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Abstract

This work was embarked upon in order to study the feasibility of employing Hamilton’s Principle as a basis for computer solution of problems in structural dynamics.

It was desired to extend the familiarity of Hamilton’s Principle, there being no obvious reason why a Least Action principle should be so rarely employed compared to other concepts such as the Energy Conservation Principle and its derivatives.

The following guide lines were laid down at the outset:
(a) the feasibility study would be based on evaluating the response of bridge girders to travelling loads, and

(b) the travelling loads would be treated strictly as masses. It was felt that this would extend the interest of the results and at the same time, provide a more appropriate challenge for the new method.

As regards item (b) above, the following remarks are relevant. If travelling loads are regarded as masses then the force that each one exerts on the bridge is affected by the vertical accelerations arising from the dynamic deflections. This means that the travelling load exerts a continually varying force as it traverses the span and at certain points this force may differ considerably from the constant gravity force on which such analysis is often based. Furthermore, the magnitude of this discrepancy will increase considerably with the speed of transit.

In point of fact it became apparent, at a fairly early stage in the investigations, that the improvement in logic due to treating loads as masses would only be significant in the case of very high speeds indeed (perhaps in excess of current practice or probability). Nevertheless, this feature was retained because an idea of "track humping" to reduce dynamic deflections had been evolved and this could not be evaluated unless the loads were treated as masses. Also it was desired to investigate the case where the load is a vehicle with elastic suspension.

In addition to the computational application of Hamilton’s Principle some further investigation was conducted with regard to its manifestation in natural vibration theory.

Publication Type:	Thesis (Doctoral)
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Departments:	School of Science & Technology > Engineering School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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