Multimode response of panels to normal and to traveling sonic booms.
Multimode response of uniform flat rectangular panels to normal and traveling sonic booms /N waves/
Crocker, M. J.↗
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SCBUCKLE user's manual: Buckling analysis program for simple supported and clamped panels
The program SCBUCKLE calculates the buckling loads and mode shapes of cylindrically curved, rectangular panels. The panel is assumed to have no imperfections. SCBUCKLE is capable of analyzing specially orthotropic symmetric panels (i.e., A(sub 16) = A(sub 26) = 0.0, D(sub 16) = D(sub 26) = 0.0, B(sub ij) = 0.0). The analysis includes first-order transverse shear theory and is capable of modeling sandwich panels. The analysis supports two types of boundary conditions: either simply supported or clamped on all four edges. The panel can be subjected to linearly varying normal loads N(sub x) and N(sub y) in addition to a constant shear load N(sub xy). The applied loads can be divided into two parts: a preload component; and a variable (eigenvalue-dependent) component. The analysis is based on the modified Donnell's equations for shallow shells. The governing equations are solved by Galerkin's method.
Cruz, Juan R.↗
Thermoelastic damping and its effect on flutter of stressed panels situated in a supersonic airflow
The effects of material damping on flutter of stressed rectangular panels are studied within the context of linear thermoelasticity theory. The closed-form expression for the thermoelastic (material) damping coefficient is obtained as a function of frequency, panel temperature and dimensions, and material properties. The solution of the stability boundary value problem is obtained by use of a generalized Galerkin method in the cross stream direction which reduces the governing partial differential equations to a system of ordinary differential equations in the streamwise direction. These equations are then solved exactly. Numerical results are given for the thermoelastic damping coefficients and for the flutter speeds of partially and fully clamped panels subjected to midplane stress.
Shieh, R. C.↗
Analysis of stresses in finite anisotropic panels with centrally located cutouts
A method for analyzing biaxial- and shear-loaded anisotropic rectangular panels with centrally located circular and elliptical cutouts is presented in the present paper. The method is based on Lekhnitskii's complex variable equations of plane elastostatics combined with a boundary collocation method and a Laurent series approximation. Results are presented for anisotropic panels with elliptical cutouts and subjected to combined shear and compression loading. The effects on the stress field of panel aspect ratio, anisotropy, cutout size, and cutout orientation are addressed. Angle-ply laminates, unidirectional off-axis laminates, and ((+ or - 45/0/90)(sub 3))s, ((+ or - 45/0(sub 2))(sub 3))s, and ((+ or - 45/90(sub 2))(sub 3))s laminates are examined.
Britt, Vicki O.↗
Acoustic plane waves incident on an oblique clamped panel in a rectangular duct
The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.
Unz, H.↗
Experimental evaluation of the aerodynamic damping of skin panels at low supersonic Mach numbers.
The aerodynamic damping of the first three vibration modes of a rectangular panel exposed to an attached turbulent boundary layer has been measured over the Mach number range of 1.10 to 1.40. Data showing that aerodynamic damping is a strong function of Mach number, dynamic pressure, mode shape, and boundary layer thickness are presented. At low supersonic Mach numbers, aerodynamic damping was found to be 20 to 100 times as large as common values of structural damping. Means of calculating aerodynamic damping, including effects of the boundary layer profile, are discussed. Calculated aerodynamic damping is compared with experimental data.
Muhlstein, L., Jr.↗
Two-Dimensional Sequential and Concurrent Finite Element Analysis of Unstiffened and Stiffened Aluminum and Composite Panels with Hole
The results of a detailed investigation of the distribution of stresses in aluminum and composite panels subjected to uniform end shortening are presented. The focus problem is a rectangular panel with two longitudinal stiffeners, and an inner stiffener discontinuous at a central hole in the panel. The influence of the stiffeners on the stresses is evaluated through a two-dimensional global finite element analysis in the absence or presence of the hole. Contrary to the physical feel, it is found that the maximum stresses from the glocal analysis for both stiffened aluminum and composite panels are greater than the corresponding stresses for the unstiffened panels. The inner discontinuous stiffener causes a greater increase in stresses than the reduction provided by the two outer stiffeners. A detailed layer-by-layer study of stresses around the hole is also presented for both unstiffened and stiffened composite panels. A parallel equation solver is used for the global system of equations since the computational time is far less than that using a sequential scheme. A parallel Choleski method with up to 16 processors is used on Flex/32 Multicomputer at NASA Langley Research Center. The parallel computing results are summarized and include the computational times, speedups, bandwidths, and their inter-relationships for the panel problems. It is found that the computational time for the Choleski method decreases with a decrease in bandwidth, and better speedups result as the bandwidth increases.
Razzaq, Zia↗
Finite element analysis of nonlinear flutter of composite panels
A finite element formulation is developed to analyze large-amplitude panel flutter of arbitrary laminated plates. The plates considered are anisotropic composite, thin rectangular panels. The equations of motion for an oscillating plate are determined and solved by linearizing the nonlinear stiffness matrices. The solution procedure is presented to determine the limit-cycle motions which are caused by the large deflections and vibrations induced by the areodynamic load. The aerodynamic load is defined by the first-order piston theory. Examples studied include cross-ply laminates with various numbers of layers and three-layer angle-ply laminates with different lamination angles. The effects of simply supported and clamped boundary conditions of a cross-ply laminate are also examined.
Dixon, Iain R.↗
Response of panels to turbulence-induced, surface-pressure fluctuations and resulting acoustic radiation to the flow field.
The response of finite rectangular panels, excited by turbulent boundary layers and the resulting acoustical radiation into the flow field is studied. The method of normal modes and the technique of spectral analysis are used to compute the power spectra of the panel amplitude and strain response. Computed results are compared with the corresponding response measurements for panels exposed to attached and separated flows at supersonic speeds and attached flow at subsonic speeds. The thin plate and the convected wave equations are coupled through the boundary condition on the panel to give a formula for the radiation pressure power spectra. A formula for the acoustical damping ratio of the panel is obtained through the principle of virtual work.-
Chyu, W. J.↗
Acoustic plane waves normally incident on a clamped panel in a rectangular duct
The theory of acoustic plane wave normally incident on a clamped panel in a rectangular duct is developed. The coupling theory between the elastic vibrations of the panel (plate) and the acoustic wave propagation in infinite space and in the rectangular duct is considered. The partial differential equation which governs the vibration of the panel (plate) is modified by adding to its stiffness (spring) forces and damping forces, and the fundamental resonance frequency and the attenuation factor are discussed. The noise reduction expression based on the theory is found to agree well with the corresponding experimental data of a sample aluminum panel in the mass controlled region, the damping controlled region, and the stiffness controlled region. All the frequency positions of the upward and downward resonance spikes in the sample experimental data are identified theoretically as resulting from four cross interacting major resonance phenomena: the cavity resonance, the acoustic resonance, the plate resonance, and the wooden back panel resonance.
Unz, H.↗
Response of nonlinear panels to random loads
Lightweight aircraft structures exposed to a high intensity noise environment can fatigue prematurely if adequate consideration is not given to the problem. Design methods and design criteria for sonic fatigue prevention were developed based on analytical and experimental techniques. Most of the analytical work was based upon small deflection or linear structural theory which did not agree with the experimental results. A large deflection geometrical nonlinearity was incorporated into the analysis methods for determining the structural response to high intensity noise. The Karman-Herrmann large deflection equations with a single mode Galerkin approximation, and the method of equivalent linearization were used to predict mean square amplitude, mean square stresses, and nonlinear frequency at various acoustic loadings for rectangular panels. Both simply supported and clamped support conditions with immovable or movable inplane edges are considered. Comparisons with experimental results are presented.
Mei, C.↗
Numerical analysis of stiffened shear webs in the postbuckling range
The postbuckling behavior of shear webs divided into rectangular panels by stiffeners (uprights) was studied numerically, using the STAGS program in which two-dimensional finite differences are used to solve buckling and nonlinear problems. Universal nondimensional parameters, suggested by linear buckling data, are found to hold for the postbuckling range. Results indicate that the postbuckling stiffness of shear webs with isotropic panels is roughly two thirds of the prebuckling stiffness. The postbuckling behavior of shear webs with isotropic and orthotropic material properties is compared. Some practical aspects of solving nonlinear problems of this type by the numerical method employed are examined.
Stein, M.↗
NASTRAN modeling and analysis of rigid and flexible walled acoustic cavities
The acoustic slot elements, CSLOTi, are applied to analyze two-dimensional enclosures with fixed or moving boundaries. The capability utilized to compute (a) the acoustic natural modes and frequencies of a rigid walled enclosure and (b) the sound pressure at any point inside an enclosure when the surrounding walls are forced to vibrate. Applications to an automobile passenger compartment illustrate the technique. The axisymmetric fluid elements, CFLUIDi, are used in conjunction with a suitable choice of symmetry planes and a model of the surrounding structure to approximate a two-dimensional enclosure with flexible walls. The enclosure walls are modeled using finite elements or structural modes. Illustrative examples include a comparison of rectangular cavity modes with those calculated using the acoustic slot element and the free vibration modes of two enclosures coupled through a flexible rectangular panel.
Wolf, J. A., Jr.↗
Magnetic shielding of large high-power-satellite solar arrays using internal currents
Present concepts for solar power satellites involve dimensions up to tens of kilometers and operating internal currents up to hundreds of kiloamperes. A question addressed is whether the local magnetic fields generated by these strong currents during normal operation can shield the array against impacts by plasma ions and electrons (and from thruster plasmas) which can cause possible losses such as power leakage and surface erosion. One of several prototype concepts was modeled by a long narrow rectangular panel 2 km wide and 20 km long. The currents flow in a parallel across the narrow dimension (sheet current) and along the edge (wire currents). The wire currents accumulate from zero to 100 kiloamp and are the dominant sources. The magnetic field is approximated analytically. The equations of motion for charged particles in this magnetic field are analyzed. The ion and electron fluxes at points on the surface are represented analytically for monoenergetic distributions and are evaluated.
Parker, L. W.↗
Substructure analysis using NICE/SPAR and applications of force to linear and nonlinear structures
Parallel computing studies are presented for a variety of structural analysis problems. Included are the substructure planar analysis of rectangular panels with and without a hole, the static analysis of space mast, using NICE/SPAR and FORCE, and substructure analysis of plane rigid-jointed frames using FORCE. The computations are carried out on the Flex/32 MultiComputer using one to eighteen processors. The NICE/SPAR runstream samples are documented for the panel problem. For the substructure analysis of plane frames, a computer program is developed to demonstrate the effectiveness of a substructuring technique when FORCE is enforced. Ongoing research activities for an elasto-plastic stability analysis problem using FORCE, and stability analysis of the focus problem using NICE/SPAR are briefly summarized. Speedup curves for the panel, the mast, and the frame problems provide a basic understanding of the effectiveness of parallel computing procedures utilized or developed, within the domain of the parameters considered. Although the speedup curves obtained exhibit various levels of computational efficiency, they clearly demonstrate the excellent promise which parallel computing holds for the structural analysis problem. Source code is given for the elasto-plastic stability problem and the FORCE program.
Razzaq, Zia↗
Noise transmission into enclosures
This paper describes analytical and experimental studies of noise transmission into rectangular and cylindrical enclosures. The solutions of the governing acoustic-structural equations are developed by modal decomposition of structural vibrations and the interior acoustic field. Particular attention is directed toward the low frequencies, that is, frequencies up through the first few structural and cavity resonant modes. The structural vibrations are driven by the external acoustic and/or mechanical point loads which are taken to be Gaussian stationary random processes. The structural models include rectangular panels and cylindrical shells.
Vaicaitis, R.↗
Probabilistic assessment of uncertain adaptive hybrid composites
Adaptive composite structures using actuation materials, such as piezoelectric fibers, were assessed probabilistically utilizing intraply hybrid composite mechanics in conjunction with probabilistic composite structural analysis. Uncertainties associated with the actuation material as well as the uncertainties in the regular (traditional) composite material properties were quantified and considered in the assessment. Static and buckling analyses were performed for rectangular panels with various boundary conditions and different control arrangements. The probability density functions of the structural behavior, such as maximum displacement and critical buckling load, were computationally simulated. The results of the assessment indicate that improved design and reliability can be achieved with actuation material.
Shiao, Michael C.↗
A Tool for Defining Tow-Steered Laminates for Finite Element Grids
Tailoring of composite laminates is traditionally performed by changing the orientation of straight fibers in one or more plies. Modern automated fiber placement machines facilitate placement of bundles of curved fibers (tows) in a process called tow-steering, but additional variables must be used to define the shapes of tow-steered fiber paths. In this paper, a Python-based tool, called Automated Tool for Steered COmposite Optimizable Laminates (ATSCOOL), is presented for modeling steered tows as chains of circular arcs. The geometry for defining tow path shapes using four input variables is described. The formulae for determining gaps and overlaps between clusters of consecutive tows, called courses, and for determining the number of steered courses needed to cover a rectangular panel are presented. Graphical representation of courses and thickness distribution in an example panel using the ATSCOOL software are presented. Finally, an example of a finite element analysis performed using the property information output from ATSCOOL is shown.
finite element analysis↗