## Dynamics of Structures

### Module aims

• To provide an in-depth understanding of the most basic principles of structural dynamics and opportunity to practice their application to the modelling, design and assessment of simple structures subjected to the most prevalent types of dynamic actions.

### Learning outcomes

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

• Understand the requirements for modelling structures subjected to dynamic actions.
• Appreciate the validity of modelling structures as single or multiple degree-of-freedom systems.
• Understand the role of damping and its influence on the structural response.
• Identify the possibility of common civil structures to be influenced by resonance and limit its effects.
• Solve the equation of motion for a variety of common cases.
• Appreciate differences among modelling assumptions regarding dynamic excitation and appreciate their limitations.
• Determine the response of linear structural systems to dynamic loadings.
• Understand how the principles of dynamic systems can be applied to structural analysis.
• Appreciate how real-world systems may be modelled as equivalent single or multi-degree of systems.
• Develop an understanding of modelling approaches to generic dynamic systems (not necessarily constrained to structural applications).
• Represent signals in both the time and frequency domains.

### Module syllabus

The course is divided in three distinct units:

·         Single Degree-of-Freedom Systems.

§     Formulation of the Equation of Motion:  Newton’s Second Law and D’Alembert’s principle. Inertia, damping and stiffness. (CM)

§     Free vibrations. (CM)

§     Forced vibration and structural response to harmonic excitation. Dynamic magnification factor. Response spectra. (CM)

·         Experimental dynamics:

§     Frequency representation of temporal signals. The Fourier Transform and its applications. Sampling and instrumentation. (CM)

·         Multiple Degree-of-Freedom Systems:

§     Formulation of the equations of motion in both a stiffness and flexibility format. (LL)

§     Use of orthogonality to uncouple equations of motion to format series of SDOF models using generalised co-ordinates. (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. (LL)

 No. Topic Staff 01 Dynamic modelling CM 02 Free vibrations CM 03 Forced harmonic vibrations CM 04 The Fourier transform and its application CM 05 Dynamic response modification of simple structures CM 06 Experimental dynamics and Coursework session CM 07 Introduction and revision of MDOF concepts. Free vibrations of lumped mass beam and frame systems LL 08 Orthogonality and uncoupling of equations of motion LL 09 Introduction to blast loads, Modal analysis of pulse loaded structures and Pressure Impulse diagrams LL 10 Use of Modal analysis to deal with ground motions on MDOF systems LL

### Teaching methods

The course has lectures and supporting tutorials.

### Assessments

Assessment information will be provided separately.

### Module leaders

Dr Christian Malaga Chuquitaype