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The equation of motion was used to examine the problem of vibrations of a thin elastic plate covered with a thin viscous layer. Mathematical formulation and the solution of the problem are given.
The hybrid stress finite element method is used to study the effects of filament angle and orthotropicity parameter on the vibration and flutter characteristics of cantilevered anisotropic plates. The results indicate a generally strong lack of monotonic dependence on filament angle. Also, the natural frequency in certain cases involving the first few modes, can become relatively insensitive to both filament angle and orthotropicity parameter for a range of filament angle beyond 70 deg. Values of critical dynamic pressure are obtained by a modal approach, in which the mode shapes are obtained by the hybrid stress method. Convergence of the modal method is rather rapid for the configurations analyzed, and a comparison of the method with an exact solution for the case of an isotropic simply supported plate shows that use of six modes gives excellent agreement.
The advantages of the digital methods over the analog vibration methods are demonstrated. The following topics are covered: (1) methods of computer-controlled random vibration and reverberation acoustic testing, (2) methods of computer-controlled sinewave vibration testing, and (3) methods of computer-controlled shock testing. General algorithms are described in the form of block diagrams and flow diagrams.
A number of techniques for dealing with important technical aspects of the random vibration control problem are described. These include the generation of pseudo-random and true random noise, the control spectrum estimation problem, the accuracy/speed tradeoff, and control correction strategies. System hardware, the operator-system interface, safety features, and operational capabilities of sophisticated digital random vibration control systems are also discussed.
The effect of rolling motion of a wing on the magnitude of error induced due to the wing vibration when measuring atmospheric turbulence with a wind probe mounted on the wing tip was investigated. The wing considered had characteristics similar to that of a B-57 Cambera aircraft, and Von Karman's cross spectrum function was used to estimate the cross-correlation of atmospheric turbulence. Although the error calculated was found to be less than that calculated when only elastic bendings and vertical motions of the wing are considered, it is still relatively large in the frequency's range close to the natural frequencies of the wing. Therefore, it is concluded that accelerometers mounted on the wing tip are needed to correct for this error, or the atmospheric velocity data must be appropriately filtered.
Signal enhancement techniques are described using recently developed digital adaptive filtering equipment. Adaptive filtering concepts are not new; however, as a result of recent advances in microprocessor-based electronics, hardware has been developed that has stable characteristics and of a size exceeding 1000th order. Selected data processing examples are presented illustrating spectral line enhancement, adaptive noise cancellation, and transfer function estimation in the presence of corrupting noise.
An interactive steady state frequency response computer program with graphics is documented. Single or multiple forces may be applied to the structure using a modal superposition approach to calculate response. The method can be reapplied to linear, proportionally damped structures in which the damping may be viscous or structural. The theoretical approach and program organization are described. Example problems, user instructions, and a sample interactive session are given to demonstate the program's capability in solving a variety of problems.
Report presents theoretical study of vibrations of plug caps placed over outer ends of some hollow turbine blades to prevent circulation through hollow cores of blades.
Vibrational motion of a harmonic oscillator was investigated using a focused continuous wave CO2 Doppler lidar at 9.1 microns wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. The spectra revealed departures from linear motion for vigorous vibrations of the oscillator. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation.
Distributed parameter transmission matrix analysis of bending vibrations of nonuniform elastic beam
The current discrete element analysis models in NASTRAN, Levels 8. 1.0 and 11. 1. 0, are evaluated for semi-rnonocoque and monocoque structures. Comparative results are presented with the FORMAT-I11 general-purpose code for a swept wing statics analysis and a Skylab substructure vibration analysis. Good agreement between Level i I. 1.0 and FORMAT-111 is demonstrated; however, a major error in Level 8. 1.0 was discovered on the Skylab vibration problem. The computational performance of NASTRAN was superior to FORMAT, but the vibration rigid format was found to have several inefficiencies. Comparative results are also presented between Level 11. 1. 0 and STACUSS, SLADE, BOND, UNIVALVE, and another special-purpose code. Results for two of the structures analyzed, a cylindrical shell and an elliptic plate, indicate curved discrete elements are significantly more accurate than the plate elements in NASTRAN for the same number of degrees of freedom.
Command runstream elements are presented for analyzing structural systems that are composed of a number of cyclically symmetrical sectors. Provisions are included for systems in which each cyclically symmetrical sector also possesses a plane of reflective symmetry. The following types of analysis may be performed: static analysis with and without preload, vibrational analysis with and without preload, and buckling analysis with and without preload.
This paper presents a novel flexure design for small scale refelectarrays, specifically CubeSats, that requires high level of deployment precision. Advantages of using a HSC flexure includes additional thermal stability, lesser part count and passive deployment mechanism using the stored strain energy. The proposed design is to use two flat HSC strips of thickness ℎ, length 2𝐿ℎ, width 𝑊ℎ that attach to the core-reflector panel interface. The flexure satisfies two main requirements: ability to fold to a specific compaction 𝑑 without material failure and sufficient stiffness in the deployed configuration. The elastica analysis was implemented to identify the maximum strains in the flexure when folded and provide relations that combine Δ, ℎ, 𝐿ℎ with the maximum allowable strain. A simplified analysis was performed of the vibration of a panel-flexure combination using a two degree of freedom system. The vibration analysis reveals a dimensionless length parameter 𝛽 = (𝐿ℎ/𝐿𝑃) (Δ/ℎ) that determines the transition between bending and shear modes. A non-dimensional relationship was obtained between the natural frequency and 𝛽 that captures the impact of each parameter on the response of the structure. Our current work involves fabricating and testing of the proposed flexures using High Strain Composite materials, with plans to build a prototype for a deployable reflectarray.
The general methodology for the analysis of arbitrary nonstationary random data is reviewed. A specific parametric model, called the product model, that has applications to space vehicle launch vibration data analysis is discussed. Illustrations are given using the nonstationary launch vibration data measured on the Space Shuttle orbiter vehicle.
Program performs stress buckling and vibrational analysis of large, linear, finite-element systems in excess of 50,000 degrees of freedom. Cost, execution time, and storage requirements are kept reasonable through use of sparse matrix solution techniques, and other computational and data management procedures designed for problems of very large size.
A complete ground vibration and aeroelastic analysis was made of a modified version of the Grumman American Yankee. The aircraft had been modified for four empennage configurations, a wing boom was added, a spin chute installed and provisions included for large masses in the wing tip to vary the lateral and directional inertia. Other minor changes were made which have much less influence on the flutter and vibrations. Neither static divergence nor aileron reversal was considered since the wing structure was not sufficiently changed to affect its static aeroelastic qualities. The aircraft was found to be free from flutter in all of the normal modes explored in the ground shake test. The analysis demonstrated freedom from flutter up to 214 miles per hour.
Actinyl–Actinyl interactions (AAIs) occur in pentavalent actinide systems, particularly for neptunium (Np), and lead to complex vibrational signals that are challenging to analyze and interpret. Previous studies have focused on neptunyl–neptunyl dimeric species, but trimers and tetramers have been identified as the primary motif for extended topologies observed in solid-state materials. Our hypothesis is that trimeric and tetrameric AAIs lead to the additional signals in the vibrational spectra, but this has yet to be explored systematically. Herein, we investigate three different neptunyl–neptunyl subunits (dimeric, trimeric, tetrameric) and determine the vibrational frequencies of the O=Np=O stretches using both computational and experimental approaches. Density Functional Theory (DFT) was used to identify distinct vibrational motions related to specific neptunyl oligomers and compared to previous literature precedent from Np(V) in HClO 4 and HCl systems. The vibrational behavior of Np(V) in HNO 3 was then evaluated via Raman spectroscopy. As the solution evaporated signals were linked to trimeric and tetrameric models. Solid phases produced in the evaporation include (NpO 2 ) 2 (NO 3 ) 2 (H 2 O) 5 and newly identified crystalline phase, Na(NpO 2 )(NO 3 ) 2 ·4H 2 O (NpNa). Furthermore, the combined computational studies and vibrational analysis provide evidence for unique observable vibrational bands for each polymerized subunit, allowing us to assign spectral features to trimeric and tetrameric models within three different simple anionic systems.
Last various accomplishments achieved during this project are : (1) A Survey of Neural Network (NN) applications using MATLAB NN Toolbox on structural engineering especially on equivalent continuum models (Appendix A). (2) Application of NN and GAs to simulate and synthesize substructures: 1-D and 2-D beam problems (Appendix B). (3) Development of an equivalent plate-model analysis method (EPA) for static and vibration analysis of general trapezoidal built-up wing structures composed of skins, spars and ribs. Calculation of all sorts of test cases and comparison with measurements or FEA results. (Appendix C). (4) Basic work on using second order sensitivities on simulating wing modal response, discussion of sensitivity evaluation approaches, and some results (Appendix D). (5) Establishing a general methodology of simulating the modal responses by direct application of NN and by sensitivity techniques, in a design space composed of a number of design points. Comparison is made through examples using these two methods (Appendix E). (6) Establishing a general methodology of efficient analysis of complex wing structures by indirect application of NN: the NN-aided Equivalent Plate Analysis. Training of the Neural Networks for this purpose in several cases of design spaces, which can be applicable for actual design of complex wings (Appendix F).