Traveling Wave Excitation Research Articles

Physics-informed machine learning approach for reduced-order modeling of integrally bladed rotors: Theory and application

Integrally bladed rotors are commonly used in aircraft and rocket turbomachinery and known to exhibit complex dynamics when subject to operational loading conditions. Though nominally cyclic symmetric structures, in practice, cyclic symmetry is destroyed due to mistuning caused by random sector-to-sector imperfections in material properties and geometry. Simulating mistuned blisk dynamics using high-fidelity models can be computationally expensive, thus, a variety of physics-based reduced-order models have been previously developed. However, these models cannot easily incorporate experimental data nor leverage potential benefits of data-driven and machine-learning-based approaches. Here, we present a novel first-of-its-kind physics-informed machine learning modeling approach that incorporates physical laws directly into a novel network architecture while maintaining a sector-level viewpoint. The approach is combined with an assembly procedure resulting in a significantly smaller linear system based on blade-alone response data, and can directly incorporate physical response data like that measured with blade tip timing and/or traveling-wave excitation. Validation is shown using a large-scale finite-element model, with multiple traveling-wave forced-response predictions and response selection cases considered. Using only as little as a single degree of freedom per sector from the blade tip, this approach shows high accuracy relative to high-fidelity simulations.

Shaking Tables Test on Seismic Responses of a Long-Span Rigid-Framed Bridge Considering Traveling Wave Effect and Soil–Structure Interaction

The traveling wave effect and soil–structure interaction have significant influence on the seismic response of large-span bridges with complex site conditions. In this paper, a 1/10 scaled-down large-span rigid-framed bridge model was designed and fabricated, and a shaking tables test considering the traveling wave effect and soil–structure interaction was carried out on a large-scale continuous rigid bridge model by a real-time substructure hybrid test technique. Influences of the traveling wave effect and soil–structure interaction on the seismic responses of the rigid-framed bridge specimen were systematically analyzed with experimental data. The test results showed that when the apparent wave speed was small, the traveling wave effect increased the seismic responses of the rigid-framed bridge. With the increase in apparent wave speed, the structural response under traveling wave excitation and uniform excitation was basically the same. The SSI effect lead to a great change in the seismic input peaks and spectral characters at the bottom of the pier, and increased the seismic responses of the rigid-framed bridge. When both traveling wave and the SSI effect were considered, there was a phase difference in the seismic excitation. The dynamic responses of a continuous rigid-framed bridge could not be simply obtained by superposition of the separate traveling wave effect or SSI effect. Meanwhile, the real-time substructure test method in this paper solved the problems that the traditional soil box experiment cannot be applied to the test of a large-scale model, the soil and bridge structure find it difficult to meet the unified similarity ratio, and the boundary conditions are difficult to simulate accurately.

Integrally Bladed Rotor Modal Identification Under Traveling Wave Excitation With High Density Measurement Points

Abstract Vibration testing of an integrally bladed rotor (IBR) is often completed through traveling wave excitation (TWE) bench tests composed of multiple, simultaneously excited inputs. Often, each blade has many output locations. For IBRs with many blades, as often found in the high pressure compressor, the total number of outputs can be several orders of magnitude. Formulation of a full output spectral density matrix from all measurements will then contain an exponential number of values at each frequency bin that can be detrimental to computational resources during the spectral density matrix formulation as well as down-stream system identification algorithms. An online algorithm is proposed for collecting and analyzing TWE data to reduce the large, computationally burdensome datasets into a manageable number of subsets for subsequent system identification. Furthermore, a frequency domain decomposition technique is also proposed for system identification that also attempts to reduce the data size through singular value decomposition. Identified system poles can be averaged from each subset, but mode shapes require stitching each subset together to identify the full mode shape at all output locations. The developed approaches are tested on synthetic TWE data and compared to baseline system identification results obtained using the full spectral density matrix. Results indicate the data subsets accurately compare to the baseline without much loss in accuracy.

Advancing Mistuning Identification and Dynamic Modeling of Blisks Through Blade Detuning Tests

Blisks extensively used in advanced aeroengines are vulnerable to vibration problems due to the high sensitivity of the blisk’s forced response to blade mistuning. This paper proposes an emerging mistuning identification technique based on blade detuning tests (BDTID) for predictive dynamic modeling of blisks. The conventional frequency-mistuning modeling approaches relying on blade mistuning identification by reduced-order model techniques and modal test data of the full blisk are also adopted to construct different mistuned models of a blisk test piece for comparison purposes. A complete assessment of these blisk models is achieved through the forced response tests in a stationary traveling wave excitation test rig. The BDTID consists of blade-detuning tests followed by a correction procedure. The detuning tests enable us to approximately evaluate the “blade-alone” frequencies through blade-by-blade impact testing in combination with a mass detuning mechanism. The correction procedure is able to evaluate the detuning test quality by the quantification of the residual interblade coupling due to mass detuning. More importantly, a robustness investigation demonstrates that this procedure is able to capture the “true” blade mistuning even in cases of poor blade detuning test quality. The resultant mistuned blisk model exhibits high accuracy in the modal correlation and forced response validation results. Compared with conventional methods, BDTID takes advantage of easy implementation with less experimental effort and has proven robust performance. It is therefore recommended for blade mistuning identification and predictive blisk dynamic modeling in a wide variety of scenarios.

Analysis of Traveling Wave and Combined Site Effect of Long-Span Upper-Bearing Concrete-Filled Steel Tubular Arch Bridge

In order to study the traveling wave effect and combined site effect of long-span steel tube concrete-filled arch bridge, a 400-m span bridge of the same type is taken as an example, and a large-mass time-history analysis method with multipoint input of recorded seismic waves is used. A total of 11 kinds of traveling wave excitations and 9 kinds of combined site excitations under 4 types of typical sites are carried out to calculate the structural response, and the chord axial force ratio and displacement changes are compared and analyzed. The results show that the long-span arch bridge also has nonuniform seismic excitation conditions in the lateral and vertical directions, and the spatial effect of the structural response is significant; under the traveling wave excitation, the change of the axial force ratio of the chord has a certain periodicity, and it is not the larger the axial force ratio is, the larger the axial force ratio is; the X direction has a significant influence, the maximum axial force ratio of the vault under the design condition is 6.26, and the changes in the Y and Z directions are relatively gentle, but there are still nearly two times the working condition; after the same amplitude modulation of different recorded waves, under the uniform excitation, the axial force is similar, but the displacement is quite different; under the unidirectional traveling wave excitation, the displacement in the X and Z directions shows an accelerating and increasing trend toward the vault. When it is relatively consistent under the unidirectional combined site excitation, and the axial force ratio changes under small and then increases, the L/4–3L/8 segment has a significant impact; the axial force ratio changes are the combined site excitation in different directions are spatially random; three under the combined site excitation. The axial force ratio in the orthogonal direction changes greatly. When the hard field is transformed into the soft field, the axial force ratio decreases, and the displacement increases continuously.

Mistuning identification and model updating of a blisk with piezoelectric excitation components

Integrally bladed disks (blisks) are extensively used in military and commercial aircraft engines. There are inevitable deviations between blades called mistuning, leading to the vibration localization of blisks, which potentially results in high cycle fatigue (HCF). Furthermore, the dynamic performance is sensitive to mistuning patterns. Hence, to predict the vibration response of mistuned blisks accurately, the mistuning pattern needs to be identified experimentally and verified under traveling wave excitation (TWE). Piezoelectric TWE is a promising testing technique for blisk dynamics in a non-rotating state, offering advantages such as high excitation force, wide bandwidth, and a simple setup. However, piezoelectric materials are generally arranged on blades forming an electromechanically coupled structure, which challenges the existing mistuning identification methods. In this paper, an integral mistuning identification and model updating method with traveling wave excitation verification is developed. The detuning strategy is used to split natural frequencies of blades, whereupon the response is measured blade by blade. Measured response functions of isolated blades can be retrieved by data reconstruction. Then, the mistuning patterns of elastic modulus and damping ratio are identified by Kirchhoff-plate theory and half-power bandwidth method, respectively. Experimental studies are carried out to validate the method. A dummy blisk with piezoelectric patches is designed and the dynamic properties are calculated. Blade-by-blade measurement and TWE test are conducted. Results show that natural frequencies of the updated model are in excellent agreement with the measured ones. Under TWE, the deviations of natural frequencies for all blades are less than 0.25%. The response deviation of the updated model is decreased by 89.4% on average compared with the original model and the average response deviation of the updated model is 7.4%.

Ultrasound vibration energy harvesting from a rotary-type piezoelectric ultrasonic actuator

Ultrasound vibrations, which are abundant in our everyday environment, have long been widely used in industrial applications and medical therapeutics. While there have massive number of studies on harvesting the low-frequency vibration energy to power the low-powered electronic devices, there are few literatures on the ultrasound vibration energy harvesting. In order to validate the feasibility of ultrasound vibration energy harvesting, this article takes a rotary-type piezoelectric ultrasound actuator (PUA) as the research object, a new PZT ring with appropriate zoning and polarization is bonded onto its elastomer top surface to harvest the vibration energy induced by the ultrasound waves. The manufacturing process and operating mechanism of the modified PUA are firstly introduced. Then, the electromechanical coupled model is derived based on the equivalent circuit method, and the dynamic and energetic characteristics of the ultrasound vibration energy harvesting under three excitation modes (i.e., two standing waves and one traveling wave excitations) are theoretically studied. The experimental results testify the theoretical values, and the feasibility of ultrasound vibration energy harvesting is also validated by experiments and an application example. When the PUA is excited by traveling ultrasound wave with amplitude 67 V and frequency 35.1 kHz, the maximum harvested power of each sector of the new PZT ring and λ/4 sector of the bottom PZT ring reach 58 mW and 82.4 mW, respectively, which fully meet the power supplying requirements of low-powered electronic products and implantable medical systems.

Analysis of the response of damped and parametrically driven, strongly anharmonic Klein-Gordon chain - Part 1: Phase locked traveling breathers

In the present study, we analyze a special type of phase-locked, compact-like, moving breather solution emerging in damped, strongly nonlinear Klein-Gordon chains subjected to parametric traveling-wave excitation. Given the strongly anharmonic nature of the system under consideration, multi-scale analysis of various nonlinear wave phenomena emerging in this model becomes a highly nontrivial task. In this work, we derive the two distinct analytical approaches that enable the analytical characterization of moving, damped-driven breather solutions. As is evident from the results of the present study, the moving breather solutions forming in the damped-driven lattice under consideration are unidirectional. Moreover, their dynamics is fully controlled by the parameters of the applied, traveling wave-like, parametric excitation. These special properties of strongly localized solutions provide the new means for active spatial-temporal control of these strongly localized wave structures.

Modal Identification for Integrally Bladed Rotors Under Traveling Wave Excitation

Abstract The safety of a fielded integrally bladed rotor (IBR) is often assessed through vibration testing. Responses due to various types of excitation are measured and processed and can be inputs to follow-on analyses, such as mistuning identification. One such excitation technique is the traveling wave excitation (TWE) where all blades are simultaneously excited at phase differences that attempt to replicate naturally occurring mode shapes and certain operating conditions. This test relies on noncontact exciters, e.g., magnets and speakers, that are often not directly measured. As a result, formulating the frequency response function (FRF) is difficult and the extraction of system modal data using FRF fitting techniques in the absence of FRFs is not possible. This paper presents an approach to use measured responses from TWE tests. It is shown that the fast Fourier transform (FFT) of the TWE inputs is mostly independent over the prescribed frequency range. Consequently, the output spectral density matrix can be formulated in an operational modal analysis (OMA) sense, where direct measurement of the inputs is not needed. A full spectral density matrix is then formulated from a single measurement on each blade obtained during a single test, thus reducing the number of measurement locations and testing excitation conditions. This matrix is fit by a polyreference-least squares complex frequency-domain (P-LSCF) system identification technique tailored for OMA-type measurements. The methodology is tested using simulated TWE data for an IBR model using different damping levels. Comparisons between identified modal data and those used to create the model are made and show the methodology accurately predicts underlying system information even for closely spaced modes that are common to IBRs. Finally, the method is used on experimental TWE data of an industrial IBR.

Shake table test and numerical analysis of the seismic response of buried long-distance pipeline under longitudinal non-uniform excitation

To investigate the seismic response characteristics of buried pipelines under longitudinal non-uniform seismic excitation, a three-dimensional finite element overall analysis model is established on finite element analysis software based on the shaking table test of buried oil and gas pipelines under longitudinal non-uniform excitation. The calculated results are compared with the experimental analysis results to evaluate the correctness and reliability of the established model. The acceleration response, strain response, and displacement response of buried oil and gas pipelines and surrounding soil under longitudinal traveling wave excitation at different seismic intensities are compared and analyzed using finite element models to supplement the test conditions. The test and analysis results show that the longitudinal displacements at each measurement point under longitudinal non-uniform excitation follow the same pattern except for differences in displacement magnitude and the vibration pattern of the tube and soil when the peak input acceleration reaches 1.00 g. As shown by both experimental and numerical simulation results, the soil acceleration amplification coefficients along the soil height fluctuate between 0.5 and 1.5. The pipe acceleration time curves and Fourier spectrum exhibit the same simulated and experimental pipe acceleration waveforms, and they both show significant amplification in the low to medium frequency band of 5–20 Hz. The testing and numerical simulated pipeline axial strain peak curves are similar and in good agreement, indicating the high reliability of the experimental results.

Automatic traveling wave excitation of structures with imperfect cyclic symmetry

A method to generate traveling waves with maximal amplitudes in elastic structures with imperfect cyclic symmetric topology is presented. Traveling waves are useful in testing turbine-bladed disks and for the propulsion of ultrasonic motors. However, open-loop excitation of traveling waves may yield a partially standing wave due to imperfections and mode-mistuning. The present work puts forward a method that automatically locks onto the optimal excitation of the system, producing the largest possible pure propagating wave. The excitation uses autoresonance with modal filtering, and force projection control, utilizing optimum-seeking methodology. To validate the presented method, an experimental system consisting of a ring of coupled acoustic Helmholtz resonators was built. The ring was excited by the proposed method, and the ability to overcome the imperfections and automatically lock onto the optimal excitation was observed. In addition, the method was realized on a simulated, ultrasonic, acoustic levitation motor that utilizes traveling waves to control levitated objects.

Data-Driven Approach for Identifying Mistuning in As-Manufactured Blisks

Abstract Sector-to-sector geometry or material property variations in as-manufactured bladed disks, or blisks, can result in significantly greater vibration responses during operation compared to nominally cyclic symmetric designs. The dynamics of blisks are sensitive to these unavoidable deviations, known as mistuning, making the identification of mistuning in as-manufactured blisks necessary for accurately predicting their vibration. As in previous mistuning modeling and identification approaches, the mistuning of interest is small and is parameterized by using deviations in cantilever blade-alone frequencies. Such mistuning parameterization is popular because it can be applied through blade-to-blade stiffness deviations in computational reduced-order models used to predict blisk dynamics. Previous approaches to identify such mistuning parameters often require the identification of modal information or blade-isolation techniques such as blade detuning using masses or adding damping pads. However, modal information can be difficult to obtain accurately even in optimal bench conditions. In addition, in practice it can be difficult to isolate individual blades by restricting blade motion around the blisk or detuning individual blades through added masses due to geometric constraints. In this article, we present a method for mistuning identification using a data-driven approach based on a neural network. The network is first trained using surrogate computational data. Thus, the data-driven portion of the approach is executed using surrogate computational methods. With the trained network, mistuning in all sectors of blisks with the same nominal geometry can be identified by using a small number of forced responses and the forcing phase information from traveling-wave excitation. In this approach, no system or sector-level modal response information, restrictive blade isolation, or mass detuning are required. We additionally present a method for forcing frequency selection and response conditioning to improve identification accuracy. Validation of this approach is presented using a finite element blisk model containing stiffness mistuning within the blades to create computationally generated surrogate data. It is shown that mistuning can be predicted accurately using forced responses containing a significant amount of absolute and relative measurement noise, mimicking responses collected from experimental measurements. In addition, it is shown that mistuning can be predicted independently and accurately using different engine orders of excitation in regions of high modal density.

Integrally Bladed Rotor Mistuning Identification and Model Updating Using Geometric Mistuning Models

Abstract Nonuniform manufacturing variations and uneven usage wear and damage, referred to as mistuning, can drastically alter the dynamic response of integrally blade rotors (IBRs). Optical scanners, combined with finite element model (FEM) mesh metamorphosis algorithms, have provided capabilities to create analytical models that reduce the effect of geometrical uncertainties in numerical predictions. However, deviations in material properties cannot be obtained via optical scanning, so additional approaches are needed. A geometric mistuning reduced-order model (ROM) is developed and modified to solve for unknown IBR sector eigenvalues that are linearly proportional to elastic modulus. The developed approach accounts for both proportional and nonproportional mistuning and allows updating of the elastic modulus for each sector in the ROM. Different tuned and mistuned modal reduction procedures are employed to understand the implications of each for identifying mistuning. Simulated test data with known inputs indicate the efficiency and accuracy of the method and improvements over using a traditional, tuned mode approach. The developed methods are then extended to bench-level traveling wave excitation (TWE) data to discern how sector frequencies vary due to geometry and modulus mistuning.

Investigation on the Robustness of Rotor/Stator Contact Interactions With Respect to Small Mistuning

Abstract In this work, the impact of small mistuning on rotor/stator contact interactions is investigated. First, a detailed study of a rotor/stator interaction between the first bending modes and the second engine order is presented in the tuned case. Then, a numerical investigation on the effect of mistuning on the studied rotor/stator contact interaction is carried out. In particular, a stochastic analysis is performed to evaluate the robustness of the interaction with respect to the mistuning level. Simulations are conducted using a reducedo rder model (ROM) of an industrial-bladed disk that combines both physical degrees-of-freedom (along blades tip for contact treatment) and modal coordinates. Mistuning is introduced in the tuned ROM by means of a modified version of the component mode mistuning method that allows to keep physical degrees-of-freedom within the reduced basis. Nonlinear amplification factors, i.e., the amplification factors in the context of contact nonlinearities, are compared with their linear counterparts, and the latter are computed using a linear forcing on each blade using a two nodal diameters traveling wave excitation on the mistuned and the tuned bladed disk. The comparison between the linear and nonlinear amplification factor for each sample highlights that no correlation exists between a mistuning pattern leading to high amplifications in a linear context or when contact nonlinearities are taken into account. Therefore, dedicated analyses on the effect of mistuning should be undertaken with contact nonlinearities considerations at the design stage especially if intentional mistuning is considered.

Experimental Investigation on a Bladed Disk with Traveling Wave Excitation.

Bladed disks are key components of turbomachines and their dynamic behavior is strongly conditioned by their small accidental lack of symmetry referred to as blade mistuning. The experimental identification of mistuned disks is complicated due to several reasons related both to measurement and data processing issues. This paper describes the realization of a test rig designed to investigate the behavior of mistuned disks and develop or validate data processing techniques for system identification. To simplify experiments, using the opposite than in the real situation, the disk is fixed, while the excitation is rotating. The response measured during an experiment carried out in the resonance-crossing condition is used to compare three alternative techniques to estimate the frequency-response function of the disk.

Spontaneous pulse formation in edgeless photonic crystal resonators

Complex systems are a proving ground for fundamental interactions between components and their collective emergent phenomena. Through intricate design, integrated photonics offers intriguing nonlinear interactions that create new patterns of light. In particular, the canonical Kerr-nonlinear resonator becomes unstable with a sufficiently intense traveling-wave excitation, yielding instead a Turing pattern composed of a few interfering waves. These resonators also support the localized soliton pulse as a separate nonlinear stationary state. Kerr solitons are remarkably versatile for applications, but they cannot emerge from constant excitation. Here, we explore an edge-less photonic-crystal resonator (PhCR) that enables spontaneous formation of a soliton pulse in place of the Turing pattern. We design a PhCR in the regime of single-azimuthal-mode engineering to re-balance Kerr-nonlinear frequency shifts in favor of the soliton state, commensurate with how group-velocity dispersion balances nonlinearity. Our experiments establish PhCR solitons as mode-locked pulses by way of ultraprecise optical-frequency measurements, and we characterize their fundamental properties. Our work shows that sub-wavelength nanophotonic design expands the palette for nonlinear engineering of light.

Travelling-Wave Dipolophoresis: Levitation and Electrorotation of Janus Nanoparticles.

We present a theoretical study of the hydrodynamic and electrokinetic response of both metallic spherical polarized colloids as well as metallodielectic Janus particles, which are subjected to an arbitrary non-uniform ambient electric field (DC or AC forcing). The analysis is based on employing the linearized ‘standard’ model (Poisson–Nernst–Planck formulation) and on the assumptions of a ‘weak’ field and small Debye scale. In particular, we consider cases of linear and helical time-harmonic travelling-wave excitations and provide explicit expressions for the resulting dielectrophoretic and induced-charge electrophoretic forces and moments, exerted on freely suspended particles. The new analytic expressions thus derived for the linear and angular velocities of the initially uncharged polarizable particle are compared against some available solutions. We also analyze the levitation problem (including stability) of metallic and Janus particles placed in a cylindrical (insulating or conducting) pore near a powered electrode.

1J2-1 Traveling wave excitation to a metal cylinder and application to object transport

1J2-1 Traveling wave excitation to a metal cylinder and application to object transport

Shake Table Test on a Long-Span Cable-Stayed Bridge with Viscous Dampers Considering Wave Passage Effects

This work focused on the damping effectiveness of additional longitudinal viscous dampers employed for seismic control of long-span cable-stayed bridges considering wave passage effects. A 1/35-scale physical model scaled from a typical long-span cable-stayed bridge was designed, constructed, and tested on four shake tables. The seismic responses of the systems with and without viscous dampers, under different types of ground motions considering uniform or traveling wave excitations, were analyzed and compared. The test results show that the damping effectiveness of the additional longitudinal viscous dampers was significantly reduced under near-field ground motion. The wave passage had a great influence on the displacement responses of the towers and the deck and the relative variation amplitudes of the cable forces near the midspan. Positive damping effectiveness was commonly achieved from the additional longitudinal viscous dampers under the far-field ground motions when considering the wave passage effect, whereas negative damping effectiveness was observed under the near-field ground motion at certain wave velocities.

Nodal diameter vibration identification of coated blisk under traveling wave excitation

It is seen that blisk will be in a nodal diameter vibration state under the engine order excitation, which can be simulated by traveling wave excitation. The nodal diameters rotate on the blisk and it is necessary to identify the specific form of the nodal diameter vibration. Here, based on the determination of nodal diameter vibration parameters, a novel identification method of the nodal diameter vibration was proposed through the experimental test. Specifically, a traveling wave excitation system was built using the LabVIEW control software and noncontact magnetic exciters. Based on the description of resonant state of blisk, the identification principle formulas of the nodal diameter vibration were derived and the identification procedure was given. Taking uncoated and coated blisks as the research objects, the identification method was demonstrated. The identification results showed that the shape, direction, speed, and period of nodal diameter vibration were successfully obtained by the proposed method. In addition, it was found that coatings have a damping effect on blisk. Because of the coating introduction, the blisk vibration response was reduced, the rotation speed of nodal diameter was slowed down, and the rotation period of nodal diameter was increased.