scholarly journals A Reduced-Order Model for the Vibration Analysis of Mistuned Blade–Disc–Shaft Assembly

2019 ◽  
Vol 9 (22) ◽  
pp. 4762
Author(s):  
Wang ◽  
Bi ◽  
Zheng
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Order Reduction ◽  
Symmetry Analysis ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Reduced Order

An effective reduced-order model is presented in this paper for the vibration analysis of a mistuned blade–disc–shaft assembly considering the flexibility of the shaft and the rotordynamic effects. For the sake of accurate modeling and quantitative analysis, three-dimensional (3D) finite element models were employed in obtaining the governing equations of motion with the Coriolis force, centrifugal stiffening, and spin softening effects taken into account. Then, an efficient model order reduction technique based on the coordinate projection by normal modes of tuned assembly and cyclic symmetry analysis was developed for mistuned blade–disc–shaft assembly. The criterion of whether one matrix could be incorporated in cyclic symmetry analysis is presented. During the modeling, the mistuning in blade and disc was taken into account and dealt with independently. In mistuning projection, the blade and disc parts were both projected onto their tuned counterparts of the sector model, where the boundary conditions were set to be fixed and free, respectively. Finally, an example of a blade–disc–shaft assembly was employed to validate the effectiveness of the presented method in free and forced vibration analysis.

scholarly journals A Hybrid Reduced-Order Model for the Aeroelastic Analysis of Flexible Subsonic Wings—A Parametric Assessment

Aerospace ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 76 ◽  
Author(s):  
Marco Berci ◽  
Rauno Cavallaro
Keyword(s):  
Structural Parameters ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Reduced Order Model ◽  
Order Model ◽  
Flexible Wings ◽  
Reduced Order ◽  
Aeroelastic Analysis ◽  
Strip Theory

A hybrid reduced-order model for the aeroelastic analysis of flexible subsonic wings with arbitrary planform is presented within a generalised quasi-analytical formulation, where a slender beam is considered as the linear structural dynamics model. A modified strip theory is proposed for modelling the unsteady aerodynamics of the wing in incompressible flow, where thin aerofoil theory is corrected by a higher-fidelity model in order to account for three-dimensional effects on both distribution and deficiency of the sectional air load. Given a unit angle of attack, approximate expressions for the lift decay and build-up are then adopted within a linear framework, where the two effects are separately calculated and later combined. Finally, a modal approach is employed to write the generalised equations of motion in state-space form. Numerical results were obtained and critically discussed for the aeroelastic stability analysis of a uniform rectangular wing, with respect to the relevant aerodynamic and structural parameters. The proposed hybrid model provides sound theoretical insights and is well suited as an efficient parametric reduced-order aeroelastic tool for the preliminary multidisciplinary design and optimisation of flexible wings in the subsonic regime.

scholarly journals Order Reduction based on Coulomb’s and Franklin’s laws Algorithm

2021 ◽  
Author(s):  
Ram Kumar ◽  
Afzal Sikander
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Absolute Error ◽  
Search Space ◽  
Engineering Problem ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Linear Time Invariant

Abstract The Coulomb and Franklin laws (CFL) algorithm is used to construct a lower order model of higher-order continuous time linear time-invariant (LTI) systems in this study. CFL is quite easy to implement in obtaining reduced order model of large scale system in control engineering problem as it employs the combined effect of Coulomb’s and Franklin’s laws to find the best values in search space. The unknown coefficients are obtained using the CFLA methodology, which minimises the integral square error (ISE) between the original and proposed ROMs. To achieve the reduced order model, five practical systems of different orders are considered. Finally, multiple performance indicators such as the ISE, integral of absolute error (IAE), and integral of time multiplied by absolute error were calculated to determine the efficacy of the proposed methodology. The simulation results were compared to previously published well-known research.

Decentralized Control of a Tower Crane

1999 ◽  
Author(s):  
Kiyoshi Takagi ◽  
Hidekazu Nishimura
Keyword(s):  
Decentralized Control ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Flexible Structure ◽  
Order Model ◽  
Modeling And Control ◽  
Reduced Order ◽  
Tower Crane ◽  
Three Dimensional Models ◽  
And Control

Abstract This paper deals with modeling and control of a crane mounted on a tower-like flexible structure. A fast transfer of the load causes the sway of the load rope and the vibration of the flexible structure. Our object is to control both the sway and the vibration by the inherent capability of the tower crane. This paper makes its three-dimensional models for simulation and reduced-order-model in order to design the decentralized control system. Then, we design the decentralized H∞ compensator and verify the efficiency by simulations and experiments.

Design of a Kangaroo Inspired Hopping Robot for Unrestricted Locomotion and Controller Development

2019 ◽  
Author(s):  
Austin Curtis ◽  
James Mynderse ◽  
Hamid Vejdani
Keyword(s):  
Frequency Response ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Design Parameters ◽  
Order Model ◽  
Reduced Order ◽  
Gait Performance ◽  
System Parameters ◽  
Hopping Robot ◽  
The Relationship

Abstract Inspired by the agility and maneuverability of running kangaroos, a prototype robot was developed using a reduced order model to constrain the system. Both passive and active models were used to understand the relationship between system parameters and gait performance. A frequency response experiment was performed on the prototype to quantify the relationship between design parameters and system responses. Additionally, preliminary tail controllers were tested. Based on the results of the initial platform, a new robot was designed and built as a platform for the study of three dimensional hopping.

Model Simplification and Stability Robustness With Elastic Flight Vehicles

1995 ◽  
Vol 117 (3) ◽  
pp. 336-342
Author(s):  
Brett Newman ◽  
David K. Schmidt
Keyword(s):  
Closed Loop ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Control Law ◽  
Model Simplification ◽  
Closed Loop System ◽  
Order Model ◽  
Reduced Order ◽  
Stability Robustness

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced order model will be preserved when controlling the higher order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. A weighted balanced order reduction technique is shown to lead to results that meet the necessary criteria. The procedure is applied to an aeroelastic vehicle model, and the results are used for control law development. Critical robustness properties designed into the lower order closed-loop system are shown to be present in the higher order closed-loop system.

A Ranking Method for the Selection of the Interior Modes of Reduced Order Resonant System Models

2014 ◽  
Author(s):  
Ilaria Palomba ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Normal Modes ◽  
Reduced Order Model ◽  
Ranking Method ◽  
Resonant System ◽  
Order Model ◽  
Reduced Order ◽  
Design And Optimization ◽  
Optimization Stage ◽  
Dimensional Models ◽  
Selection Of

Resonant system design and optimization is usually supported by finite element models. Large dimensional models are often needed to achieve the desired accuracy in the representation of the vibrational behaviour at the frequency of interest. Unfortunately, large dimensional models are frequently too cumbersome to be actually useful, mainly at the optimization stage. On the other hand, the choice of the most appropriate reduction strategy and dimension for a reduced-order model is generally left to designers’ experience. Having recognized the effectiveness and spreading of the Craig Bampton reduction technique, the aim of this paper is to propose a rigorous ranking method, called Interior Mode Ranking (IMR), for the selection of the interior normal modes of the full order model to be inherited by the reduced order one. The method is aimed at finding the set of interior modes of minimum dimensions which allows achieving a desired level of accuracy of the reduced order model at a frequency of interest. The method is here applied to a resonator widely employed in industry: an ultrasonic welding bar horn, which is usually designed to operate excited in resonance. The results achieved through the application of the IMR method are compared with those yielded by other ranking techniques available in literature in order to prove its effectiveness.

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

scholarly journals A Reduced-Order Model of Detuned Cyclic Dynamical Systems With Geometric Modifications Using a Basis of Cyclic Modes

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Moustapha Mbaye ◽  
Christian Soize ◽  
Jean-Philippe Ousty
Keyword(s):  
Reduction Method ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Element Analysis ◽  
Disk Model ◽  
Reduced Order ◽  
Bladed Disk ◽  
Forced Responses ◽  
Sector Matrix

A new reduction method for vibration analysis of intentionally mistuned bladed disks is presented. The method is built for solving the dynamic problem of cyclic structures with geometric modifications. It is based on the use of the cyclic modes of the different sectors, which can be obtained from a usual cyclic symmetry modal analysis. Hence the projection basis is constituted; as well as, on the whole bladed disk, each sector matrix is reduced by its own modes. The method is validated numerically on a real bladed disk model, by comparing free and forced responses of a full model finite element analysis to those of a reduced-order model using the new reduction method.

scholarly journals Suboptimal Control Using Model Order Reduction

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Avadh Pati ◽  
Awadhesh Kumar ◽  
Dinesh Chandra
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Suboptimal Control ◽  
Order Model ◽  
Model Order ◽  
Markov Parameters ◽  
Reduced Order ◽  
Partial Feedback

A Padé approximation based technique for designing a suboptimal controller is presented. The technique uses matching of both time moments and Markov parameters for model order reduction. In this method, the suboptimal controller is first derived for reduced order model and then implemented for higher order plant by partial feedback of measurable states.

On a New Nonlinear Reduced-Order Model for Capturing Internal Resonances in Intentionally Mistuned Cyclic Structures

2020 ◽  
Author(s):  
Samuel Quaegebeur ◽  
Benjamin Chouvion ◽  
Fabrice Thouverez ◽  
Loïc Berthe
Keyword(s):  
Nonlinear Response ◽  
Forced Response ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Internal Resonances ◽  
Present Material ◽  
Reduced Order ◽  
Modal Synthesis ◽  
Excitation Force

Abstract Cyclic structures such as turbomachinery present material and geometrical variations between sectors. These discrepancies are called mistuning and break the cyclic symmetry of the structure. Computing the forced response of mistuned cyclic structures is thus a numerical challenge. The Component Nonlinear Complex Mode Synthesis (CNCMS) is one of the few nonlinear reduced-order model formulations that allow to compute the nonlinear response of tuned and mistuned structures. It has been validated successfully for friction problems. However, in the presence of geometric nonlinearities, internal resonances may arise and they cannot be captured correctly with the CNCMS method. The purpose of this work is therefore to present a new methodology for developing a nonlinear reduced-order model that can successfully capture internal resonances for tuned and mistuned structures. This method, called Component Mode Synthesis with Nonlinear Re-evaluation (CMSNR), is based on a variation of the CNCMS approach. The final modal synthesis uses a multi-harmonic procedure and a re-evaluation of the nonlinear forces on each sector independently. The performance and limitations of the proposed approach are assessed using a simplified example of a blisk subject to polynomial nonlinearities. Different internal resonances are exhibited and studied depending on the type of excitation force and on the level of mistuning.

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