Abstract
The main purpose of this paper is the presentation of a semianalytical method for the prediction of the non-linear forced response of beams to harmonic excitation forces using a multi-mode approach. Various types of excitation forces such as distributed and concentrated are considered. The governing equation of motion is obtained and can be considered as a multidimensional form of the Duffing equation. Using the harmonic balance method, the equation of motion is converted into non-linear algebraic form. Numerical solutions are obtained using iterative-incremental procedures. The non-linear frequency and the nonlinear modes are determined at large amplitudes of vibration. The basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated. The percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution.