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Structural dynamics · seismic isolation

Why Isolation Changes Response

See how flexibility and damping reshape earthquake demand.

Approx. 32 min

Learning objectives

By the end of this lesson

  • Define seismic isolation in physical engineering terms.
  • Use isolated-system period with consistent quantities and units.
  • Change model inputs and explain the resulting trend.
  • Separate an educational model result from a code-based safety decision.

Before you calculate

What this means in the real world

01

What the formula is for

Reducing isolation stiffness lengthens period, while required displacement and stability checks become central.

Tᵢ = 2π√(M/Kᵢ)
02

Where an engineer uses it

Isolation concept for an essential facility: This application turns seismic isolation into a real modelling decision.

Separate isolation-layer movement from superstructure deformation and estimate displacement demand.

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

seismic isolation

A strategy that introduces a flexible, energy-dissipating layer to reduce motion and force transmitted into the superstructure.

Why it mattersIt provides the central modelling idea for why isolation changes response and connects observed motion to a solvable engineering representation.

Build the physical picture

See how flexibility and damping reshape earthquake demand. Start by identifying the system boundary, response coordinates, applied action, and the properties that store or dissipate energy. A useful model is the simplest one that preserves the behaviour needed for the engineering question.

Formula

Isolated-system period

Tᵢ = 2π√(M/Kᵢ)

Reducing isolation stiffness lengthens period, while required displacement and stability checks become central.

u
response displacement or displacement vectorm
t
times
ω
angular frequency where usedrad/s

Formula experiment

Explore seismic isolation

Change the available model inputs, watch the motion or force relationship, and describe the trend before reading the numerical result.

equilibrium
m
/\/\/\/\/

One full left-right cycle represents the calculated natural period.

Natural periodTₙ = 0.702 s
Natural frequencyfₙ = 1.424 Hz
Circular frequencyωₙ = 8.944 rad/s

Idealized undamped linear SDOF result. Changing mass or stiffness updates the model, not the safety of a real structure.

25

Real-world application

Isolation concept for an essential facility

This application turns seismic isolation into a real modelling decision.

Modelling move
Separate isolation-layer movement from superstructure deformation and estimate displacement demand.
Engineering question
Is there enough clearance and restoring capacity for the expected isolation movement?

Calculate, compare, interpret

Editable formula question

Experiment with period: Why Isolation Changes Response

Change mass and stiffness, predict the period, and check your result.

Tₙ = 2π√(m/k)
Substitute your current valuesTₙ = 2π√(1000 ÷ 40000)Answer format: enter the numerical result only in s. Example: 12, not “answer = 12”.
s
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

Compare a model demand with your entered criterion

Enter a demand and a comparison value chosen for this exercise, then interpret the ratio.

utilization indicator = model demand / entered criterion
Substitute your current valuesratio = 4 ÷ 5Answer format: enter the numerical result only (no unit for this dimensionless result). Example: 12, not “answer = 12”.
—
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.