Pub Date : 1997-11-16DOI: 10.1080/03052159908941291
R. Jha, A. Chattopadhyay
An integrated multidisciplinary procedure has been developed for structural and aeroelastic optimization of composite wings based on refined analysis technique. A refined higher-order theory is used to analyze composite box beam, which represents the load carrying member of the wing. Unsteady aerodynamic computations are performed using a panel code based on the Doublet Lattice Method. Flutter/divergence dynamic pressure is obtained by the Laplace domain method through rational function approximation of unsteady aerodynamic loads. The objective of the optimization procedure is to minimize wing structural weight with constraints on flutter/divergence speed and stresses at the root due to the static load. Composite ply orientations and laminate thicknesses are used as design variables. The Kreisselmeier-Steinhauser function approach is used to efficiently integrate the objective function and constraints into a single envelope function. The resulting unconstrained optimization problem is solved using the Davidon-Fletcher-Powell algorithm. Numerical results are presented showing significant improvements, after optimization, compared to a reference design.
{"title":"Multidisciplinary Optimization of Composite Wings Using Refined Structural and Aeroelastic Analysis Methodologies","authors":"R. Jha, A. Chattopadhyay","doi":"10.1080/03052159908941291","DOIUrl":"https://doi.org/10.1080/03052159908941291","url":null,"abstract":"\u0000 An integrated multidisciplinary procedure has been developed for structural and aeroelastic optimization of composite wings based on refined analysis technique. A refined higher-order theory is used to analyze composite box beam, which represents the load carrying member of the wing. Unsteady aerodynamic computations are performed using a panel code based on the Doublet Lattice Method. Flutter/divergence dynamic pressure is obtained by the Laplace domain method through rational function approximation of unsteady aerodynamic loads. The objective of the optimization procedure is to minimize wing structural weight with constraints on flutter/divergence speed and stresses at the root due to the static load. Composite ply orientations and laminate thicknesses are used as design variables. The Kreisselmeier-Steinhauser function approach is used to efficiently integrate the objective function and constraints into a single envelope function. The resulting unconstrained optimization problem is solved using the Davidon-Fletcher-Powell algorithm. Numerical results are presented showing significant improvements, after optimization, compared to a reference design.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115509834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper describes extensive computer-based analytical studies on the details of unsteady flow behavior around oscillating airfoils in turbomachinery. To consider the time-dependent motions of airfoils, a complete Navier-Stokes solver incorporating a moving mesh was applied, and the drag and lift coefficients for the cases of stationary airfoils and airfoils subjected to forced oscillation were examined. In order to clarify the interaction between the airfoil structure and the flow induced force, the exact fluctuation of the drag and lift coefficients with time needed to be determined. Although two-dimensional analyses have been performed for two-dimensional airfoils, it has suggested to be difficult to obtain the true separation vortex in such analyses because the vortex structure is essentially three-dimensional. Therefore, in the present study, a comparison was made between the two- and three-dimensional analyses for NACA0012 airfoils, and the separation vortex structure was examined in detail. From the numerical results, it was found that the separation vortex consisted of large-scale rolls with axes in the span direction, and rib substructures with axes in the stream direction. The three-dimensional analysis could simulate these rolls and ribs, but the two-dimensional analysis was inadequate to realize this vortex structure. This is the main difference between the two- and three-dimensional analyses. In addition, the formation of ribs was found to be affected by the forced oscillation, and the transformation of rolls increased and the vortex structure became more fine as the oscillation frequency increased.
{"title":"Two- and Three-Dimensional Analyses of Flow Around Airfoils Subjected to Forced Oscillation","authors":"Y. Yokono","doi":"10.1115/imece1997-0170","DOIUrl":"https://doi.org/10.1115/imece1997-0170","url":null,"abstract":"\u0000 This paper describes extensive computer-based analytical studies on the details of unsteady flow behavior around oscillating airfoils in turbomachinery. To consider the time-dependent motions of airfoils, a complete Navier-Stokes solver incorporating a moving mesh was applied, and the drag and lift coefficients for the cases of stationary airfoils and airfoils subjected to forced oscillation were examined. In order to clarify the interaction between the airfoil structure and the flow induced force, the exact fluctuation of the drag and lift coefficients with time needed to be determined. Although two-dimensional analyses have been performed for two-dimensional airfoils, it has suggested to be difficult to obtain the true separation vortex in such analyses because the vortex structure is essentially three-dimensional. Therefore, in the present study, a comparison was made between the two- and three-dimensional analyses for NACA0012 airfoils, and the separation vortex structure was examined in detail.\u0000 From the numerical results, it was found that the separation vortex consisted of large-scale rolls with axes in the span direction, and rib substructures with axes in the stream direction. The three-dimensional analysis could simulate these rolls and ribs, but the two-dimensional analysis was inadequate to realize this vortex structure. This is the main difference between the two- and three-dimensional analyses. In addition, the formation of ribs was found to be affected by the forced oscillation, and the transformation of rolls increased and the vortex structure became more fine as the oscillation frequency increased.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124322603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rotorcraft stability investigation involves a nonlinear trim analysis for the control inputs and periodic responses, and, as a follow-up, a linearized stability analysis for the Floquet transition matrix (FTM), and its eigenvalues and eigenvectors. The trim analysis is based on a shooting method with damped Newton iteration, which gives the FTM as a byproduct, and the eigenanalysis on the QR method; the corresponding trim and stability analyses are collectively referred to as the Floquet analysis. A rotor with Q blades that are identical and equally spaced has Q planes of symmetry. Exploiting this symmetry, the fast-Floquet analysis, in principle, reduces the run time and frequency indeterminacy of the conventional Floquet analysis by a factor of Q. It is implemented on serial computers and on all three types of mainstream parallel-computing hardware: SIMD and MIMD computers, and a distributed computing system of networked workstations; large models with hundreds of states are treated. A comprehensive database is presented on computational reliability such as the eigenvalue condition number and on parallel performance such as the speedup and efficiency, which show, respectively, how fast a job can be completed with a set of processors and how well their idle times are minimized. Despite the Q-fold reduction, the serial run time is excessive and grows between quadratically and cubically with the number of states. By contrast, the parallel run time can be reduced dramatically and its growth can be controlled by a judicious combination of speedup and efficiency. Moreover, the parallel implementation on a distributed computing system is as routine as the serial implementation.
{"title":"Serial and Parallel Fast-Floquet Analyses in Rotorcraft Aeroelasticity","authors":"S. Subramanian, S. Venkataratnam, G. Gaonkar","doi":"10.1115/imece1997-0158","DOIUrl":"https://doi.org/10.1115/imece1997-0158","url":null,"abstract":"Rotorcraft stability investigation involves a nonlinear trim analysis for the control inputs and periodic responses, and, as a follow-up, a linearized stability analysis for the Floquet transition matrix (FTM), and its eigenvalues and eigenvectors. The trim analysis is based on a shooting method with damped Newton iteration, which gives the FTM as a byproduct, and the eigenanalysis on the QR method; the corresponding trim and stability analyses are collectively referred to as the Floquet analysis. A rotor with Q blades that are identical and equally spaced has Q planes of symmetry. Exploiting this symmetry, the fast-Floquet analysis, in principle, reduces the run time and frequency indeterminacy of the conventional Floquet analysis by a factor of Q. It is implemented on serial computers and on all three types of mainstream parallel-computing hardware: SIMD and MIMD computers, and a distributed computing system of networked workstations; large models with hundreds of states are treated. A comprehensive database is presented on computational reliability such as the eigenvalue condition number and on parallel performance such as the speedup and efficiency, which show, respectively, how fast a job can be completed with a set of processors and how well their idle times are minimized. Despite the Q-fold reduction, the serial run time is excessive and grows between quadratically and cubically with the number of states. By contrast, the parallel run time can be reduced dramatically and its growth can be controlled by a judicious combination of speedup and efficiency. Moreover, the parallel implementation on a distributed computing system is as routine as the serial implementation.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"136 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114926331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Unsteady flowfields around airfoils pitching or/and plunging are investigated. The objective of this study is to test the ability of our computational code to predict unsteady fluid/structure interaction in the context of the incompressible Navier-Stokes equations. A physically consistent method is used for the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balance. To validate the code, a dynamic-stall case is presented. Different cases in fluid/structure interaction are studied. Firstly, we examine the case where the airfoil have only a single plunging degree of freedom. Then, the airfoil can just pitch about the mid-chord. Endly, the airfoil motion consits in plunging and pitching.
{"title":"Unsteady Aeroelastic Simulations for Airfoils","authors":"E. Guilmineau, P. Queutey","doi":"10.1115/imece1997-0164","DOIUrl":"https://doi.org/10.1115/imece1997-0164","url":null,"abstract":"\u0000 Unsteady flowfields around airfoils pitching or/and plunging are investigated. The objective of this study is to test the ability of our computational code to predict unsteady fluid/structure interaction in the context of the incompressible Navier-Stokes equations. A physically consistent method is used for the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balance. To validate the code, a dynamic-stall case is presented. Different cases in fluid/structure interaction are studied. Firstly, we examine the case where the airfoil have only a single plunging degree of freedom. Then, the airfoil can just pitch about the mid-chord. Endly, the airfoil motion consits in plunging and pitching.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115836742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe a new method for computing an arbitrary number of eigen solutions of a given aeroelastic problem. The proposed method is based on the re-engineering of a three-way coupled formulation previously developed for the solution in the time domain of nonlinear transient aeroelastic problems. It is applicable in subsonic, transonic, and supersonic flow regimes, and independently from the frequency or damping level of the target aeroelastic modes. It is based on the computation of the complex eigen solution of a carefully linearized fluid/structure interaction problem, and relies on the inverse orthogonal iteration algorithm. We illustrate this method with the stability analysis of a flat panel with infinite aspect ratio in supersonic airstreams and the AGARD 445.6 aeroelastic wing. For these aeroelastic problems, we show that the results produced by the proposed eigen solution method are in excellent agreement with those predicted analytically and numerically as well as with experimental data.
{"title":"Re-Engineering of an Aeroelastic Code for Solving Eigen Problems in All Flight Regimes","authors":"M. Lesoinne, C. Farhat","doi":"10.1115/imece1997-0171","DOIUrl":"https://doi.org/10.1115/imece1997-0171","url":null,"abstract":"\u0000 We describe a new method for computing an arbitrary number of eigen solutions of a given aeroelastic problem. The proposed method is based on the re-engineering of a three-way coupled formulation previously developed for the solution in the time domain of nonlinear transient aeroelastic problems. It is applicable in subsonic, transonic, and supersonic flow regimes, and independently from the frequency or damping level of the target aeroelastic modes. It is based on the computation of the complex eigen solution of a carefully linearized fluid/structure interaction problem, and relies on the inverse orthogonal iteration algorithm. We illustrate this method with the stability analysis of a flat panel with infinite aspect ratio in supersonic airstreams and the AGARD 445.6 aeroelastic wing. For these aeroelastic problems, we show that the results produced by the proposed eigen solution method are in excellent agreement with those predicted analytically and numerically as well as with experimental data.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126863969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we study the requirements that must be satisfied by a fluid-structure coupling scheme, in order to obtain a dynamically consistent aeroelastic code. Both spatial compatibility and time synchronization requirements must be met, to assure that the time-marching simulations exhibit the physically correct stability behavior. Inconsistent or inaccurate implementation of the fluid-structure boundary conditions can cause the aeroelastic code to converge to an incorrect aeroelastic solution. It is shown that CFD codes based on linear interpolations for the velocities cannot be fully compatible with structural FE codes that use plate or shell elements to model the wing skin. Numerical examples are presented for three different nonlinear aeroelastic models, using Euler-based aerodynamics and two different fluid-structure coupling schemes. The results indicate that for Mach numbers in the upper transonic range, past the transonic dip, the aeroelastic solution appears very sensitive to the fluid-structure coupling scheme used. In the case of the NACA 0012 model, the two different schemes studied predicted entirely different stability behaviors.
{"title":"Fluid-Structure Coupling Requirements for Time-Accurate Aeroelastic Simulations","authors":"O. Bendiksen","doi":"10.1115/imece1997-0161","DOIUrl":"https://doi.org/10.1115/imece1997-0161","url":null,"abstract":"\u0000 In this paper we study the requirements that must be satisfied by a fluid-structure coupling scheme, in order to obtain a dynamically consistent aeroelastic code. Both spatial compatibility and time synchronization requirements must be met, to assure that the time-marching simulations exhibit the physically correct stability behavior. Inconsistent or inaccurate implementation of the fluid-structure boundary conditions can cause the aeroelastic code to converge to an incorrect aeroelastic solution. It is shown that CFD codes based on linear interpolations for the velocities cannot be fully compatible with structural FE codes that use plate or shell elements to model the wing skin. Numerical examples are presented for three different nonlinear aeroelastic models, using Euler-based aerodynamics and two different fluid-structure coupling schemes. The results indicate that for Mach numbers in the upper transonic range, past the transonic dip, the aeroelastic solution appears very sensitive to the fluid-structure coupling scheme used. In the case of the NACA 0012 model, the two different schemes studied predicted entirely different stability behaviors.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114798452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to study the effects of wing mounted stores upon the aeroelasticity of advanced aircraft wings, a comprehensive structural model has been developed. The wing structure is idealized as a laminated composite plate thus leading to the concept of a shear deformable plate-beam model. Free body motions at the wing root are induced by the motion of the airframe in pitching, plunging, and rolling. Non-classical effects like warping inhibition and transverse shear flexibility are included in the structural model. The relevant equations of motion as well as the appropriate boundary conditions are obtained via Hamilton’s variational principle and application of generalized function theory in order to exactly consider the spanwise location and properties of the attached stores. Numerical predictions for divergence behavior and static aeroelastic response of the system using extended Galerkin’s Method are supplied.
{"title":"Modeling and Aeroelasticity of Advanced Aircraft Wings Carrying External Stores","authors":"F. Gern, L. Librescu","doi":"10.1115/imece1997-0169","DOIUrl":"https://doi.org/10.1115/imece1997-0169","url":null,"abstract":"\u0000 In order to study the effects of wing mounted stores upon the aeroelasticity of advanced aircraft wings, a comprehensive structural model has been developed. The wing structure is idealized as a laminated composite plate thus leading to the concept of a shear deformable plate-beam model. Free body motions at the wing root are induced by the motion of the airframe in pitching, plunging, and rolling. Non-classical effects like warping inhibition and transverse shear flexibility are included in the structural model. The relevant equations of motion as well as the appropriate boundary conditions are obtained via Hamilton’s variational principle and application of generalized function theory in order to exactly consider the spanwise location and properties of the attached stores. Numerical predictions for divergence behavior and static aeroelastic response of the system using extended Galerkin’s Method are supplied.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"386 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114090132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A two-dimensional unsteady potential flow outside an elastic partially cavitating wing is analyzed numerically by using the Birnbaum equation on hydrofoil chord and the Lagrange-Cauchy integral on the cavity. An angle of attack has a small periodic perturbation, and cavity thickness and length have got perturbations too. Wing vibration is considered as vibration of a variable thickness beam with two clamp bolts near the beam center. A mono-frequency flow perturbation induces mono-frequency flexural vibration of a non-cavitating wing, but the vibration of a cavitating wing is multy-frequency one, and a spectrum of a cavitating wing response can depend on an amplitude of the incoming flow perturbation. Numerical simulation of NACA-16009 hydrofoil vibration was made for various free-stream speeds, module of elasticity, fluid and wing densities, and as a result, three frequency bands of a vibration increase are found. The low-frequency band is connected with a cavity volume oscillation. There is a considerable effect of cavity length, therefore the cavitation number influences on vibration as a parameter. The high-frequency band is connected with elastic resonances of wing. Besides, resonance-like frequencies were found in the middle band. This phenomenon has not a dependence on cavity dimensions and wing elasticity, but appears as a result of an interaction between hydrodynamic damping and media inertia forces.
{"title":"Parametric Vibration of Elastic Cavitating Wing in Unsteady Flow","authors":"S. Kovinskaya, E. Amromin","doi":"10.1115/imece1997-0163","DOIUrl":"https://doi.org/10.1115/imece1997-0163","url":null,"abstract":"\u0000 A two-dimensional unsteady potential flow outside an elastic partially cavitating wing is analyzed numerically by using the Birnbaum equation on hydrofoil chord and the Lagrange-Cauchy integral on the cavity. An angle of attack has a small periodic perturbation, and cavity thickness and length have got perturbations too. Wing vibration is considered as vibration of a variable thickness beam with two clamp bolts near the beam center. A mono-frequency flow perturbation induces mono-frequency flexural vibration of a non-cavitating wing, but the vibration of a cavitating wing is multy-frequency one, and a spectrum of a cavitating wing response can depend on an amplitude of the incoming flow perturbation.\u0000 Numerical simulation of NACA-16009 hydrofoil vibration was made for various free-stream speeds, module of elasticity, fluid and wing densities, and as a result, three frequency bands of a vibration increase are found. The low-frequency band is connected with a cavity volume oscillation. There is a considerable effect of cavity length, therefore the cavitation number influences on vibration as a parameter. The high-frequency band is connected with elastic resonances of wing. Besides, resonance-like frequencies were found in the middle band. This phenomenon has not a dependence on cavity dimensions and wing elasticity, but appears as a result of an interaction between hydrodynamic damping and media inertia forces.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121882604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The flow field around a lifting rotor in hover or forward flight is represented by a matched expansion that includes an inner expansion (near the blade chord) and an outer expansion that encompasses the rotor disk. The inner expansion is expanded in Glauert variables and is completely unsteady. It is driven by blade motions and the global flow-field variable λ0 which is provided by the outer expansion. The outer expansion is in terms of rotor harmonics and radial Legendre functions (which are polynomials in r− on the blade). It is driven by the time-rate of change of bound circulation as provided from the inner expansion. Together, these form a robust convergent expansion of the rotor flow field that is good over a broad range of frequencies.
{"title":"Extension of Dynamic Wake Models for Moderate to High Reduced Frequencies","authors":"D. Peters, S. Karunamoorthy, Michael Sobol","doi":"10.1115/imece1997-0157","DOIUrl":"https://doi.org/10.1115/imece1997-0157","url":null,"abstract":"\u0000 The flow field around a lifting rotor in hover or forward flight is represented by a matched expansion that includes an inner expansion (near the blade chord) and an outer expansion that encompasses the rotor disk. The inner expansion is expanded in Glauert variables and is completely unsteady. It is driven by blade motions and the global flow-field variable λ0 which is provided by the outer expansion. The outer expansion is in terms of rotor harmonics and radial Legendre functions (which are polynomials in r− on the blade). It is driven by the time-rate of change of bound circulation as provided from the inner expansion. Together, these form a robust convergent expansion of the rotor flow field that is good over a broad range of frequencies.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125825047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-11-16DOI: 10.1061/(ASCE)0893-1321(1998)11:2(59)
N. Namachchivaya, A. Lee
This paper investigates the effects of nonlinearities on the dynamics of flat panels in supersonic flow and presents new bifurcation results for a fairly general nonlinear aeroelastic system. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools. The first part of this paper deals with modeling unsteady aerodynamic forces and moments acting on flat panels undergoing arbitrary motion in supersonic flow. This modeling also considers the structural nonlinearities inherent in panels. While deriving the equations of motion, many in the past have neglected some nonlinear aerodynamic terms as insignificant from the modeling point of view. However, inclusion of these terms in the analysis may completely change the bifurcation behavior. In aeroelastic systems it is the nonlinear dissipative terms that can change the behavior, and it is essential to carefully model these terms in the physical problems. In the absence of dissipative terms the nonlinear system is reversible, which provides the governing equations with near integrable structure. Thus certain analytical methods are used to study the bifurcation behavior of the system near critical points. For general nonlinear fiat panels in supersonic flow, we present these effects as various bifurcation results due to symmetry-breaking imperfections. For aeroelastic systems, the reversible symmetry is broken by the addition of unsteady aerodynamic terms.
{"title":"Dynamics of Nonlinear Aeroelastic Systems","authors":"N. Namachchivaya, A. Lee","doi":"10.1061/(ASCE)0893-1321(1998)11:2(59)","DOIUrl":"https://doi.org/10.1061/(ASCE)0893-1321(1998)11:2(59)","url":null,"abstract":"\u0000 This paper investigates the effects of nonlinearities on the dynamics of flat panels in supersonic flow and presents new bifurcation results for a fairly general nonlinear aeroelastic system. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools. The first part of this paper deals with modeling unsteady aerodynamic forces and moments acting on flat panels undergoing arbitrary motion in supersonic flow. This modeling also considers the structural nonlinearities inherent in panels. While deriving the equations of motion, many in the past have neglected some nonlinear aerodynamic terms as insignificant from the modeling point of view. However, inclusion of these terms in the analysis may completely change the bifurcation behavior. In aeroelastic systems it is the nonlinear dissipative terms that can change the behavior, and it is essential to carefully model these terms in the physical problems. In the absence of dissipative terms the nonlinear system is reversible, which provides the governing equations with near integrable structure. Thus certain analytical methods are used to study the bifurcation behavior of the system near critical points. For general nonlinear fiat panels in supersonic flow, we present these effects as various bifurcation results due to symmetry-breaking imperfections. For aeroelastic systems, the reversible symmetry is broken by the addition of unsteady aerodynamic terms.","PeriodicalId":166345,"journal":{"name":"4th International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise: Volume III","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129342575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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