Modeling Natural Frequencies Of Vibration Of Three Dimensional Frames Under Two Dimensional Loading  

Abstract Category: Engineering
Institution / University: University of Nairobi, Kenya
Published in: 2011

Thesis Abstract / Summary:

The aim of this study was to determine the relationship between natural frequency of vibration, the height of the structure, the stiffnesses of members and number bays of a structure. The relationship was to be developed based on data obtained using two methods. The methods were theoretical whereby Computer Modeling was undertaken based on structural theory, and experimental, whereby physical prototypes of structures were subjected to free vibrations.
In the theoretical method, a matrix approach to analysis was adopted to develop a computer program which generated structural models. A horizontal force would be applied at the top-most joint of each model and deflection at the centre of mass was calculated, which was the amplitude of vibration. The overall stiffness of the structure was calculated using the structural amplitude obtained. The overall stiffness was then used to calculate the frequency of vibration for each structural model.

In the experimental method, physical models of miniature structures were built with different heights, member stiffnesses and number of bays. Each model was subjected to free vibrations and the deflections against time were measured. To simulate a free vibration in a model, a measured horizontal force was applied at a joint located at the top of the structure to produce an initial deflection and then the force was withdrawn to allow free vibrations. The deflections at the centre of gravity for free vibrations were measured against time.
The equipment used to measure the free vibrations was horizontal motion transducer. The instrument has a probe which gets depressed when an object is pushed against it. The transducer was attached to a TDS 302 data-logger which printed deflection against time.

The data obtained was analysed graphically. It was found that the theoretical values were very close to the experimental values, with very high positive correlation coefficients. It was found that a suitable formula for the natural frequency of vibration, F, is F= C*(H1.1)*(Npr0.17)*(Npp0.38)*(Sv1.23)*(1/(Spl1.46))*Spp0.02 where C is a constant, H is the structure height, Npr is the number of bays parallel to motion, Npp is the number of bays perpendicular to motion, Sv is the stiffness ratio of the columns, Spl is the stiffness ratio (I/L) of beams parallel to motion and Spp is the stiffness ratio of beams perpendicular to motion. The relationships obtained will enable the engineering design of tall buildings against dangerous resonance with the forces they are subjected to. The relationship will be predetermined and adequately designed for.

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This Thesis Abstract may be cited as follows:
MUTALA,G.N. Modeling Natural Frequencies of vibration of three Dimensional Frames under two dimensional loading

Submission Details: Thesis Abstract submitted by GIDEON MUTALA from Kenya on 06-Nov-2015 10:55.
Abstract has been viewed 2430 times (since 7 Mar 2010).

GIDEON MUTALA Contact Details: Email: mutalagn@yahoo.com

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