Abstract
The thesis is concerned with the vibrational characteristics of straight and pre-twisted cantilever beams of uniform rectangular and aerofoil cross-section. Two methods are presented for the solution of the differential equations of motion of pre-twisted rectangular cross-section beams neglecting shear and rotary inertia effects. The first method consists of transforming the original equations into a set of first order simultaneous equations and solving by a step-by-step finite difference procedure. The second method is a Rayleigh Ritz procedure for which two types of approximating functions are considered. The natural frequencies and mode shapes of vibration are obtained up to the fifth mode by both methods. The results are compared to each other and to the work of other investigators where available and good agreement is obtained. The Rayleigh Ritz method is extended to allow for shear and rotary inertia effects for both straight and pre-twisted rectangular cross-section beams. For straight beams good agreement is shown to exist with known solutions. The effect of variation in the value of the shear stress factor upon natural frequencies of pre-twisted rectangular cross-section beams is also examined. The transformation method has been extended to solve the equations of motion of aerofoil cross-section beams. The natural frequencies and mode shapes of vibration are obtained up to the fifth mode for both clockwise and anti-clockwise pre-twist relative to the root cross-section. The natural frequencies, for the case of zero pre-twist, are compared to results obtained by an analytical solution of the equations of motion and to standard solutions for certain special cases and good agreement is obtained. The effect of variation of the value of centre-of-flexure co-ordinates upon beam natural frequencies and mode shapes is also discussed. The natural frequencies and mode shapes of vibration are obtained by experiment for both rectangular and aerofoil cross-section beams and are compared to theoretical results.