Nonlinear natural frequencies and primary resonance of Euler-Bernoulli beam with initial deflection using nonlocal elasticity theory

In the present work,we study the primary responses of euler-bernoulli beam with initial imperfection/rise. the nonlocal elasticity theory was used to derive the mathematical model to account for the scale effect of the considered beam. one type of beams was considered in the analysis; simply supported beam. the multi-mode approach was used to obtain the reduced nonlinear temporal equations of motion that contain quadratic and cubic nonlinear terms. the method of multiple-scales was applied to obtain approximate analytical solutions for the nonlinear natural frequencies in addition to the primary and resonance responses. the obtained results were presented over a selected range of physical parameters for the two types of beams such as; beam initial rise/imperfection,scale effect parameter and excitation level. © 2016 jordan journal of mechanical and industrial engineering.