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UBC Theses and Dissertations

Steady state vibrations of framed structures Maini, Rameshwar Kumar


This thesis is concerned with the determination of Internal Stress Resultants produced in different structural elements of framed structures due to harmonic disturbances. The analysis of frames under vibrating loads has so far been dealt with with physical lumping of the structural mass at the node points where the stiffness influence coefficients are defined. To improve the accuracy of the results, a consistent mass matrix approach is dealt with in few of the latest solutions giving higher degree of precision compared with the results of problems solved by lumped mass system. Keeping in mind the criteria of efficiency for solving any structural dynamic response problem, a stiffness matrix is generated which depends upon the distributed mass of the member and the frequency of vibrations of the impressed force. The stiffness influence coefficients are derived for a plane frame member of uniformly distributed mass from the general differential equation of motion under longitudinal and lateral vibrations. This concept is then extended to generate a stiffness matrix for a space frame member including torsional vibrations. The effects of rotary inertia and shear deformations being predominant for framed structures such as turbine foundations, are also included. The generated stiffness matrix is called the "Frequency and Mass Dependent Stiffness Matrix" (F.M.) which is used for the dynamic analysis of some structural problems and the results are compared with those of lumped mass and consistent mass matrix approaches. The F. M. Stiffness Matrix approach is then applied to the dynamic analysis of full size turbine foundations in comparison with other methods of solution. In this thesis major emphasis is stressed upon the dynamic analysis of turbine foundations.

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