Jing Yuan

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The use of artificial springs in the Rayleigh-Ritz method is proposed in this thesis for the study of free structural vibration. It is shown to be accurate in calculation, simple in concept, and straightforward and versatile in application. In this novel approach, appropriate artificial springs are introduced between the constituent members and at the boundaries of the system. The admissible functions are chosen simply to satisfy the free conditions at the boundaries of each component. The necessary boundary and continuity conditions between components are enforced by permitting the values of stiffness of the appropriate springs to become very high compared with the values of stiffness of the components. In the event that the system has flexible boundaries and/or flexible joints between components, then each artificial spring is simply assigned the actual stiffness of the appropriate boundary or joint.;A computer symbolic calculation package is used to simplify the analytical procedure and to improve the accuracy of calculation. Numerical results are generated both for new problems and for problems for which comparison results are available in the literature.;Firstly, for the vibration of systems comprised of straight and curved beams, a straight stepped beam, a combined straight and curved beam structure and a quasi-elliptical ring, are treated.;Secondly, the approach is applied to the free vibration of plate problems: a stepped thickness plate, plates with slits (which approximate cracks) and box-structures with rotationally rigid or flexible joints.;Thirdly, the analysis is applied to the study of the free vibration of several systems comprising cylindrical shells and annular plates.;In addition, the method is successfully extended to apply the study of periodically supported structures, such as periodically simply supported, uniform beams, thin plates and doubly curved shallow shells; here the springs provide the required relationships between the end or edge conditions for the same span.



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