Vibration isolation: Harmonic and seismic forcing using the Wilson Theta Method

James A. Carlson, Joseph Turner

Research output: Contribution to journalConference articlepeer-review


It is well known that equipment can cause unwanted vibrations in buildings. Springs have been used to isolate these vibrations and reduce transmitted forces to building structures. For simple vertical harmonic motion and free vibration, the problem is easily evaluated using simple charts and figures. Evaluation of spring-isolated equipment responding to earthquakes is not simple. A numerical method is included to evaluate response of equipment to earthquakes and harmonic forcing functions. Configuration of equipment on springs is simplified for numerical analysis. A simplified approach and associated equations of motion can be developed to evaluate the response of the equipment with vertical and horizontal forcing functions. Response of spring isolation in the vertical direction is based on the vertical forcing function acting on the center of mass and results in the translation of the total mass (up and down). Horizontal forcing functions result in a change in the angle around the center of mass. If the mass of the equipment is offset from the center of mass, then the vertical and angular responses are coupled. Resulting tension and compression forces at the spring can be directly related to the center of mass vertical and rotational displacements and velocities. Results of this numerical method may be used to verify simplified methods.

Original languageEnglish (US)
Pages (from-to)321-328
Number of pages8
JournalASHRAE Transactions
Volume110 PART 1
StatePublished - 2004
EventASHRAE Transactions - Anaheim, CA, United States
Duration: Jan 25 2004Jan 25 2004

ASJC Scopus subject areas

  • Building and Construction
  • Mechanical Engineering


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