Nonlinear vibration analysis of Z-shaped pipes with CLD considering amplitude-dependent characteristics of clamps

Abstract

Under external excitation, the clamp-pipe structures may exhibit nonlinear vibration behavior due to stiffness softening and damping energy dissipation of the clamp. To implement vibration suppression on pipes, a semi-analytical modeling method is proposed for the Z-shaped pipe structure with partial constrained damping layer (CLD) treatment under the constraint of the clamp. The nonlinear vibration characteristics of the Z-shaped pipe with CLD in both in-plane and out-of-plane directions are further investigated by considering the nonlinear mechanical properties of the clamp. Specifically, the energy expressions of the laminated straight and curved pipe segments are deduced based on the Timoshenko beam theory. The coupling of pipe segments is introduced by the improving artificial spring technology. A novel equivalent mechanical model is developed to simulate the nonlinear mechanical properties of the clamp, which are expressed by nonlinear stiffness and damping with the amplitude-dependent characteristic. Next, an effective algorithm is presented for solving nonlinear dynamic equations in the frequency domain with the amplitude-dependent characteristic. The proposed linear and nonlinear models are verified by the FE analysis and experimental test results. The comparison demonstrates that the proposed method can accurately replicate the nonlinear vibration of the Z-shaped pipe with CLD treatment. Finally, the suppression mechanism of the CLD on the vibration of Z-shaped pipes and the nature of the amplitude-dependent characteristic are further investigated, which can guide the design and vibration reduction of pipes.