Structural Engineering

Dynamics of Structures

An original, experiment-led learning path through structural motion, vibration, resonance, earthquake response, and isolation.

Intermediate to advanced7 chapter available

Learning path

Chapters

Develop physical intuition for moving structures and translate real systems into solvable models.

When Structures Begin to Move
Explore how loading speed, mass, stiffness, and time change structural behaviour.
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From Real Structure to Dynamic Model
Choose meaningful degrees of freedom and create a mass-spring-damper representation.
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The Forces That Govern Motion
Connect displacement, velocity, and acceleration to restoring, damping, and inertia forces.
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Building the Motion Equation
Assemble a consistent time-dependent force balance for a single response coordinate.
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Study how a disturbed structure moves on its own and how real systems gradually lose motion.

Motion After Release
Connect initial displacement and velocity to natural oscillation.
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How Vibration Fades
See how damping changes amplitude, frequency, and return to rest.
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Measuring Damping from Response
Estimate damping from observed decay and frequency-response behaviour.
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Understand what happens when repeated loading interacts with a structure's preferred motion.

Response to Repeating Loads
Build the undamped response to sinusoidal excitation.
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Damping Under Repeated Loading
Compare transient and steady response when energy is dissipated.
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Reading Resonance Curves
Interpret amplification across different forcing frequencies.
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How Motion and Force Travel
Track how vibration passes through supports and isolation elements.
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Energy In, Energy Out
Relate work input, stored energy, and dissipated energy.
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Move beyond repeating loads to impacts, pulses, arbitrary histories, and earthquake response.

Response to a Brief Impulse
Use an impulse response as a building block for general loading.
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Sudden and Gradual Loading
Compare step, ramp, and finite-duration actions.
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Pulse Shape and Duration
Explore how impulse area and duration affect peak response.
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Computing Response Through Time
Advance displacement and velocity when a closed-form solution is unavailable.
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Reading a Response Spectrum
Relate oscillator period and damping to peak earthquake response.
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Extend single-coordinate intuition to structures with distributed properties and interacting motions.

From Continuous Structure to Generalized Coordinate
Approximate a distributed system using a selected deformation shape.
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Building a Lumped-Mass Model
Place mass and stiffness where they preserve the important motion.
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Coupled Equations of Motion
Form mass, damping, and stiffness matrices for multiple coordinates.
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Modelling Coupled Structures
Apply equilibrium and influence-based modelling to structural examples.
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Decompose complex motion into natural patterns and combine their contributions to structural demand.

Natural Shapes of Motion
Find the frequencies and deformation patterns a coupled system prefers.
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Combining Modal Motion
Construct free response from individual modal contributions.
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Damping Across Multiple Modes
Represent energy loss in a coupled structural model.
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Coupled Response to Applied Forces
Transform force patterns into modal coordinates and recover physical response.
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Modal Superposition in Practice
Use a selected set of modes to efficiently estimate response.
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Combining Peak Seismic Effects
Estimate structural demand when modal peaks do not occur simultaneously.
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Use dynamic principles to reduce the transfer of damaging motion into a structure.

Why Isolation Changes Response
See how flexibility and damping reshape earthquake demand.
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Modelling an Isolated Structure
Examine the coupled motion of an isolation layer and superstructure.
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