Eigenvibrations of curved elastic bars according to the „Method of internal constraints“

Conclusions

In the present paper it has been shown how it is possible to discuss the problem of vibrations of curved bars once that the solution of the corresponding problem for the straight bar is known. The method of approach in deriving the equations of motion being completely contained in the constraint equation (5) and in the application of Hamilton Principle, while the method of solving the equations being based on a perturbation method which utilizes as first approximation the solution of the straight case.

More general dynamic problems of elongated solids in which the inertia characteristics of the cross-section of the bar are known functions of the variable x can be attacked and solved by the same method which has so far been demonstrated for the simple cases of bars having constant inertia characteristics.