Vibration Localization and Anti-Localization of Nonlinear Multi-Support Beams with Support Periodicity Defect

A response analysis method for nonlinear beams with spatial distribution parameters and non-periodic supports was developed. The proposed method is implemented in four steps: first, the nonlinear partial differential equation of the beams is transformed into linear partial differential equations with space-varying parameters by using a perturbation method; second, the space-varying parameters are separated into a periodic part and a non-periodic part describing the periodicity defect, and the linear partial differential equations are separated into equations for the periodic and non-periodic parts; third, the equations are converted into ordinary differential equations with multiple modes coupling by using the Galerkin method; fourth, the equations are solved by using a harmonic balance method to obtain vibration responses, which are used to discover dynamic characteristics including the amplitude–frequency relation and spatial mode. The proposed method considers multiple vibration modes in the response analysis of nonlinear non-periodic structures and accounts for mode-coupling effects resulting from structural nonlinearity and parametric non-periodicity. Thus, it can handle nonlinear non-periodic structures with a high parameter-varying wave in wide frequency vibration. In numerical studies, a nonlinear beam with non-periodic supports (resulting in non-periodic distribution parameters or periodicity defect) under harmonic excitations was explored using the proposed method, which revealed some new dynamic response characteristics of this kind of structure and the influences of non-periodic parameters. The characteristics include remarkable variation in frequency response and spatial mode, and in particular, vibration localization and anti-localization. The results have potential applications in vibration control and the support damage detection of nonlinear structures with non-periodic supports.

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.

Angular Rate Sensor Based on a Solid-State Wave Gyroscope with a Metal Resonator for Attitude Control, Stabilization and Navigation Systems

The article describes the methods and test results of a solid-wave gyroscope (SVG) — an angular rate sensor (ARS), developed at the Department of Control Devices, Tula State University and manufactured by the serial plant of JSC "Michurinsky Plant" Progress "according to the technology it worked out. The metal resonator SVG-ARS is made of an elinvar alloy and has a cylindrical structure of different thickness, the lower part of which, with a smaller wall thickness, acts as a suspension for the upper cylinder, the resonator itself, which has a conical shape, providing better vibration localization at its end edge. Technological manufacturing defects, different frequencies and variability, are eliminated by balancing " by mass" based on the removal of excess metal at certain points on the end edge of the resonator. The electronic module provides the second mode of primary and secondary oscillations of the resonator edge arising during rotation and creates a signal to compensate for the Coriolis and quadrature components of the output signal at the nodes. The maximum amplitudes of the excitation and compensation signals do not exceed 10 V. Therefore, at large values of mechanical influences, the compensation circuit may not work out the increased signal and the SVG-ARS loses its operability. The total processing time of the compensation signal does not exceed 1 μs. The maximum power consumption of the electronic module is not more than 4 W. When testing for mechanical and temperature effects, the norms were used that are typical for similar devices (angular rate sensors) used on board aircraft. The tests were carried out on the bench equipment of a specialized enterprise. The stability of the zero signal and the scale factor was determined under the simultaneous action of the measured speed and temperature on the SVG-ARS. The values of the random walk and the instability of the zero signal were obtained from the Allan deviation plots. Their values provide a basis for the conclusion about the possibility of using the developed SVG for several hours on board dynamic aircraft in orientation, stabilization and navigation systems. It was found that SVG-ARS possesses impact strength and restores its measuring ability after impact. Tests for vibration resistance revealed resonance frequencies and frequency rangesin which the tested VTG-DUS sample can be used without significant modification. The results of vibration tests can be used to refine the design and control electronics for the operating conditions of a particular aircraft.

Effect of Bladed Packets on Transient Vibration Localization Behaviors of Mistuned Whole Bladed Disk System

The multi-packets whole bladed disks are usually used in the turbo-machineries. The most different characteristic of the multi-packets whole bladed disk is that some blades are connected by lacing forming a bladed packet, and several bladed packets are assembled to form a multi-packets whole bladed disk system. Mistuning of blades is an attractive vibration subject due to vibration localization problems that vibration energy focuses on some blades. The vibration localization characteristics of steady state of bladed disk are mainly discussed in previous studies, and few works focus on the transient vibration localization behaviors of the multi-packets whole mistuned bladed disk. Transient vibration characteristics of bladed disk are crucial during startup. Therefore, in this paper, transient vibration characteristics of the multi-packets whole bladed disk are studied. A developed mathematical model is used to calculate the transient vibration response of the multi-packets whole bladed disk. The number of bladed packets on the transient vibration localization of the multi-packets mistuned whole bladed disk is discussed. The results indicate that the bladed packets are able to reduce the transient vibration localization. The results suggest that the bladed packet is an alternative approach to reduce the vibration localization of bladed disk caused by mistuning. Moreover, the different number of bladed packets will produce various behaviors of transient vibration localization of multi-packets whole mistuned bladed disk system.

Dynamics of Quasiperiodic Beams

Quasiperiodic metastrucures are characterized by edge localized modes of topological nature, which can be of significant technological interest. We here investigate such topological modes for stiffened and sandwich beams, which can be employed as structural members with inherent vibration localization capabilities. Quasiperiodicity is achieved by altering the geometric properties and material properties of the beams. Specifically, in the stiffened beams, the geometric location of stiffeners is modulated to quasiperiodic patterns, while, in the sandwich beams, the core’s material properties are varied in a step-wise manner to generate such patterns. The families of periodic and quasiperiodic beams for both stiffened and sandwich-type are obtained by varying a projection parameter that governs the location of the center of the stiffener or the alternating core, respectively. The dynamics of stiffened quasiperiodic beams is investigated through 3-D finite element simulations, which leads to the observation of the fractal nature of the bulk spectrum and the illustration of topological edge modes that populate bulk spectral bandgaps. The frequency spectrum is further elucidated by employing polarization factors that distinguish multiple contributing modes. The frequency response of the finite stiffened cantilever beams confirms the presence of modes in the non-trivial bandgaps and further demonstrates that those modes are localized at the free edge. A similar analysis is conducted for the analysis of sandwich composite beams, for which computations rely on a dynamic stiffness matrix approach. This work motivates the use of quasiperiodic beams in the design of stiffened and sandwich structures as structural members in applications where vibration isolation is combined with load-carrying functions.