Abstract
This thesis is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method developed by Dawson for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. This method consists in transforming the original equations into a set of first order differential equations and solving by Runga-Kutta step-by-step integration method. The method has been programmed for an Elliot-503 computer in Algol language and the natural frequencies and mode shapes of vibration are obtained for various breadth to depth ratio beams of lengths ranging from 3 inches to 20 inches ana pre-twisted angle up to 90 degrees, for up to fifth mode of vibration. The results are compared with other investigators work where available and good agreement is obtained. The natural frequencies and mode shapes of vibration are obtained by experiment and are compared to theoretical results. The effect of the variation of the shear stress factor upon the natural frequencies and mode shapes of vibration of pre-twisted cantilever beams is also examined.