Domain Modal Analysis Research Articles

A multizone sound field reproduction method based on modal domain analysis

Multizone sound field reproduction for synthesizing desired sound fields over multiple spatial zones has been widely studied. In the traditional multizone sound field reproduction modal domain method, the final loudspeaker weights required to reproduce the desired sound field are obtained by translating the optimal equivalent global modal domain coefficients, which is susceptible to the characteristics and location of the loudspeakers and reduces the reproduction performance. This paper investigates a multizone sound field reproduction in modal domain for directly obtaining the reproducing loudspeaker weights. The optimization model is formulated to the objective of reproducing a desired sound field within the bright zone and with constraints on acoustic energy in the dark zone. The loudspeaker weights for reproducing the desired sound field are solved by the CVX toolbox. The numerical simulation results indicate that the proposed method is superior to the acoustic contrast control method and the mode matching method in terms of the accuracy of the reproduction desired sound field in the bright zone and the acoustic contrast between the bright and dark zones.

Fault Section Identification of Hybrid Transmission Lines by the Transients in Modal Domain Free From the Refractions and Reflections at Cross-Bonded Nodes

Compared with the homogeneous transmission lines, the hybrid ones are composed of the overhead, underground and submarine cable lines, resulting in three different sets of parameters over the transmission path and posing great challenge to fault location. This paper proposes a fault section identification method for two types of the hybrid lines based on modal-domain analysis which eliminates the effects of the refractions and reflections at the cross-bonded nodes. First, a method for decoupling the transients in the high-voltage cable is proposed to obtain the unified model of two types of the hybrid lines in modal domain. Then, the concept of the energy of the decoupled transient is defined, the reflection and refraction features of the energy of the transient signal are analyzed, and a novel fault section identification method is developed based on the transient energy ratio. Finally, the model of a 110kV hybrid transmission line is established in PSCAD/EMTDC. Various fault experiments are conducted. The results show the effectiveness of the proposed method.

Dynamic Response Analysis of Wind Turbine Structure to Turbulent Wind Load: Comparative Assessment in Time and Frequency Domains

This study investigates wind turbine structural dynamics using stochastic analysis and computational methods in both the time and frequency domains. Simulations and experiments are utilized to evaluate the dynamic response of a wind turbine structure to turbulent wind loads, with the aim of validating the results based on real wind farm conditions. Two approaches are employed to analyze the dynamic responses: the frequency domain modal analysis approach, which incorporates von Kármán spectra to represent the turbulent wind loads, and the time domain Monte Carlo simulation and Newmark methods, which generate wind loads and determine dynamic responses, respectively. The results indicate that, for a larger number of samples, both methods consistently yield simulated turbulent wind loads, dynamic responses and peak frequencies. These findings are further validated through experimental data. However, when dealing with a smaller number of samples, the time domain analysis produces distorted results, necessitating a larger number of samples to achieve accurate findings, while the frequency domain method maintains accuracy. Therefore, the accurate analysis of wind turbine structural dynamics can be achieved using simulations in both the time and frequency domains, considering the importance of the number of samples when choosing between time domain and frequency domain analyses. Taking these considerations into account allows for a more comprehensive and robust analysis, ultimately leading to more effective outcomes.

Multi-Inverter Resonance Modal Analysis Based on Decomposed Conductance Model

The Norton equivalent model based on the transfer function and the frequency domain analysis method for inverter resonance analysis lacks a comprehensive analysis of the resonant characteristics, and more information about the resonant key components and the degree of participation cannot be obtained. In this paper, a decomposed conductance model is proposed to characterize the resonance characteristics of the multi-inverter grid-connected system and the effect of the equivalent control link of the inverter on the resonance in more detail by combining the modal analysis method and the sensitivity analysis method. Firstly, based on αβ coordinates, the conductance division is carried out for the dual-loop inverter control link with the voltage external loop and current internal loop using capacitor-current feedback damping, and the inverter model based on the decomposition conductance is derived. The mathematical model of the multi-inverter grid-connected system is then established. Secondly, the resonance characteristics of the system are analyzed by combining the modal and frequency domain analysis methods when the number of inverters, inverter parameters, and grid-side impedance are changed. Thirdly, the degree of involvement of the system components, especially the equivalent control link of the inverter in resonance conditions, is determined in combination with the proposed model and the sensitivity analysis method, which is the basis for proposing an effective suppression strategy. Finally, a simulation model is built to verify the proposed method and the analysis results.

Discrete-Time Domain Modal Analysis of Oscillatory Stability of Renewables Integrated Power Systems

Modal analysis in the continuous-time state-space is a mature and effective method for analyzing the subsynchronous oscillation (SSO) problems of power systems. But it has limitations on oscillation traceability analysis due to the loss of system topology information. To address this issue, a discrete-time domain modal analysis method is developed in this paper. It represents the target system as a networked discrete-time equivalent circuit and uses the nodal method to generate the state matrix, from which the discrete-time eigenvalues in the z-plane can be solved. Based on the oscillation frequency and damping ratio defined in the discrete-time domain, the stability of the oscillatory mode can be quantitatively analyzed. Then, participation factors analysis is carried out similarly to the continuous-time method to locate the contributive components. Most importantly, the distribution coefficients of branch currents/ node voltages are finally defined and derived for in-depth analysis of the oscillatory mode. With this index, the propagation path of the oscillation in the mesh power system is expected to be identified.The proposed method has been applied in several case systems with wind farms integrated. Theoretical analysis results are highly consistent with the electromagnetic transient simulation results in PSCAD/ EMTDC, thus verifying its effectiveness.

Efficient Analytical Model for the Transfer Impedance and Admittance of Noncoaxial/Twinax Braided–Shielded Cables

An efficient analytical model for the transfer impedance and admittance of a noncoaxial/twinax braided–shielded cable with apertures on its sheath is proposed by generalizing the old Vance's and Kley's formulas, and it is derived using the complex analyses with an appropriate conformal mapping. Therefore, such a noncoaxial cable is converted into a coaxial one which can be studied using the traditional multiconductor transmission line method. It is shown that the aperture inductance is related to the position of the inner conductor and the radial position of each aperture on its sheath. In addition, the modal domain analysis is performed to obtain the common-mode (CM) and differential-mode (DM) transfer impedance/admittance of the twinax braided–shielded cable, with CM and DM currents inside the inner conductors examined. The proposed model is validated by comparing the results with that obtained by the method of moments (MoM)-based commercial software FEKO. It is found that the uniform distribution of the apertures on the sheath reduces the induced DM current significantly

An Improved DC Fault Protection Algorithm for MMC HVDC Grids Based on Modal-Domain Analysis

To detect the dc faults for the modular multilevel converter (MMC)-based dc grids using overhead line transmission, many protection methods in phase-domain have been proposed. These existing protection methods suffer from incomplete function, weak theoretical basis, and sensitivity to fault resistance and noise disturbance. To overcome these shortcomings, this article proposes an improved dc fault protection algorithm using the modal-domain approach for the MMC-based overhead dc grids, which decouples the interaction between positive and negative poles and mitigates the strong frequency dependence of the characteristic impedance in phase-domain. The dc fault equivalent circuits are established in modal-domain and the fault characteristics during the initial stage are analyzed. Based on the modal-domain analysis, the line-mode reactor voltage which combines the fault characteristics of negative and positive reactor voltages is used to identify the internal faults. The zero-mode reactor voltage which enlarges the differences between faulty and healthy poles is used to select the faulted pole. This method is robust to fault resistance and noise with high detection speed. In addition, it is not affected by power reversal, ac faults, and dc circuit breaker (DCCB) operation, which are validated and evaluated by the simulations in PSCAD/EMTDC.

Lamb Wave Focusing Transducer for Efficient Coupling to Wavelength-Scale Structures in Thin Piezoelectric Films

This paper describes the theoretical and experimental investigation of interdigitated transducers capable of producing focused acoustical beams in thin film piezoelectric materials. A mathematical formalism describing focused acoustical beams, lamb beams, is presented and related to their optical counterparts in two- and three-dimensions. A novel Fourier domain transducer design methodology is developed and utilized to produce near diffraction limited focused beams within a thin film AlN membrane. The properties of the acoustic beam formed by the transducer were studied by means of Doppler vibrometry implemented with a scanning confocal balanced homodyne interferometer. The Fourier domain modal analysis confirmed that 83% of the acoustical power was delivered to the targeted focused beam which was constituted from the lowest order symmetric mode, while 1% was delivered unintentionally to the beam formed from the anti-symmetric mode, and the remaining power was isotropically scattered. The transmission properties of the acoustic beams as they interact with devices with wavelength scale features were also studied, demonstrating minimal insertion loss for devices in which a subwavelength and pinhole apertures were included. [2018-0059]

Vibration of carbon nanotubes with defects: order reduction methods.

Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone-Wales defects, though the methods described can be extended to other defects.

On the efficient time domain stress analysis for the rolling chock of an independent type LNG tank targeting fatigue damage evaluation

This paper targets to develop the procedure of stress analysis of the structural details near the rolling chock by using the time domain modal analysis technique where both the contact and friction behavior can be accurately simulated. In order to perform the time domain analysis focused on the contact and friction, the interaction between hull and tank was modeled via Coulomb friction which were combined with modal analysis technique. Modal analysis using the quasi-static deformation modes is chosen as a cost effective time domain simulation method and this is based on the fact that the structural response of the tank, together with hull, is quasi-static. Based on the developed cost effective time domain simulation method, the long-term fatigue analysis procedure for the structural details near the rolling chock and key of independent type tank is targeted to be established. The developed fatigue assessment procedure takes into account, wave induced stresses and both contact and friction induced stresses without loss of accuracy.

Analysis and control of multi-zone sound field reproduction using modal-domain approach.

Multi-zone sound control aims to reproduce multiple sound fields independently and simultaneously over different spatial regions within the same space. This paper investigates the multi-zone sound control problem formulated in the modal domain using the Lagrange cost function and provides a modal-domain analysis of the problem. The Lagrange cost function is formulated to represent a quadratic objective of reproducing a desired sound field within the bright zone and with constraints on sound energy in the dark zone and global region. A fundamental problem in multi-zone reproduction is interzone sound interference, where based on the geometry of the sound zones and the desired sound field within the bright zone the achievable reproduction performance is limited. The modal-domain Lagrangian solution demonstrates the intrinsic ill-posedness of the problem, based on which a parameter, the coefficient of realisability, is developed to evaluate the reproduction limitation. The proposed reproduction method is based on controlling the interference between sound zones and sound leakage outside the sound zones, resulting in a suitable compromise between good bright zone performance and satisfactory dark zone performance. The performance of the proposed design is demonstrated through numerical simulations of two-zone reproduction in free-field and in reverberant environments.

Estimation of Forcing Function for a Geometrically Mistuned Bladed Rotor Via Modified Modal Domain Analysis

Modified modal domain analysis (MMDA) is a method to generate an accurate reduced-order model (ROM) of a bladed disk with geometric mistuning. An algorithm based on the MMDA ROM and a state observer is developed to estimate forcing functions for synchronous (including integer multiples) conditions from the dynamic responses obtained at few nodal locations of blades. The method is tested on a simple spring-mass model, finite element model (FEM) of a geometrically mistuned academic rotor, and FEM of a bladed rotor of an industrial-scale transonic research compressor. The accuracy of the forcing function estimation algorithm is examined by varying the order of ROM and the number of vibration output signals.

Surrogate model reduction for linear dynamic systems based on a frequency domain modal analysis

A novel model reduction methodology for linear dynamic systems with parameter variations is presented based on a frequency domain formulation and use of the proper orthogonal decomposition. For an efficient treatment of parameter variations, the system matrices are divided into a nominal and an incremental part. It is shown that the perturbed part is modally equivalent to a new system where the incremental matrices are isolated into the forcing term. To account for the continuous changes in the parameters, the single-composite-input is invoked with a finite number of predetermined incremental matrices. The frequency-domain Karhunen---Loeve procedure is used to calculate a rich set of basis modes accounting for the variations. For demonstration, the new procedure is applied to a finite element model of the Goland wing undergoing oscillations and shown to produce extremely accurate reduced-order surrogate model for a wide range of parameter variations.

Modified Modal Domain Analysis of a Bladed Rotor Using Coordinate Measurement Machine Data on Geometric Mistuning

Modified modal domain analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistuned integrally bladed rotor to obtain its natural frequencies, mode shapes, and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 deg) rotor Ansys model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from frequency mistuning approaches, fundamental mistuning model (FMM) and subset of nominal modes (SNM), are also generated and compared to those from full (360 deg) rotor Ansys model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

Effects of a Group of High-Rise Structures on Ground Motions under Seismic Excitation

A three-dimensional simulation was created to determine the seismic performance of coupled systems with a group of up to 100 pile-high-rise structures resting on soil layers using system modal, harmonic, and time domain analysis. The results demonstrated that the existence of a structural group mitigates the structural responses with respect to the single-structure-soil interaction (SSI) and results in significantly nonuniform ground seismic motions. Due to the influence of a structural group, adjacent structures can exhibit fully alternating mechanical behavior, and buildings in the urban fringe are subjected to stronger shaking than downtown buildings. The overall trend of the influence of structural groups is that ground motions are lessened inside an urban area, and ground motions at the locations between structures differ from those at the locations of the structures. Moreover, the effective distance of a structural group on ground motions is associated with the urban width. Less distance between structures enhances the interaction effect. In addition, the soil properties can greatly influence the system’s seismic responses and can even completely change the effect trends. The results in our paper are consistent with the phenomena observed in the Mexico City earthquake and the 1976 earthquake in Friuli, Italy.

Geometric Mistuning Identification of Integrally Bladed Rotors Using Modified Modal Domain Analysis

Modified modal domain analysis (MMDA) is a novel method for the development of a reduced order model of a bladed rotor with geometric mistuning. This method utilizes proper orthogonal decomposition (POD) of coordinate measurement machine (CMM) data on blades' geometries, and sector analyses using ansys and solid modeling. In a recent paper, MMDA has been extended to use second order Taylor series approximations of perturbations in mass and stiffness matrices (δM and δK) instead of exact δM and δK. Taylor series expansions of deviations in mass and stiffness matrices due to geometric mistuning give a direct approach for generating the reduced order model from the components of POD features of spatial variations in blades' geometries. Reversing the process, algorithms for mistuning identification based on MMDA are presented in this paper to calculate the geometric mistuning parameters. Two types of algorithm, one based on modal analyses and the other on the forced responses, are presented. The validity of these methods are then verified through a mistuned academic rotor.

Vega In-Flight Modal Identification with the Operational Modal Analysis Technique

Operational modal analysis is an interesting procedure that allows identification of the modal characteristic parameters of structures excited randomly by environmental loads. In this paper, an existing operational modal technique, the natural excitation technique is studied and implemented to obtain the modal parameters of the Vega launcher excited by in-flight loads during its maiden flight. The modal parameters of the Vega launcher, obtained with the operational modal technique, are compared with those from a finite element model designed for the same flight event. Because the dynamic system is not stationary due to propellant mass loss, modal identification is only possible using a series of linearized models over short periods of time. In this work, the extraction of modal parameters is performed in the time window that shows the highest excitation of mode shapes. The time domain modal analysis method, Least-Squares Complex Exponential, is used to extract the modal parameters from the correlation functions generated by the natural excitation technique. Results show good agreement with the corresponding ones obtained from the finite element model; this demonstrates that the natural excitation technique can be successfully employed for the extraction of modal parameters of launch vehicles during the flight phase.

Design and Analysis of Ultrasonic Motor for Driving Sphere Wheel

In this paper, a new omnidirectional driving system is proposed that is composed of an ultrasonic motor, a sphere wheel, and ball bearings. The sphere wheel is driven by an ultrasonic motor, which is a Λ-type motor developed in the previous research. If the piezo-ceramic plates of the ultrasonic motor vibrate at the resonant frequency, the displacement of the ellipse orbit is generated at a sharp end of Λ-type. Modal analysis and time domain analysis were performed. The proposed omnidirectional driving system was validated by analyzing its motion characteristics.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

Reduced Order Modeling of a Bladed Rotor With Geometric Mistuning Via Estimated Deviations in Mass and Stiffness Matrices

This paper deals with further development of modified modal domain analysis (MMDA), which is a breakthrough method in the reduced order modeling of a bladed rotor with geometric mistuning. The main focus of this paper is to show that deviations in mass and stiffness matrices due to mistuning, estimated by Taylor series expansions in terms of independent proper orthogonal decomposition variables representing geometric variations of blades, can be used for MMDA. This result has rendered Monte Carlo simulation of the response of a bladed rotor with geometric mistuning to be easy and computationally efficient.