Learnwith MYLARU INFRA

Foundations of structural motion · Model building

From Real Structure to Dynamic Model

Learn how to preserve important behaviour while simplifying a complex structure into a useful analytical model.

Approx. 32 min

Learning objectives

By the end of this lesson

  • Define a degree of freedom as an independent displacement needed to describe motion.
  • Map a real system to mass, stiffness, and damping components.
  • Distinguish a single-degree-of-freedom model from a multi-degree model.
  • Recognise the assumptions behind linear stiffness and viscous damping.

Before you calculate

What this means in the real world

01

What the formula is for

For the linear model used at this stage of the course, restoring force is proportional to deformation and acts toward the equilibrium position.

Fₛ = k u
03

What a wrong value can do

A wrong unit, sign, scale, boundary condition, or property can produce a believable number with the wrong physical meaning. It may understate demand, exaggerate it, or lead to the wrong failure check.

Definition

Idealization

The deliberate replacement of a real structural system with a simpler mathematical model that retains the behaviour needed for a specific analysis.

Why it mattersA useful model is simple enough to solve but detailed enough to represent the important mass, deformation, energy loss, and loading path.

Why engineers idealize

A real structure contains distributed mass, many deformable members, connections, and several energy-dissipation mechanisms. Dynamic analysis begins by retaining the behaviour that matters for the question and replacing the rest with a manageable mathematical model.

Formula

Linear elastic stiffness

Fₛ = k u

For the linear model used at this stage of the course, restoring force is proportional to deformation and acts toward the equilibrium position.

Fₛ
stiffness or restoring forceN
k
stiffnessN/m
u
displacement relative to equilibriumm

Model-building lab

Build an idealized model

Choose a familiar system and inspect what becomes mass, stiffness, damping, and the independent displacement.

MassReal system
m/\/\/cIdealized SDOF model
Mass, m
Roof and supported floor
Stiffness, k
Columns resisting lateral deformation
Damping, c
Energy dissipated by materials and connections
Degree of freedom
One horizontal displacement

The three model components

Mass represents resistance to acceleration. Stiffness represents the restoring action produced by deformation. Damping represents energy dissipation that causes vibration amplitudes to reduce with time. Together they form the basic mass-spring-damper model used throughout structural dynamics.

Formula

Linear viscous damping

Fᴅ = c u̇

Equivalent viscous damping represents energy dissipation with a force proportional to relative velocity and opposing motion.

Fᴅ
damping forceN
c
viscous damping coefficientN·s/m
u̇
relative velocitym/s

Editable formula question

Find the restoring force

Choose stiffness and displacement values, convert the displacement correctly, and calculate Fₛ.

Fₛ = ku
Substitute your current valuesFₛ = 30 × (15 ÷ 1000)Answer format: enter the numerical result only in kN. Example: 12, not “answer = 12”.
kN
Round only at the final step. The accepted tolerance for this exercise is ±0.01.

The displayed minimum, maximum, and textbook values define this learning exercise only. They are not universal design limits.

Editable formula question

Find the damping force

Choose an equivalent viscous damping coefficient and relative velocity, then calculate Fᴅ.

Fᴅ = c u̇
Substitute your current valuesFᴅ = 6 × 0.2Answer format: enter the numerical result only in kN. Example: 12, not “answer = 12”.
kN
Round only at the final step. The accepted tolerance for this exercise is ±0.01.

The displayed minimum, maximum, and textbook values define this learning exercise only. They are not universal design limits.