Offshore and civil structures are exposed to loads that vary in time, such as waves, wind, earthquakes, machinery and impacts, and their response can be dramatically amplified near resonance. This structural dynamics course for offshore and civil structural engineers develops the analysis of dynamic loads, discrete and continuous vibration systems, damping, modal methods and wave dynamics. It starts with modelling structures for dynamics and reviewing single-degree-of-freedom response, then moves to multi-degree-of-freedom systems built using displacement and force methods, the eigenvalue problem, mode shapes and orthogonality, forced response and modal superposition, damping and the Rayleigh method. Continuous systems, including bending beams, bars, cables and shear beams, are then analysed. The course finishes with practical dynamic loads from wind, waves and earthquakes, physical damping mechanisms, wave motion in strings and rods and pile-soil interaction with beams on elastic foundations.
Course at a glance: Duration 20 hours · Self-paced online · Level: Advanced · 14 sections, 38 lessons, a 167-page downloadable course book
What you will learn
- Classify dynamic load types and choose appropriate structural models for dynamic analysis.
- Analyse single-degree-of-freedom response, including resonance, damping and impulse response.
- Assemble multi-degree-of-freedom equations of motion using displacement and force methods.
- Solve the eigenvalue problem and use mode shapes, orthogonality and modal superposition.
- Analyse damped systems and estimate natural frequencies with the Rayleigh method.
- Derive and apply governing equations for vibrating beams, bars, cables and shear beams.
- Explain damping mechanisms, wave propagation, reflection and pile-soil interaction.
Inside the course: a high-level summary, section by section.
Modelling structures for dynamics
The course begins with the choice of model. Single-degree-of-freedom models capture the essence of vibration, resonance and damping in a controlled setting. Multi-degree-of-freedom lumped models represent real structural assemblies such as towers, foundations and machine supports, and are often built from finite element idealisations that lead naturally to matrix equations of motion. Continuous-system and wave-propagation models are needed when the distribution of mass and stiffness, or the travel of stress waves, matters. Dynamic load types, including harmonic, periodic, impulsive and random loads, are classified to help select an appropriate model.
Single-degree-of-freedom response
The single-degree-of-freedom review covers free vibration, natural frequency, damping ratio and critical damping, and the forced response to harmonic loading, including the dynamic amplification factor and phase lag. The impulse response and the Duhamel integral allow the response to arbitrary loading to be computed, and the review also introduces vibration isolation and tuned mass absorbers, which can reduce vibration of a primary system at a specific frequency.
Multi-degree-of-freedom systems
The displacement method assembles stiffness matrices by imposing unit displacements and reading the resulting forces, while the force method uses unit loads to build a flexibility matrix, which can be inverted to obtain stiffness. Both lead to finite element assembly. The eigenvalue problem yields natural frequencies and mode shapes, and mode orthogonality with respect to mass and stiffness allows the coupled equations to be uncoupled.
Forced response of multi-degree-of-freedom systems is analysed directly and by modal superposition, which represents the response as a combination of modal contributions, often requiring only a few modes. Damped systems are treated using proportional damping and modal damping ratios. The Rayleigh method provides a quick and often accurate estimate of the fundamental frequency using an assumed deflected shape and energy principles.
Continuous systems
Bending beams are governed by a fourth-order partial differential equation, and the course derives their natural frequencies and mode shapes for different boundary conditions. Bars in axial vibration, taut cables and shear beams are governed by second-order wave equations, and the Rayleigh method is extended to continuous systems. These models are directly relevant to piles, towers, risers, tethers and tall buildings.
Dynamic loads in practice
Load types in practice are reviewed, from machinery and impact loads to environmental loading. Wind loads include mean and fluctuating components, and gusts can excite flexible structures. Wave loads drive the response of offshore platforms, and seismic loads require response spectrum or time-history methods. The course explains how each is characterised and how it is applied in dynamic analysis.
Damping mechanisms
Damping determines the peak response at resonance, yet it is often the most uncertain parameter. Physical damping mechanisms include material hysteresis, friction at joints, radiation of energy into soil or water and hydrodynamic drag. Equivalent viscous damping provides a practical way to represent these mechanisms in linear analysis, and the course explains how damping is estimated from tests and measurements.
Wave motion and pile-soil interaction
The wave equation and d’Alembert’s solution describe how disturbances travel along strings and rods. Reflection and transmission at boundaries and changes of section are explained, which is important for pile driving and impact problems. Dispersion and pile-soil waves show how wave propagation in piles is affected by surrounding soil, and beams on elastic foundations model piles and pipelines supported by soil, giving insight into load distribution and dynamic behaviour.
How the topics fit together
The course moves deliberately from simple to complex. The single-degree-of-freedom system introduces the vocabulary of natural frequency, damping and amplification. Matrix methods extend these concepts to real assemblies, modal analysis provides an efficient way to compute response, continuous models capture distributed systems and wave methods address rapid transient loading. At each stage, the emphasis is on choosing the simplest model that captures the behaviour of interest, and on understanding the assumptions behind it.
Why this matters in practice
Dynamic effects govern the design of offshore wind turbine foundations, jackets, risers, bridges, tall buildings and machinery supports. Engineers who understand natural frequencies, modal response and damping can avoid resonance, assess fatigue, interpret vibration measurements and check results from finite element programs with confidence. As offshore wind turbines grow larger and more flexible, and as civil structures become lighter and longer, the margin between natural frequencies and excitation frequencies shrinks, making a sound grasp of structural dynamics more important than ever. The course also prepares engineers to discuss dynamic behaviour credibly with specialists in geotechnics, hydrodynamics and wind engineering, whose inputs all feed into a dynamic analysis.
Key takeaways
You leave able to choose suitable dynamic models, analyse single- and multi-degree-of-freedom systems, apply modal superposition and the Rayleigh method, analyse continuous systems, characterise dynamic loads and damping and understand wave propagation and pile-soil interaction.
How you study
The course is delivered fully online and is self-paced, so you can fit roughly 20 hours of study around professional commitments. Lessons combine clear explanation with examples, diagrams and short interactive checks, and the main sections end with graded quizzes (12 in total) so you can confirm you can apply each method before moving on. A 167-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Introduction to Dynamic Loads and Structural Response: Dynamic Loads and Inertia; Modelling Structures for Dynamics
- SDOF Review and Aeroelastic Instabilities: SDOF Response Review; 2DOF and Aeroelastic Instability
- Equations of Motion for N-DOF Systems: Displacement Method; Force Method and FE Assembly
- Free Vibration of N-DOF Systems: Eigenvalue Problem; Modes and Orthogonality
- Forced Vibration and Modal Analysis: Forced Response of N-DOF Systems; Modal Superposition
- Damped N-DOF Systems and Rayleigh Method: Damped N-DOF Response; Rayleigh Method
- Continuous Systems I – Bending Beams: Beam Governing Equation; Beam Modes and Frequencies
- Continuous Systems II – Bars, Cables, Shear Beams: Bars, Cables and Shear Beams; Rayleigh for Continuous Systems
- Dynamic Loads from Wind, Waves and Earthquakes: Load Types in Practice; Wind, Waves and Seismic Loads
- Damping Mechanisms in Structures: Physical Damping Mechanisms; Equivalent Viscous Damping
- Wave Motion in Strings and Rods: Wave Equation and D’Alembert; Reflection and Transmission
- Pile-Soil Interaction and Elastic Foundations: Dispersion and Pile-Soil Waves; Beams on Elastic Foundation
- Summary: Key Takeaways
Who this course is for
This course is for engineering graduates and practising offshore, civil and structural engineers who analyse structures under dynamic loads. The course assumes an engineering degree or equivalent experience, with prior knowledge of structural mechanics, linear algebra and ordinary differential equations.
Frequently asked questions
How long does Structural Dynamics take?
The course is designed for about 20 hours of study. It is self-paced and fully online, so you can spread it over a few weeks or complete it more quickly.
What is covered?
The course is organised into 14 sections with 38 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 167-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (12 in total, with a pass mark of 80%). The quizzes test understanding of the concepts and methods explained in the lessons rather than memorisation, and you can review the relevant lessons before attempting them.
Can I record this study for my own professional development?
Yes. The course notebook includes a self-assessment of the course objectives before and after study, a reflection page and a learning log, which you can use to keep your own record of professional development.
Level: Advanced
Duration: 20 hours
Related courses: D05 – Offshore Hydromechanics; D07 – Safety in Offshore Engineering; C06 – FEM Masterclass for Ship Structures; A13 – Naval Architecture and Ship Production Technology (Part 4 of 4)
Enrol
Study at your own pace and work through the full course material, worked examples and section quizzes. Enrol in D06 – Structural Dynamics →
Recent Comments