On the use of artificial springs in the study of the free vibrations of systems comprised of straight and curved beams

An approach is presented for the solution of the free vibration problem of systems comprised of straight and/or curved beam components. The Rayleigh-Ritz method is used, and the choice of the deflection functions is simplified through the introduction of artificial springs at the joints between the components. The necessary continuity conditions are enforced through allowing the spring stiffness to become very large compared to the stiffness of the components. Three relatively simple systems, a straight stepped beam, a combined straight and curved beam structure and a quasi-elliptical ring, are used to illustrate the approach and the convergence and accuracy of the solution.

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