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Simplified method for calculating modal frequencies of four types of large area planar trusses (tetrahedral, pentahedral, hexahedral, and radial rib) treat trusses as equivalent circular plates thus allowing classical plate theories to be used.
The objectives, state-of-the-art, and problems of large space structures control are outlined. The general objectives range from basic deployment and maneuvering, where some vibration modes may be suppressed, to disturbance rejection for very high performance imaging applications. The controls selected generally must produce some combination of eigenvalue/eigenvector and loads modification in order to achieve the mission objectives. An experiment illustrating the dynamic control of a suspended circular plate is described. Analysis methods used in system modelling, signal processing, and process control and monitoring are discussed. Sensor and actuator performance are assessed.
Impact damage in graphite/epoxy laminates was characterized and transient strain history during impact was correlated. The material investigated was AS-4/3501-6 graphite/epoxy. Eight-ply and sixteen-ply quasi-isotropic laminates of 45/0/-45/90 sub s and 45/0/-45/90 sub 2s layups were fabricated with strain gages embedded between plies during the strain gages and leads from the highly conductive graphite fibers. The specimens were circular plates 12.7 cm (5 in.) in diameter and clamped along their circumference. The specimens were impacted with a 185 gm impactor, dropped from heights of 1.20 m and 1.65 m. An accelerometer was attached to the back surface of the specimen opposite the impact point and was used to trigger the recording instrumentation. The transient strain data were recorded with an eight channel waveform digitizer capable of sampling data at 0.5 microsec intervals. The data were stored, processed, and plotted by means of a microcomputer. Transient strain data were correlated with results from ultrasonic inspection of the specimens.
An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbofans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.
The equation of the original curved surface of end harmonic gearing is determined by displacement analysis of flat flexible gear. The displacement analysis is also used to calculate the strength and rigidity of the gear. The latter is regarded as a circular plate with two concentrated loads, since its torsional rigidity is much larger than its bending rigidity. Small-deflection theory of thin plates is used to solve for the displacement of any point in the middle plane of the gear. New expressions are given for radial and tangential displacements of the middle plane under asymmetrical loading. A digital computer is used to obtain numerical values for the displacements.
An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbufans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.
A squeeze-film damper, consisting of two circular plates, having only normal oscillatory relative motion is considered. The liquid lubricant between the plates is assumed to contain a single central gas bubble. The effect of the bubble on the damper performance is analyzed. Comparison is made with the performance of a pure liquid damper. Substantial deviations in peak dynamic pressures are predicted which explain discrepancies between experimental and theoretical results reported in the literature.
Theoretical models were developed capable of predicting structural response and noise transmission to random point mechanical loads. Fiber reinforced composite and aluminum materials were considered. Cylindrical shells and circular plates were taken as typical representatives of structural components for space station habitability modules. Analytical formulations include double wall and single wall constructions. Pressurized and unpressurized models were considered. Parametric studies were conducted to determine the effect on structural response and noise transmission due to fiber orientation, point load location, damping in the core and the main load carrying structure, pressurization, interior acoustic absorption, etc. These analytical models could serve as preliminary tools for assessing noise related problems, for space station applications.
Analytical models were developed to predict vibrations and structureborne noise generation of cylindrical and rectangular acoustic enclosures. These models are then used to determine structural vibration levels and interior noise to random point input forces. The guidelines developed could provide preliminary information on acoustical and vibrational environments in space station habitability modules under orbital operations. The structural models include single wall monocoque shell, double wall shell, stiffened orthotropic shell, descretely stiffened flat panels, and a coupled system composed of a cantilever beam structure and a stiffened sidewall. Aluminum and fiber reinforced composite materials are considered for single and double wall shells. The end caps of the cylindrical enclosures are modeled either as single or double wall circular plates. Sound generation in the interior space is calculated by coupling the structural vibrations to the acoustic field in the enclosure. Modal methods and transfer matrix techniques are used to obtain structural vibrations. Parametric studies are performed to determine the sensitivity of interior noise environment to changes in input, geometric and structural conditions.
Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.
Spaceflight, stellar pointing telescopes require baffle systems to define the field of view and protect this observational area from stray and scattered light. In the case of near normal incidence telescope systems, the problem consists in controlling the stray/scattered radiation reaching the image plane when circular plates, the primary and secondary mirrors, are the imaging elements. The case addressed in this paper is quite different in that it involves baffling two conical surfaces, i.e., the primary and secondary mirrors of a Wolter Type II telescope. A strategy is described for systematically moving through the telescope system and establishing criteria for placement of baffles. Calculations are given which determine the size and number of permitted baffles as a function of practical physical parameters. Clear options are given for the design of minimum baffle lengths to meet packaging constraints.
Finite difference method is used to analyze the problem of smooth contact between a rigid indenter and a laminated circular plate clamped at the edges. The plate consists of transversely isotropic layers. The interlaminar shear stresses in the contact region are found to be much different from the laminate plate theory solutions. It has been found that low-modulus interlayers cause significant reduction in the maximum interlaminar shear stresses.
The generation, reflection and propagation of flexural waves created by electroimpulsive deicing forces are demonstrated both experimentally and analytically in a thin circular plate and a thin semicylindrical shell. Analytical prediction of these waves with finite element models shows good correlation with acceleration and displacement measurements at discrete points on the structures studied. However, sensitivity to spurious flexural waves resulting from the spatial discretization of the structures is shown to be significant. Consideration is also given to composite structures as an extension of these studies.
Clinostat rotates coaxial pair of plant-growth cabinets about horizontal axis while supplying cabinets with electric power for built-in computers, lamps, fans, and auxiliary equipment, such as nutrient pumps. Each cabinet self-contained unit for growing plants in controlled environment. By rotating cabinets and contents about horizontal axis, scientists simulate and study some of effects of microgravity on growth of plants. Clinostat includes vertical aluminum mounting bracket on horizontal aluminum base. Bearings on bracket hold shaft with V-belt pulley. At each end of shaft, circular plate holds frame mount for cabinet. Mounting plates also used to hold transparent sealed growth chambers described in article, "Sealed Plant-Growth Chamber For Clinostat" (KSC-11538).
A theory has been developed for small bending and stretching of sandwich-type shells. This theory is an extension of the known theory of homogeneous thin elastic shells. It was found that two effects are important in the present problem, which are not normally of importance in the theory of curved shells: (1) the effect of transverse shear deformation and (2) the effect of transverse normal stress deformation. The first of these two effects has been known to be of importance in the theory of plates and beams. The second effect was found to occur in a manner which is typical for shells and has no counterpart in flat-plate theory. The general results of this report have been applied to the solution of problems concerning flat plates, circular rings, circular cylindrical shells, and spherical shells. In each case numerical examples have been given, illustrating the magnitude of the effects of transverse shear and normal stress deformation.
A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.
A problem of continued interest concerns the control of vibrations in a flexible structure and the related problem of reducing structure-borne noise in structural acoustic systems. In both cases, piezoceramic patches bonded to the structures have been successfully used as control actuators. Through the application of a controlling voltage, the patches can be used to reduce structural vibrations which in turn lead to methods for reducing structure-borne noise. A PDE-based methodology for modeling, estimating physical parameters, and implementing a feedback control scheme for problems of this type is discussed. While the illustrating example is a circular plate, the methodology is sufficiently general so as to be applicable in a variety of structural and structural acoustic systems.
Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.