A beam-like model is proposed to address nonlinear dynamic response of a thin pipe, under the action of a resonant transverse load. The mechanical model consists of a Timoshenko beam enriched with further kinematic and dynamic variables which, besides extension and bending, consistently describe local effects, related to ovalization and warping of the cross-section. The nonlinear equations of motions are derived via the principle of virtual work, and internal resonance between the global and local modes is addressed by the multiple scale method, after a Galerkin projection of the equations on the first significant modes. The softening behavior induced by the local deformation remarkably affects the asymptotic solution, which turns out to be in good agreement with that provided by numerical integration.

提出了一种梁状模型来解决在共振横向载荷作用下细管的非线性动态响应问题。机械模型由 Timoshenko 梁组成，该梁富含更多运动学和动力学变量，除了延伸和弯曲之外，还一致地描述了与横截面椭圆化和翘曲相关的局部效应。非线性运动方程是通过虚功原理推导出来的，全局和局部模式之间的内部共振通过多尺度方法在方程对第一有效模式进行伽辽金投影后得到解决。局部变形引起的软化行为显着影响渐近解，结果与数值积分提供的结果非常一致。