Results for “Modal coupling” — Page 7

NASA NTRS1989

Vortical flow computations on swept flexible wings using Navier-Stokes equations

A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of swept flexible wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The calculations are compared with the experiment when available. Effects of flexibility, sweep angle, and pitch rate are demonstrated for flows with vortices.

Guruswamy, Guru P.↗

NASA NTRS1990

Navier-Stokes computations on swept-tapered wings, including flexibility

A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of flexible fighter wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The coupled calculations are compared with experiments when available. Effects of flexibility and pitch rate are demonstrated for flows with vortices. Turbulent flow computations are also compared with laminar flow computations.

Guruswamy, Guru P.↗

NASA NTRS1993

Piezoelectric actuator models for active sound and vibration control of cylinders

Analytical models for piezoelectric actuators, adapted from flat plate concepts, are developed for noise and vibration control applications associated with vibrating circular cylinders. The loadings applied to the cylinder by the piezoelectric actuators for the bending and in-plane force models are approximated by line moment and line force distributions, respectively, acting on the perimeter of the actuator patch area. Coupling between the cylinder and interior acoustic cavity is examined by studying the modal spectra, particularly for the low-order cylinder modes that couple efficiently with the cavity at low frequencies. Within the scope of this study, the in-plane force model produced a more favorable distribution of low-order modes, necessary for efficient interior noise control, than did the bending model.

Lester, Harold C.↗

NASA NTRS1988

Aeroelastic analysis of hammerhead payloads

A launch vehicle aeroelastic stability method is presented in order to treat transonic flight problems that are characteristic of 'hammerhead' payload geometries. Navier-Stokes formulation-based CFD techniques are used to simulate the unsteady aerodynamic flowfields, and time-domain aeroelastic analyses are performed by coupling this flow solver with a modal representation of the vehicle's structural-dynamic characteristics. Numerical applications encompass the study of an Atlas-Able IV configuration in various flight conditions; good qualitative agreement with observations is obtained.

Azevedo, Joao Luis F.↗

NASA NTRS1991

Maneuver simulations of flexible spacecraft by solving TPBVP

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

Bainum, Peter M.↗

NASA NTRS1991

Simulation of the Space Station strut-out condition

A method is presented for reanalyzing a truss structure when one of the truss elements (struts) has failed. The method uses a modal model of the nominal structure coupled with a residual flexibility term to predict the effect of the failed strut without resolving the finite element model. By implementing the method as part of the transient simulation, it is feasible to consider a large number of potential strut failures with a minimum amount of extra effort. Preliminary application of the method to the Space Station indicates excellent agreement with results based on modifying and resolving the finite element model.

Blelloch, Paul A.↗

NASA NTRS1992

Computation of antenna vibration mode elastic-rigid and effective-weight coefficients

A significant amount of both qualitative and quantitative information about structures can be derived from the elastic-rigid structural coupling matrices, and from the effective modal inertias and masses. Typical finite-element analysis programs do not provide this information as part of the regular output. This report presents an easy way to develop the necessary information from ordinary program output, and shows how to deal with alternative origins for the reference coordinate system.

Levy, R.↗

NASA NTRS1999

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗

NASA NTRS2004

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗

NASA NTRS2005

Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Przekop, Adam↗

NASA NTRS2006

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Przekop, Adam↗

NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗

NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗

NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗

NASA NTRS1995

Calculated coupling efficiency between an elliptical-core optical fiber and an optical waveguide over temperature

To determine the feasibility of coupling the output of a single-mode optical fiber into a single-mode rib waveguide in a temperature varying environment, a theoretical calculation of the coupling efficiency between the two was investigated. Due to the complex geometry of the rib guide, there is no analytical solution to the wave equation for the guided modes, thus, approximation and/or numerical techniques must be utilized to determine the field patterns of the guide. In this study, three solution methods were used for both the fiber and guide fields; the effective-index method (EIM), Marcatili's approximation, and a Fourier method. These methods were utilized independently to calculate the electric field profile of each component at two temperatures, 20 C and 300 C, representing a nominal and high temperature. Using the electric field profile calculated from each method, the theoretical coupling efficiency between an elliptical-core optical fiber and a rib waveguide was calculated using the overlap integral and the results were compared. It was determined that a high coupling efficiency can be achieved when the two components are aligned. The coupling efficiency was more sensitive to alignment offsets in the y direction than the x, due to the elliptical modal field profile of both components. Changes in the coupling efficiency over temperature were found to be minimal.

Tuma, Margaret L.↗

NASA NTRS2020

Passive Aeroelastic Tailored Wing Modal Test Using the Fixed Base Correction Method

In modal testing and finite element model correlation, analysts desire modal results using free-free or rigid boundary conditions to ease comparisons of test versus analytical data. It is often expensive both in cost and schedule to build and test with boundary conditions that replicate the free-free or rigid boundaries. Static test fixtures for load testing are often large, heavy, and unyielding, but do not provide adequate boundaries for modal tests because they are dynamically too flexible and often contain natural frequencies within the frequency range of interest of the test article. Dynamic coupling between the test article and test fixture complicates the model updating process because significant effort is required to model the test fixture and boundary conditions in addition to the test article. If there were a way to correct the modal results for fixture coupling, then setups used for other structural testing could be adequate for modal testing. In the case described in this paper, a partial static loads testing setup was used, which allowed significant schedule and cost savings by eliminating a unique setup for a modal test. A fixed base correction technique was investigated during modal testing of a flexible wing cantilevered from part of a static test fixture. The technique was successfully used to measure the wing modes de-coupled from the dynamically active test fixture. The technique is promising for future aircraft applications, but more research is needed.

structural dynamics↗

NASA NTRS2024

X-57 Cruise Motor GVT Using Fixed-Base Correction Technique

The National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC) completed a modal survey of the X-57 Maxwell aircraft cruise motor system to help inform cruise motor redesign efforts. X-57 Maxwell was an electric propulsion demonstrator aircraft developed by NASA to inform airworthiness standards for electrified-aircraft. The cruise motor system modal survey was completed in spring of 2023 utilizing the fixed-base correction (FBC) ground vibration test (GVT) technique developed by ATA Engineering, to decouple the motor modes from the aircraft modes. Previously during the full aircraft GVT, a detailed modal assessment of the cruise motors was not performed. Owing to the X-57 project’s phase in the aircraft development cycle when the motor redesign effort occurred, the cruise motor GVT could only be performed with the cruise motor system installed on the aircraft, with most of its installation hardware (wiring, baffling, sensors, etc.) attached. An impact hammer was used to provide excitation input at various locations within the tight confines of the cruise motor installation. To better support motor redesign efforts, the FBC methodology was utilized to fix, separate and de-couple the cruise motor modes from aircraft modal response. During the GVT, this required additional impact tap tests on candidate fixed-boundary points for each degree of freedom (DOF) to be fixed. Additional triaxial accelerometers installed at the candidate points were used to compute frequency response functions (FRFs) in X, Y, and Z directions to enable those DOFs to be numerically fixed. Test data was acquired using Hottinger Brüel & Kjær’s LAN-XI data acquisition hardware and BK Connect software. FBC post-test processing was performed using the Structural Modification Using Frequency Response Functions (SMURF) technique with ATA Engineering’s Interface between MATLAB, Analysis, Test (IMAT) software. Utilizing the FBC technique relieved test engineers from having to instrument the entire aircraft to identify and separate aircraft response from cruise motor modes of interest. The FBC technique also permitted structural analysis engineers to omit secondary components from their finite element model (FEM) of the cruise motor system. This FBC modal survey was successful, and the first time NASA AFRC utilized the FBC method on an aircraft rather than a test fixture, and also using an impact hammer rather than multiple shakers allowing significant project schedule and cost savings

Modal Survey↗

NASA NTRS1986

Radiation of sound from an infinite cylindrical elastic shell excited by an internal monopole source

The radiation of sound from an infinite elastic cylindrical shell excited by an internal monopole source is investigated analytically. Coupled equations of motion are used. The modal mobility of the shell wall at the source plane is examined for differing source locations and the behavior is explained in terms of free wave propagation. The radiated pressure and line power from the shell surface is then evaluated for a similar range of source positions and frequencies. A real surface power flow, that circulates backwards and forward between the shell and fluid while propagating axially, but does not contribute to the radiated far field, is uncovered. Finally, the transmission loss of the shell wall is evaluated and found to be between 10 and 35 dB lower than predicted by existing simplified theories. The lower transmission losses predicted by the coupled analysis presented here are shown to be due to excitation of higher order 'shell' type waves at the source plane.

Fuller, C. R.↗