Modeling Natural Frequencies of Vibration of Three Dimensional Frames under Two Dimensional Loading

Gideon Nzioki Mutala

doi:10.18034/ajase.v5i1.67

Authors

Gideon Nzioki Mutala Department of Civil and Construction Engineering, University of Nairobi, Box 5633-00200, Nairobi, KENYA

Keywords:

Vibrations

Frequencies

Natural

Resonance

Structures

Abstract

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 and experimental. In the theoretical method Computer Modeling was done based on structural theory. In the experimental method physical prototypes of structures were made to vibrate freely.

In the theoretical approach, a matrix approach a computer program which generated structural models was developed using a matrix method. A horizontal force would be input at a top joint of each model and deflection at the centre of mass was calculated. The deflection was the amplitude of vibration. The stiffness of the structure was then calculated using the structural amplitude obtained. The stiffness would then be used to calculate the natural frequency of vibration for the structural model.

In the experimental approach, physical miniature structures were fabricated with different heights, member stiffnesses and number of bays. An increasing force would be applied on each structure using a magnet which would release it, at a certain magnitude of force, to vibrate freely. Deflections against time at the centre of mass were then measured using an horizontal motion transducer. The transducer has a probe which gets depressed on contact with a vibrating object. The instrument was connected to a TDS 302 data-logger which displayed deflection against time on a screen.

Analysis of data obtained from the two approaches was done using a graphical method. The experimental data correlated very closely to the theoretical data. The results of the analysis enabled development of a formula for obtaining the natural frequency of vibration using the various parameters. The formula will aid the engineering design of tall buildings such that they do not resonate with the forces acting on them. In this way it will be possible to avoid catastrophic resonance disasters.

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