Webinar 43 – Two-degree-of-freedom System, Two-stage Isolation


webinar_43_two_dof_systems.pptx & Alternate Link

Audio/Visual File:

NESC Academy Two-stage Isolation – Recommend viewing in Firefox with Sliverlight Plugin

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Matlab script: Vibrationdata Signal Analysis Package

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Reference Paper:

two_stage_isolation.pdf & Alternate Link

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See also:  Two-degree-of-freedom Systems

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– Tom Irvine

Isolator Photo Gallery


SCUD-B Typical Avionics Component

The avionics shelves were made from hardwood. The wooden fibers may provide better damping then, say, an aluminum shelf. A possible disadvantage of wood is that the shelf would be unable to serve as an electrical or thermal ground plane.

The bushings are made from some type of rubber or elastomeric compound.

The bushings provide damping, but their main benefits are:

1. To render the isolated system as a single-degree-of-freedom system
2. To lower the natural frequency of the system

The isolators thus attenuate the shock and vibration energy which flows from the instrument shelf into the avionics component.

See also: Vibrationdata May 2010 Newsletter, Scud-B Missile Design



NASA/JPL, Mars Science Laboratory

Sensor Support Electronics mounted on wire rope isolators



European Space Agency Inertial Measurement Unit (IMU) mounted to outer bracket via four black conical isolators, vibration test



Automobiles usually have a fundamental spring-mass frequency of 1 to 2.5 Hz depending on the model type.  The shock absorbers provide about 33% viscous damping.







Titan II Missile Silo, Launch Control Room

The control room is mounted underground via huge isolation springs. A typical spring is shown in the background. The purpose is to isolate the control room from mechanical shock and vibration in the event of a nuclear strike above the launch site. The springs allow 18 inches of relative displacement. The control room could thus carry out a retaliatory strike, as ordered by the U.S. president.

This site is located south of Tucson, Arizona. It has been decommissioned and is now a museum.

– Tom Irvine




Ariane 5 MLP Damper for Reducing Wind Response



The USS Alabama World War II Battleship.
Photos Courtesy of Robert Towner.


An isolation spring inside the ship is shown in the center of the photo.


Isolation springs for the ship’s piping system.




RESTON-SA shock absorber for seismic isolation of Taipei City Hospital.  Link



Spring-Mass System Natural Frequency


Here is a Matlab GUI script for calculating the natural frequency of a spring-mass system:  sdof_fn.zip

It can also be used to select total isolator stiffness for a given mass and intended natural frequency.

It is version 1.1, so please let me know if there are any bugs or errors.

Thank you,
Tom Irvine

Transmissibility of a Three-Parameter Isolation System

I recently came across a vendor that offers an isolator design using the concept in the figure above.

The system is also referred to as the standard-linear solid model (SLS) by Zener, and is used as a simplified model for structural damping.    It is a special case of the Maxwell-Weichert model.

Here is a paper showing the derivation of the transmissibility function:  three_parameter_isolation.pdf

Matlab script:  three_parameter_isolation.m

The three parameter isolation system is also included in the GUI package at:  Vibrationdata Matlab Signal Analysis & Structural Dynamics Package

It can be accessed via

>> vibrationdata > Structural Dynamics > Spring-Mass Systems > Two DOF >
Three Parameter Isolation System

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See also:

Avionics Box Isolation

Damping, Isolation & Vibration Absorbers Page

More later…

– Tom Irvine

Avionics Box Isolation

I have written some tutorials on avionics component isolation which may be downloaded at:



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The Matlab GUI scripts are given in the GUI package at:  Vibrationdata Matlab GUI Package

The function is accessed via:

Miscellaneous > Structural Dynamics > Spring-Mass Systems > MDOF > Six-DOF Mass with Four Isolators

The Six-DOF scripts calculate the natural frequencies and mode shapes for a component mounted via four isolators. It also has options for the acceleration response to base input excitation.

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See also:

Damping, Isolation & Vibration Absorbers Page

Vibration Isolation Basics

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Tom Irvine

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