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The results of investigations to determine the elastic-plastic behaviour of unpressurised pipes with long offset indentations and unsymmetric support conditions are presented in this paper. They include the results of experimental tests, FE analyses and analytical methods. Three different materials and five different geometries are used to investigate their effects on the behaviour. A comparison of the experimental results, FE and analytical solutions indicates that the general analytical formulation developed in this paper for predicting the peak indenter loads in offset indented pipes, is reasonably accurate. Also, the analyses presented in this paper indicate that using a representative nominal flow stress, which is the average of yield and ultimate tensile stresses, in the analytical method, is appropriate for predicting the peak indenter loads.

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This paper investigates the natural frequency of free transverse vibration of blades in rotating disks to examine the relationship of natural frequencies, blade stiffness and nodal diameters to study how neighboring blades react upon each other and affect blade natural frequency. With the use of elastic hinge theory and a cantilever beam model subjected to either a transverse concentrated force or a bending moment at the free end, the force-deflection stiffness/moment-rotation stiffness of the beam have been developed. Thereafter, the reaction forces and moments from the neighboring blades have been determined without the need for an exact solution of large deformation of cantilever beams including geometrical nonlinearity effects. With the use of the energy conservation principle and modal theory, the natural frequency of free transverse vibration of blades in rotating disks has been determined for any nodal diameter. A comparison of the analytical and finite element solutions for a bladed disk with uniform aerofoils shows that the analytical method presented in this paper is accurate.

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