This paper aims to investigate the three-dimensional (3-D) nonlinear dynamics of a porous functionally graded (FG) pipe subjected to lateral harmonic excitation. Material properties of the porous pipe are graded across the radius in a power-law distribution form. Based on the Euler–Bernoulli beam theory, the nonlinear equations of motion are derived employing the Hamilton’s principal to achieve third-order accuracy with the fluid-related loads associated with the bending–torsional vibration. The new nonlinear model, consisting of three strongly coupled nonlinear partial differential equations, is discretized into second-order ordinary differential equations via Galerkin method. Subsequently, the pseudo-arclength continuation technique together with a direct time-integration method are employed to perform nonlinear static and dynamic responses of this gyroscopic system. Numerical parametric investigations are conducted to assess the significant effects of different parameters on the resonant dynamic behavior of system, with special focus on the modal interaction that could lead to multiple coexisting solutions including planar and nonplanar motions. Moreover, the nonplanar resonance behavior is revealed that the influences of structural symmetries and symmetry-breaking effects on bifurcations and instabilities in comparison to the previously classical planar resonance behavior.

本文旨在研究受横向谐波激励的多孔功能梯度 (FG) 管的三维 (3-D) 非线性动力学。多孔管的材料特性在半径上以幂律分布形式分级。基于 Euler-Bernoulli 梁理论，非线性运动方程采用 Hamilton 原理导出，以实现与弯曲-扭转振动相关的流体相关载荷的三阶精度。新的非线性模型由三个强耦合非线性偏微分方程组成，通过Galerkin方法离散为二阶常微分方程。随后，采用伪弧长延拓技术和直接时间积分方法来执行该陀螺系统的非线性静态和动态响应。进行数值参数研究以评估不同参数对系统共振动态行为的显着影响，特别关注可能导致多种共存解决方案（包括平面和非平面运动）的模态相互作用。此外，与以前经典的平面共振行为相比，非平面共振行为揭示了结构对称性和对称性破坏效应对分叉和不稳定性的影响。进行数值参数研究以评估不同参数对系统共振动态行为的显着影响，特别关注可能导致多种共存解决方案（包括平面和非平面运动）的模态相互作用。此外，与以前经典的平面共振行为相比，非平面共振行为揭示了结构对称性和对称性破坏效应对分叉和不稳定性的影响。进行数值参数研究以评估不同参数对系统共振动态行为的显着影响，特别关注可能导致多种共存解决方案（包括平面和非平面运动）的模态相互作用。此外，与以前经典的平面共振行为相比，非平面共振行为揭示了结构对称性和对称性破坏效应对分叉和不稳定性的影响。