Abstract In this paper integral equations are applied for the calculation of the normal modes of vibrating beams. Both exact and approximate methods of solving the integral equation are considered. The Green's function, or kernel, of the integral equation is constructed for both uniform and nonuniform beams. Solutions for the normal modes of a uniform cantilever are given. A nonuniform, naturally-twisted turbine blade is studied in detail and the first and second normal modes are calculated by the integral-equation method.

Integral equations can effectively calculate the normal modes of vibrating beams, including uniform cantilevers and naturally-twisted turbine blades.

An integral-equation approach to problems of vibrating beams☆

Key Takeaway: Integral equations can effectively calculate the normal modes of vibrating beams, including uniform cantilevers and naturally-twisted turbine blades.