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A tip-rub model is developed for nonlinear dynamics analysis of contact-induced vibrations of the rotating variable thickness plate under large deformations. Variable thickness, coupled with large deformations, contact-impact and centrifugal stiffening, increases complexity of the nonlinear system. Natural frequencies for different variable thickness are compared to indicate a great precision of the present method. Solution procedure for tip-rub has been proved to be in good agreement with existing experimental results. Numerical simulation for tip-rub reveals the requirement of large deformation analysis. Then special attention is given to nonlinear characteristics of the rotating rubbing plate with variable thickness. Results show that there are very rich and complex nonlinear dynamics of contact-induced vibrations of the rotating variable thickness plate under large deformations such as multi-period, bifurcation and chaotic motions. And effects of thickness strategies of exponential and linear decrease along the span used in engineering on nonlinear characteristics induced by tip-rub are investigated. Numerical results reveal that smaller thickness at the free end used to reduce centrifugal stress should not be too small to avoid aggravation of contact-induced bifurcation and chaos. Moreover, in order to obtain less centrifugal stress and weak chaotic behavior, there is an optimal thickness at the fixed end when the smaller thickness at the free end is unchanged. As the order of thickness function increasing, the trend of bifurcation and chaotic motions is gradually aggravated. It is better to choose a small order of thickness function to ensure stable operation. • Tip-rub model of rotating variable thickness plate with large deflection is developed. • Large thickness at free end can avoid aggravation of bifurcation and chaos in tip-rub. • There is an optimal thickness at fixed end for less centrifugal stress and weak chaos. • It is good to choose small order of thickness function to ensure stable operation. [ABSTRACT FROM AUTHOR]

Bragg scattering and local resonance are two fundamental mechanisms for bandgap (BG) formation of phononic crystals (PCs) and acoustic metamaterials (AMs). In this paper, a new class of motional two-dimensional (2D) hybrid Bragg-locally resonant (LR) meta-pipe model is developed, and the BG interaction behaviors of such a meta-structure are explored. The pipe is axially composed of alternate materials, and is periodically encircled with dual-layer rings, which are used to simultaneously trigger Bragg scattering and local resonance. Meanwhile, the pipe conducts an axially spinning motion, and a steady fluid flows inside the pipe. Compared to static periodic structures, the orthogonal traveling waves due to spin bring about a 2D meta-structure, and the spinning local resonators yield an additional centrifugal effect on the pipe. The results reveal the formation of hybrid Bragg-LR BGs in such a motional meta-structure, and further demonstrate their complicated evolutions with the location, number and geometry of the local resonators as well as the pipe material. The impacts of motional properties on the hybrid BGs are discussed, and they are compared with the behavior of Euler-Bernoulli model. This study provides a more in-depth interpretation for the interaction of Bragg and LR BGs, which is especially beneficial to the vibration and noise reduction of rotors and fluid-transporting devices. • A new class of motional hybrid Bragg-LR meta-pipe structure is constructed. • Bragg, LR and coupled BGs are all detected in the proposed structure. • Coupled effective BG is triggered when local resonators yield effects on Bragg effective BG. • Complicated evolutions of hybrid BGs with the location, number and geometry of local resonators are revealed. • Bragg effective BG and LR effective BG have different variations for Timoshenko model and Euler-Bernoulli model. [ABSTRACT FROM AUTHOR]