The response of box-type structures to vibration.

The work described in this thesis deals with the vibration study of an open ended folded plate box type structure leading up to the prediction of its response to random excitation. Theoretical and experimental results for the box are presented as one of the main aims of the work is to predict theoretically the response of the structure to random excitation and compare these results with experimentally obtained values using various methods available. The determination of the response of a structure to random excitation depends on the prediction of the response spectral density. To determine the response spectral density of any point on a structure a knowledge of its natural frequencies and mode shapes and modal damping factors is required. In this work the finite-element method of analysis is used to determine the natural frequencies of vibration and the corresponding mode shapes of the box structure and computer programs were developed to perform this analysis. During the project, beam and plate structures have also been investigated to assess the accuracy of the technique and some results for these are included in chapter 7. The natural frequencies and mode shapes obtained are compared with experimental results as well as with those obtained using other theoretical analyses. For the beam the exact method was used and for the plate, the energy method using Warburton's formulae. Computer programs were also developed to calculate the structural receptance from the natural frequencies and mode shapes calculated using the finite element technique and damping factors obtained experimentally. From this, the response spectral density of the structure to a known excitation spectrum was obtained. Experimental work include a) sinusoidal excitation tests to determine natural frequencies, mode shapes and damping factors and b) random excitation using pseudo-random binary sequence signals to determine response to random excitation using narrow band frequency analysis and correlation techniques. The experimental apparatus and techniques used, including the development of a non-contacting combined exciter pickup probe, are described and discussed. The response to random excitation is obtained experimentally using a pseudo-random binary sequence signal generator and a time domain analyser, giving the cross-correlation function from which the cross spectral density is calculated in a Fourier transform. A Fast Fourier Transform computer program was developed during the work to perform this. The response spectral density is then obtained from a knowledge of the excitation spectral density. Finally the values of the response spectral density obtained were compared v/ith those obtained using the results of the finite element analysis and using the results of the sine sweep test and narrow band frequency analysis. The technique used in this work has proved satisfactory and the experimental apparatus and computer programs developed, suitable for the investigation. The work described in this thesis provides the necessary basic requirements for future work in the establishment of suitable experimental apparatus setup and provision of essential computer software. Suggestions as to possible extension of this work are made in the concluding chapter.