Mistuning parameter identification and vibration localization analysis of the integration rotor

This paper deals with the coupling vibration characteristic of the disk-blade-shaft integration rotor. First, a reduced-order model (ROM) based on an improved hybrid interface component mode synthesis method (IHISCMSM) is carried out, which takes the prestress effect into account. The frequency of the disk-blade-shaft integration rotor at different rotating speeds are calculated and the influence of selecting different mode truncation numbers is investigated. In order to quantitatively evaluate the coupling degree of blade and disk, the coupling factor is defined from the perspective of strain energy, and the influence of prestress on system’s dynamic is discussed. Then, an experimental modal analysis is performed on blades to identify the mistuning parameters, and the mode localization of the disk-blade-shaft integration rotor is analyzed with and without blade mistuning. The results indicate that there are several types of coupling modes among blade, disk and shaft of the integration rotor. After considering the prestress, the frequency increases, and the axial coupling vibration degree and radial coupling vibration degree of the integration rotor change. The mode localization of mistuned rotor is more likely to occur in the modes dominated by mistuning stage blades. There also exists a subtle mode localization phenomenon for tuned integration rotor.

The localization of non-backtracking centrality in networks and its physical consequences

The spectrum of the non-backtracking matrix plays a crucial role in determining various structural and dynamical properties of networked systems, ranging from the threshold in bond percolation and non-recurrent epidemic processes, to community structure, to node importance. Here we calculate the largest eigenvalue of the non-backtracking matrix and the associated non-backtracking centrality for uncorrelated random networks, finding expressions in excellent agreement with numerical results. We show however that the same formulas do not work well for many real-world networks. We identify the mechanism responsible for this violation in the localization of the non-backtracking centrality on network subgraphs whose formation is highly unlikely in uncorrelated networks, but rather common in real-world structures. Exploiting this knowledge we present an heuristic generalized formula for the largest eigenvalue, which is remarkably accurate for all networks of a large empirical dataset. We show that this newly uncovered localization phenomenon allows to understand the failure of the message-passing prediction for the percolation threshold in many real-world structures.

A one-dimensional model for elasto-capillary necking

We derive a nonlinear one-dimensional (1d) strain gradient model predicting the necking of soft elastic cylinders driven by surface tension, starting from three-dimensional (3d) finite-strain elasticity. It is asymptotically correct: the microscopic displacement is identified by an energy method. The 1d model can predict the bifurcations occurring in the solutions of the 3d elasticity problem when the surface tension is increased, leading to a localization phenomenon akin to phase separation. Comparisons with finite-element simulations reveal that the 1d model resolves the interface separating two phases accurately, including well into the localized regime, and that it has a vastly larger domain of validity than 1d models proposed so far.

Exploiting Nonlinear Dynamics and Energy Localization to Enhance the Performances of an Electromagnetic Vibration Energy Harvester

A multimodal electromagnetic vibration energy harvester based on a nonlinear quasi-periodic system is proposed. The multimodal approach and the nonlinearity are implemented in order to improve the output performances of the studied device. The present study investigates a periodic system composed of two weakly coupled magnets and mechanically guided by two elastic beams. The quasi-periodic system is obtained by varying the mass of one of the moving magnets which leads to the vibration energy localization in regions close to the imperfections introduced. This phenomenon is exploited to maximize the harvested energy. The mechanical nonlinearity is introduced by considering large displacements of the beams which is also investigated to maximize the harvested energy and to enlarge the bandwidth of the device. The quasi-periodic system is modeled by two coupled forced Duffing equations, which are solved using finite difference method combined with arc-length continuation method. The obtained results of the mass mistuning are analyzed and discussed in depth. It is shown that the introduction of the nonlinearity and the functionalization of the energy localization phenomenon lead to the enlargement of the bandwidth and the increase of the vibration amplitudes.