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At least 55 records · Page 3

Analysis of lateral and torsional vibration characteristics of beams and shafts with end located rotational masses

Partial differential equations are derived for free lateral and torsional vibration of a uniform free-free beam with a rotational mass attached to each extremity. For appropriate boundary conditions, nonlinear algebraic equations are obtained using a symbolic manipulation computer program, the solutions of which enable the computation of the neutral frequencies and mode-shapes. The mode-shapes are linear combinations of trigonometric and hyperbolic sine and cosine functions. A computer program is written for the numerical solution of the algebraic equations mentioned above, which can compute the natural frequencies, mode-shapes, and node points for any given set of parameters, for any given number of modes.

Robertson, D. K.

Nonlinear structural dynamics analysis using a modified modal method

The procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures which exhibit a stiffening behavior and to those with a softening behavior is presented.

Knight, N. F., Jr.

Modal identities for elastic bodies, with application to vehicle dynamics and control

It is a standard procedure to analyze a flexible vehicle in terms of its vibration frequencies and mode shapes. However, the entire mode shape is not needed per se, but two integrals of the mode shape, pi and hi, which correspond to the momentum and angular momentum in Mode i. Together with the natural frequencies omega-i, these modal parameters satisfy several important identities, 25 of which are derived in this paper. Expansions in terms of both constrained and unconstrained modes are considered. A simple illustrative example is included. The paper concludes with some remarks on the theoretical and practical utility of these results, and several potential extensions to the theory are suggested.

Hughes, P. C.

A hybrid approach to test-analysis-model development for large space structures

The present FEM reduction method for the generation of test-analysis-models (TAMs) in test-analysis correlation addresses contentions that the current modal TAM is hypersensitive to differences between test model shapes and analysis mode shapes, thereby generating large off-diagonal terms within the orthogonality and cross-orthogonality matrices employed in test-analysis mode-shape correlation. A hybrid TAM methodology is accordingly developed which combines the exact representation of the FEM target modes from the modal TAM with the more accurate TAM representation of the residual modes; the superior residual dynamics representation of the hybrid TAM is demonstrated for a detailed representation of a large space structure.

Kammer, D. C.

A hybrid formulation of a component mode synthesis method

Component mode synthesis is a substructuring technique frequently employed in structural dynamics. In this method, a given structure is subdivided into components or substructures, each of which is analyzed independently for natural frequencies and for mode shapes. The substructure mode shapes are then assembled to give displacement shapes or load patterns of the original structure. An analytical justification of the basic concept is presented using spectral decompositions, and a variant substructuring approach where intersubstructure continuity is enforced in a weak form is derived. This leads to a hybrid formulation of the basic method which is particularly suitable for assembling heterogeneous substructures and analyzing nonconforming and incompatible finite element substructure models. For problems where both the basic and hybrid methods are applicable, the hybrid variant can be computationally more advantageous.

Farhat, Charbel

Optical Calibration Process Developed for Neural-Network-Based Optical Nondestructive Evaluation Method

A completely optical calibration process has been developed at Glenn for calibrating a neural-network-based nondestructive evaluation (NDE) method. The NDE method itself detects very small changes in the characteristic patterns or vibration mode shapes of vibrating structures as discussed in many references. The mode shapes or characteristic patterns are recorded using television or electronic holography and change when a structure experiences, for example, cracking, debonds, or variations in fastener properties. An artificial neural network can be trained to be very sensitive to changes in the mode shapes, but quantifying or calibrating that sensitivity in a consistent, meaningful, and deliverable manner has been challenging. The standard calibration approach has been difficult to implement, where the response to damage of the trained neural network is compared with the responses of vibration-measurement sensors. In particular, the vibration-measurement sensors are intrusive, insufficiently sensitive, and not numerous enough. In response to these difficulties, a completely optical alternative to the standard calibration approach was proposed and tested successfully. Specifically, the vibration mode to be monitored for structural damage was intentionally contaminated with known amounts of another mode, and the response of the trained neural network was measured as a function of the peak-to-peak amplitude of the contaminating mode. The neural network calibration technique essentially uses the vibration mode shapes of the undamaged structure as standards against which the changed mode shapes are compared. The published response of the network can be made nearly independent of the contaminating mode, if enough vibration modes are used to train the net. The sensitivity of the neural network can be adjusted for the environment in which the test is to be conducted. The response of a neural network trained with measured vibration patterns for use on a vibration isolation table in the presence of various sources of laboratory noise is shown. The output of the neural network is called the degradable classification index. The curve was generated by a simultaneous comparison of means, and it shows a peak-to-peak sensitivity of about 100 nm. The following graph uses model generated data from a compressor blade to show that much higher sensitivities are possible when the environment can be controlled better. The peak-to-peak sensitivity here is about 20 nm. The training procedure was modified for the second graph, and the data were subjected to an intensity-dependent transformation called folding. All the measurements for this approach to calibration were optical. The peak-to-peak amplitudes of the vibration modes were measured using heterodyne interferometry, and the modes themselves were recorded using television (electronic) holography.

Decker, Arthur J.

Direct correlation of test-analysis cross-orthogonality

This paper presents an alternative to the correlation of individual components of a mode shape vectors by directly examining the sensitivity of the cross-orthogonality between test and analytical mode shapes. If the test and analysis mode shapes are identical, the diagonal elements of the cross-orthogonality will be identical to the test orthogonality matrix, so the cross-orthogonality matrix provides a concise measure of the 'closeness' between test and analysis mode shapes. There are two major advantages to the cross-orthogonality correlation approach. The first is that a direct correlation of this matrix will more directly meet the goal of the correlation effort (measured by cross-orthogonality). Secondly, and more importantly, the correlation of cross-orthogonality greatly reduces the amount of data that needs to be handled when compared to the correlation of mode shapes.

Blelloch, P. A.

Inertial sensor and method of use

The inertial sensor of the present invention utilizes a proof mass suspended from spring structures forming a nearly degenerate resonant structure into which a perturbation is introduced, causing a split in frequency of the two modes so that the mode shape become uniquely defined, and to the first order, remains orthogonal. The resonator is provided with a mass or inertia tensor with off-diagonal elements. These off-diagonal elements are large enough to change the mode shape of the two nearly degenerate modes from the original coordinate frame. The spring tensor is then provided with a compensating off-diagonal element, such that the mode shape is again defined in the original coordinate frame. The compensating off-diagonal element in the spring tensor is provided by a biasing voltage that softens certain elements in the spring tensor. Acceleration disturbs the compensation and the mode shape again changes from the original coordinate frame. By measuring the change in the mode shape, the acceleration is measured.

Gutierrez, Roman C.

An experimental modal testing/identification technique for personal computers

A PC-based system for mode shape identification is evaluated. A time-domain modal identification procedure is utilized to identify the mode shapes of a beam apparatus from discrete time-domain measurements. The apparatus includes a cantilevered aluminum beam, four accelerometers, four low-pass filters, and the computer. The method's algorithm is comprised of an identification algorithm: the Eigensystem Realization Algorithm (ERA) and an estimation algorithm called Minimum Model Error (MME). The identification ability of this algorithm is compared with ERA alone, a frequency-response-function technique, and an Euler-Bernoulli beam model. Detection of modal parameters and mode shapes by the PC-based time-domain system is shown to be accurate in an application with an aluminum beam, while mode shapes identified by the frequency-domain technique are not as accurate as predicted. The new method is shown to be significantly less sensitive to noise and poorly excited modes than other leading methods. The results support the use of time-domain identification systems for mode shape prediction.

Roemer, Michael J.

Fixed- and Free-Mode Flutter Derivatives during Aeroelastic Optimization

Aeroelastic flutter design derivatives may be approximated by ignoring the sensitivity of the structural mode shapes. This “fixed-mode” derivative is less-expensive to compute than the exact “free-mode” derivative (which accommodates the mode shape dependency), but also may provide inaccurate sensitivities for optimization. This work formulates both fixed- and free-mode flutter derivatives, and demonstrates the conditions under which they are equivalent. Two different types of fixed-mode derivatives are also developed in this work. Using a cantilevered-plate demonstration problem with both shape and sizing design parameters, the accuracy of the free-mode derivative and the two fixed-mode derivatives, are all demonstrated via gradient-based optimization.

Bret K. Stanford

To the Moon! Space Launch System Modal Testing with Video and Motion Magnification

MIT Lincoln Laboratory and NASA Marshall Space Flight Center have been collaborating on using video camera measurements and motion magnification for modal testing of large aerospace components for several years. This presentation will discuss results from the Space Launch System Integrated Modal Test (IMT) and Dynamic Rollout/Rollback Test (DRRT) in support of the Artemis I mission. During the IMT, the data collection focused on operational mode shapes. In addition, the cameras were repositioned mid-test to better understand the physics of a low-frequency torsion mode. The non-contact nature of video data capture allowed for the quick redeployment of the cameras while not causing any delay in test schedule, whereas traditional instrumentation would have required a pause in testing to attach the sensors to the test article. The motion magnification analysis was able to find the low-frequency operational mode shapes and help the test team better understand the physics of the torsion mode. Building upon the success of the IMT motion magnification work, a camera system was used during the DRRT to find operational mode shapes, if the physics of the low-frequency torsion mode remained with different boundary conditions, and relative deflection of the vehicle and ML tower during the roll. In this paper we will present operational mode shape results, discuss the physics of the torsion mode, and review experimental setup idiosyncrasies to help the community in designing video camera measurement systems.

optical

Structures research

The main objective of the structures group is to provide quality aerospace research with the Center for Aerospace Research - A NASA Center for Excellence at North Carolina Agricultural and Technical State University. The group includes dedicated faculty and students who have a proven record in the area of structures, in particular space structures. The participating faculty developed accurate mathematical models and effective computational algorithms to characterize the flexibility parameters of joint dominated beam-truss structures. Both experimental and theoretical modelling has been applied to the dynamic mode shapes and mode frequencies for a large truss system. During the past few months, the above procedures has been applied to the hypersonic transport plane model. The plane structure has been modeled as a lumped mass system by Doctor Abu-Saba while Doctor Shen applied the transfer matrix method with a piecewise continuous Timoshenko tapered beam model. Results from both procedures compare favorably with those obtained using the finite element method. These two methods are more compact and require less computer time than the finite element method. The group intends to perform experiments on structural systems including the hypersonic plane model to verify the results from the theoretical models.

Abu-Saba, Elias

Enhanced realization identification of physical modes

Physical structures are often sufficiently complicated to preclude constructing an accurate mathematical model of the system dynamics from simple analysis using the laws of physics. Consequently, determination of an accurate model requires utilization of (generally noisy) output measurements from dynamic tests. In this paper, a robust method for constructing accurate, structural-dynamic models from discrete time-domain measurements is presented. The method processes the measurements in order to determine the number of modes present, the damping and frequency of each mode, and the mode shape. The structure may be highly damped. Although the mode-shape identification is more sensitive to measurement noise than the order, frequency, and damping identification, the method is considerably less sensitive to noise than other leading methods. Accurate detection of the modal parameters and mode shapes is demonstrated for modes with damping ratios exceeding 15 percent.

Roemer, Michael J.

Simultaneous expansion and orthogonalization of measured modes for structure identification

Tests of large structures on-orbit will be performed with measurements at a relatively few structure points. Values for the unmeasured degrees of freedom (dofs) can be estimated based on measured dofs and analytical model dynamic information. These 'expanded' mode shapes are useful for optimal-update identification and damage location as well as test/analysis correlation. A new method of expansion for test mode shape vectors is developed from the orthogonal Procrustes problem from computational linear algebra. A subspace defined by the set of measured dofs is compared to a subspace defined by mode shapes from an analytical model of the structure. The method simultaneously expands and orthogonalizes the mode shape vectors. Two demonstration problems are used to compare the new method to current expansion techniques. One demonstration uses test data from a laboratory scale-model truss structure. Performance of the new method is comparable or superior to that of the previous expansion methods which require separate orthogonalization.

Smith, Suzanne Weaver

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

Robertson, D. K.

International Space Station Model Correlation Analysis

This paper summarizes the on-orbit structural dynamic data and the related modal analysis, model validation and correlation performed for the International Space Station (ISS) configuration ISS Stage ULF7, 2015 Dedicated Thruster Firing (DTF). The objective of this analysis is to validate and correlate the analytical models used to calculate the ISS internal dynamic loads and compare the 2015 DTF with previous tests. During the ISS configurations under consideration, on-orbit dynamic measurements were collected using the three main ISS instrumentation systems; Internal Wireless Instrumentation System (IWIS), External Wireless Instrumentation System (EWIS) and the Structural Dynamic Measurement System (SDMS). The measurements were recorded during several nominal on-orbit DTF tests on August 18, 2015. Experimental modal analyses were performed on the measured data to extract modal parameters including frequency, damping, and mode shape information. Correlation and comparisons between test and analytical frequencies and mode shapes were performed to assess the accuracy of the analytical models for the configurations under consideration. These mode shapes were also compared to earlier tests. Based on the frequency comparisons, the accuracy of the mathematical models is assessed and model refinement recommendations are given. In particular, results of the first fundamental mode will be discussed, nonlinear results will be shown, and accelerometer placement will be assessed.

Modal Analysis

Analysis of structural dynamic data from Skylab. Volume 2: Skylab analytical and test modal data

A compendium is presented of orbital configuration test modal data, analytical test modal data, analytical test correlation modal data and analytical flight configuration 1.2 modal data. Section A presents tables showing the generalized mass contributions for each of the thirty test modes. Section B presents the two dimensional mode shape plots for the thirty test modes. Tables of GMC's for the test correlated analytical modes are presented in Section C. These analytical modes were generated from a model that was adjusted to match test results by use of the methodology discussed in Sections 2.3 and 5.4 of Volume I of this report. Section D presents the two dimensional mode shape plots for the analytical modes. Sections E and F contain the uncoupled and coupled modes of the orbital flight configuration 1.2 at three development phases of the model.

Demchak, L.

Finite element solution of low bond number sloshing

The dynamics of liquid propellant in a low Bond number environment which are critical to the design of spacecraft systems with respect to orbital propellant transfer and attitude control system were investigated. Digital computer programs were developed for the determination of liquid free surface equilibrium shape, lateral slosh natural vibration mode shapes, and frequencies for a liquid in a container of arbitrary axisymmetric shape with surface tension forces the same order of magnitude as acceleration forces. A finite volume element representation of the liquid was used for the vibration analysis. The liquid free surface equilibrium shapes were computed for several tanks at various contact angles and ullage volumes. A configuration was selected for vibration analysis and lateral slosh mode shapes and natural frequencies were obtained. Results are documented.

Wohlen, R. L.