Research Article
Feb 1970
Free Vibration of Two-Dimensional Frameworks
Publication: Journal of the Structural Division
Volume 96, Issue 2
Abstract
A set of three partial difference equations is derived which describes exactly the in-plane free vibrational motion of the joints of a regular, orthogonal, two-dimensional framework having rigid joint connections. The equations include concentrated masses and inertias at the joints. Two cases are treated in detail; one in which the joints have rotational freedom and one in which rotation and horizontal displacement are permitted. For specific boundary conditions, transcendental equations for the free vibration frequencies and solutions for the modal functions are obtained in the form of discrete trigonometric functions. A method is outlined for finding solutions to the frame having three degrees-of-freedom at all interior joints but with highly specialized conditions along the vertical boundaries. For comparison, the governing difference equations for two lumped parameter models are obtained as special cases of the general equations. Numerical results for specific frames illustrate typical frequency spectra and indicate application of the results to evaluating the accuracy of approximate models.
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Published In
Journal of the Structural Division
Volume 96 • Issue 2 • February 1970
Pages: 267 - 289
Copyright
© 1970 American Society of Civil Engineers.
History
Published in print: Feb 1970
Published online: Feb 1, 2021
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Authors
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Karl-Robert Leimbach
Sr. Assoc. Engr., Lockheed Missiles and Space Co., Huntsville Res. and Engrg. Ctr., Huntsville, Ala.
Donald McDonald, M.ASCE
Manager; Structures and Mechanics, Lockheed Missiles and Space Co., Huntsville Res. and Engrg. Ctr., Huntsville, Ala.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.