating their limitations.

### Module syllabus

• Dynamic loads and types. Introduction to the Fourier Transform and its mathematical background. Discrete signals and the Discrete Fourier Transform. Code representation of dynamic loads. (CM)
• Single-degree-of-freedom models. Formulation of the Equation of Motion:  Newton’s second law and D’Alembert’s principle. Impulse response and transfer functions. Damping and stiffness of simple structural systems. (CM)
• Undamped free vibrations. Damped free vibrations. Response to transient loads: impulse and irregular dynamic loads. Duhamel’s integral. (CM)
• Forced vibration response to harmonic excitation. Dynamic magnification factor and response spectra. (CM)
• Introduction to non-linear dynamics of single-degree-of-freedom systems. Dynamic characteristics of non-linear systems. Friction damping. Simplified approximations and ductility-reduced spectra. (CM)
• Multi-degree-of-freedom models. Formulate equations of motion in both a stiffness and flexibility format and determine natural frequencies. (LL)
• Use orthogonality to uncouple equations of motion to format series of SDOF models using generalised coordinates. (LL)
• Use of response spectra to solve MDOF systems subjected to either pulse loads or a ground motion. (LL)
• Use conservation of energy to formulate pressure impulse diagrams for idealised systems subjected to blast loads. (LL)
 No. Topic Staff 01 Dynamic loads. Time and frequency domains. CM 02 Equation of motion and modelling of structural systems. CM 03 Free vibration and response to transient loads. CM 04 Forced vibration response to harmonic excitation. CM 05 Introduction to non-linear dynamics of simple systems. CM 06 Introduction and revision of MDOF concepts. Free vibrations of lumped mass beam and frame systems. LL 07 Forced vibrations of MDOF systems and modal superposition. LL 08 Vibration caused by motion of supports. Earthquake response spectra. LL 09 Introduction to blast loads. Modal analysis of pulse loaded structures. LL 10 Development and use of Pressure Impulse diagrams for blast loaded problems. LL

### Teaching methods

A combination of lectures and tutorials.

### Assessments

Assessment will be by a written examination.