Date of Award

Spring 1984

Project Type


Program or Major

Engineering (Theoretical and Applied Mechanics)

Degree Name

Doctor of Philosophy


The dynamic equilibrium equations for thin-walled beams of open cross section are derived with reference to an arbitrary system of coordinates. Exact stress resultant-displacement relation of the bending theory of cylindrical shells has been used and therefore the shell curvature, secondary warping, and rotary inertia effects are included in the derivation.

The equilibrium equations have been referred to principal coordinates in order to reduce the coupling between the different displacement components. The principal coordinates and the associated cross sectional properties for some sections have been studied. This study has indicated that the shell curvature and secondary warping effects cannot be ignored for some sections.

The structural damping effect has been introduced to the equilibrium equations through complex moduli concept. The dynamic direct stiffness has been used as a base for a numerical solution of the complex frequency response problem. A computer program has been written to perform the process.

This program has been used in both free and forced response of thin-walled beams. The natural frequencies calculated are compared with solutions obtained by the finite element method as well as experimental work of other investigators. Shell elements and thin-walled beam elements have been used in the finite element solution. Satisfactory results were obtained in this comparison.

Dynamic magnification in the vicinity of resonant frequencies for some beams has also been presented. Substantial effect of shell curvature and secondary warping on the response has been observed for certain sections. The study also indicated the great effect of the value of the damping coefficient on the response. The algorithm used is stable and less costly in computer time in comparison to the finite element method.