Modal interactions of a dual-joint cylindrical shell system via Nonlinear Normal Modes

Abstract

Bolted flange joints are commonly encountered in engineering structures. One specific challenge that is regularly encountered is the modeling of connecting interfaces between flanges. Indeed, for large amplitudes of vibration, due to discontinuity of the structure and mechanical contact of the connecting interface, clearances may occur between flanges and cause local stiffness loss, exhibiting complicated nonlinear dynamic behavior. In this paper, a simplified dynamic model for bolted flange joint via structural static analysis is proposed, in which the stiffness nonlinearity due to the non-smoothness of jointed interface is characterized by piecewise-smooth springs. The proposed simplified model has demonstrated good accuracy and precision in capturing the nonlinear dynamic characteristics of bolted flange connections. Following the simplified modeling technique and focusing on the stiffness nonlinearities, an analytical dual-joint system with free–free boundary conditions is established capturing the interaction of a longitudinal mode with two bending modes. The Harmonic Balance Method combined with Asymptotic Numerical Method (HBM–ANM) is utilized to estimate Nonlinear Normal Modes (NNMs) of the system, which provide an interpretation of the underlying nonlinear dynamic behavior, including bifurcation analysis, internal resonances characterization, and stability properties. Especially, internal resonances between the three modes can be triggered at high energy (oscillation amplitude) level, without having commensurate linear natural frequencies, leading to qualitative changes in periodic motions and internal loads environment of the system. The influences of linear frequency ratios and stiffness nonlinearity of each joint on the dynamics of the system are discussed in terms of NNMs. It is interesting to reveal that reducing the stiffness nonlinearity of joint may grow the complexity of the nonlinear dynamics of the system, from the perspective of motion stability, and trigger internal resonance with a complex topology. The studies in this paper provide an in-depth understanding of the nonlinear dynamic behavior of dual-joint systems, and the NNMs certainly represent a useful framework that could lead to a better dynamic design of jointed structures.