An Investigation for Nonlinear Dynamic Behavior of Flange Joints Under Lateral Loading

Flange joints are one of the most widely used industrial and aerospace connection parts. Therefore, investigating the static and dynamic behavior of these joints is very important. In this study, a model consisting of two beams connected by a single screw flange joint is intended. Then a mass-spring model consisting of linear axial and nonlinear torsional springs is considered. Dynamic equations of the system are derived considering the beam equations, boundary conditions and compatibility equations. Assuming equivalent linear springs, bending frequencies and mode shapes for several joint stiffnesses are obtained. Using the mode superposition method and approximating the first mode, the dynamic equation is converted to a 1-DOF nonlinear stiffness equation. Curve approximation method is used to describe the nonlinear stiffness with equivalent polynomial equation. Then the perturbation method is used to solve the nonlinear equation of free and forced vibrations of the system, near natural frequencies, subharmonic and super harmonic regions. The numerical solution result of the bilinear and its equivalent polynomial equation is compared with the the perturbation method results. Accuracy of the results obtained by the polynomial approximation and perturbation solution is guaranteed by conformity of numerical and semi-analytical results. Then the effect of changing system parameters on the frequency response is studied. Finally, frequency response, which is obtained by the numerical and multiple scale perturbation methods is compared.