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At least 145 records · Page 8

Influence of large deflection and transverse shear on random response of rectangular symmetric composite laminates to acoustic loads

Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived accounting for von Karman strains. The effect of transverse shear is included in the formulation and the rotatory inertia effect is ignored. Using a single-mode Galerkin procedure the nonlinear modal equation is obtained. Direct equivalent linearization is employed. The response of acoustic excitation on moderately thick composite panels is studied. Further, the effects of transverse shear on large deflection vibration of laminates under random excitation are studied. Mean-square deflection and mean-square inplane stresses are obtained for some symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for simply supported plate. The analogous equations for a clamped case are given in the appendix.

Mei, Chuh↗

Nonlinear Dynamic Analysis of Deploying Flexible Space Booms

A fundamental investigation of the planar deployment and lock-up of two flexible boom type appendages which have attached tip masses and are connected to a central rigid body through a rotational spring is presented. Nondimensional parameters are identified and it is shown that, in general, the solution depends only on two mass ratios and one nondimensional stiffness parameter. Results are presented for boom tip deflections, deployment time and root moments at lock-up. A threshold value of the nondimensional stiffness parameter is identified beyond which boom deflections become large. Also, a thorough examination of the effect of nonlinear terms in the equations governing the deployment phase is performed. Nonlinear terms in the deployment equations due to kinematics and structural deformation are required to predict more accurately boom deflections, but retention of an inconsistent set of nonlinear terms leads to erroneous results. In particular, retaining nonlinear kinematic terms while neglecting nonlinear structural terms can produce inaccurate results even below the threshold stiffness value.

Mcgowan, P. E.↗

Theory and procedure for determining loads and motions in chine-immersed hydrodynamic impacts of prismatic bodies

A theoretical method is derived for the determination of the motions and loads during chine-immersed water landings of prismatic bodies. This method makes use of a variation of two-dimensional deflected water mass over the complete range of immersion, modified by a correction for three-dimensional flow. Equations are simplified through omission of the term proportional to the acceleration of the deflected mass for use in calculation of loads on hulls having moderate and heavy beam loading. The effects of water rise at the keel are included in these equations. In order to make a direct comparison of theory with experiment, a modification of the equations was made to include the effect of finite test-carriage mass. A simple method of computation which can be applied without reading the body of this report is presented as an appendix along with the required theoretical plots for determination of loads and motions in chine-immersed landings.

Schnitzer, Emanuel↗

Effective Elastic Modulus as a Function of Angular Leaf Span for Curved Leaves of Pyrolytic Boron Nitride

A theoretical equation was derived to predict the spring constant (load/deflection) for a simply supported cylindrical section with a line force applied at the center. Curved leaves of PBN were mechanically deformed and the force versus deflection data was recorded and compared to the derived theoretical equation to yield an effective modulus for each leaf. The effective modulus was found to vary from the pure shear modulus for a flat plate to a mixed mode for a half cylinder as a function of the sine of one half the angular leaf span. The spring constants of individual PBN leaves were usually predicted to within 30%.

Kaforey, M. L.↗

Vapor concentration measurement with photothermal deflectometry

Theoretical and experimental results for using the photothermal deflection technique to measure vapor species concentration, while minimizing the disturbance of the transport (material) parameters due to vapor heating, are developed and described. In contrast to common practice, the above constraints require using a pump-beam duty cycle of less than 50 percent. The theoretical description of the shortened heating time is based on a step-function formulation of the pumping cycle. The results are obtained as closed-form solutions of the energy equation for many chopping cycles until steady state is reached, by use of a Green's-function method. The Euler formulation of the Fermat principle is used to calculate the deflection angle. The equations are expanded to include the effects of vapor velocity on both the temperature and temperature gradient profiles. The effects of finite (unfocused) pump and probe beams and thermal (Soret) diffusion are also accounted for. Excellent agreement between theory and experiment is obtained.

Banish, R. Michael↗

Application of the TRPLT1 element to large amplitude free vibrations of plates

A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.

Mei, C.↗

Small-angle approximation to the transfer of narrow laser beams in anisotropic scattering media

The broadening and the signal power detected of a laser beam traversing an anisotropic scattering medium were examined using the small-angle approximation to the radiative transfer equation in which photons suffering large-angle deflections are neglected. To obtain tractable answers, simple Gaussian and non-Gaussian functions for the scattering phase functions are assumed. Two other approximate approaches employed in the field to further simplify the small-angle approximation solutions are described, and the results obtained by one of them are compared with those obtained using small-angle approximation. An exact method for obtaining the contribution of each higher order scattering to the radiance field is examined but no results are presented.

Box, M. A.↗

Minimum Weight Design of a Leaf Spring Tapered in Thickness and Width for the Hubble Space Telescope-Space Support Equipment

A linear elastic solution to the problem of minimum weight design of cantilever beams with variable width and depth is presented. The solution shown is for the specific application of the Hubble Space Telescope maintenance mission hardware. During these maintenance missions, delicate instruments must be isolated from the potentially damaging vibration environment of the space shuttle cargo bay during the ascent and descent phases. The leaf springs are designed to maintain the isolation system natural frequency at a level where load transmission to the instruments in a minimum. Nonlinear programming is used for the optimization process. The weight of the beams is the objective function with the deflection and allowable bending stress as the constraint equations. The design variables are the width and depth of the beams at both the free and the fixed ends.

Rodriguez, P. I.↗

Antarctic marine gravity field from high-density satellite altimetry

High-density (about 2-km profile spacing) Geosat/GM altimetry profiles were obtained for Antarctic waters (6-deg S to 72 deg S) and converted to vertical gravity gradient, using Laplace's equation to directly calculate gravity gradient from vertical deflection grids and Fourier analysis to construct gravity anomalies from two vertical deflection grids. The resultant gravity grids have resolution and accuracy comparable to shipboard gravity profiles. The obtained gravity maps display many interesting and previously uncharted features, such as a propagating rift wake and a large 'leaky transform' along the Pacific-Antarctic Rise.

Sandwell, David T.↗

Displacement based multilevel structural optimization

Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Striz, Alfred G.↗

Steady detonation propagation in thin channels with strong confinement

We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.

42 ENGINEERING↗

Effect of canard deflection on close-coupled canard-wing-body aerodynamics

The thin-layer Navier-Stokes equations are solved for the flow about a canard-wing-body configuration at transonic Mach numbers of 0.85 and 0.90, angles of attack from -4 to 10 degrees and canard deflection angles from -10 to +10 degrees. Effects of canard deflection on aerodynamic performance, including canard-wing vortex interaction, are investigated. Comparisons with experimental measurements of surface pressures, lift, drag and pitching moments are made to verify the accuracy of the computations. The results of the study show that the deflected canard downwash not only influences the formation of the wing leading-edge vortex, but can cause the formation of an unfavorable vortex on the wing lower surface as well.

Tu, Eugene L.↗

Smooth indentation of orthotropic beams

An approximate Green's function for surface displacements in an orthotropic beam is derived as the superposition of the half-plane solution for displacements and the beam theory deflections. The Green's function is used to formulate the integral equation for the problem of smooth contact between a rigid-cylinder and a simply supported orthotropic beam. The integral equation is solved using a least-squares approximation procedure. The contact stress distribution is presented for three materials with different degrees of orthotropy. Numerical results are given for contact force-contact length and contact force-indentation relations. The effects of curvature of the deflected beam, shear deformation and length-to-thickness ratio of the beam on the contact behavior are discussed.

Sankar, B. V.↗

Large-deflection theory for end compression of long rectangular plates rigidly clamped along two edges

The von Karman equations for flat plates are solved beyond the buckling load up to edge strains equal to eight time the buckling strain, for the extreme case of rigid clamping along the edges parallel to the load. Deflections, bending stresses, and membrane stresses are given as a function of end compressive load. The theoretical values of effective width are compared with the values derived for simple support along the edges parallel to the load. The increases in effective width due to rigid clamping drops from about 20 percent near the buckling strain to about 8 percent at an edge strain equal to eight times the buckling strain. Experimental values of effective width in the elastic range reported in NACA Technical Note No. 684 are between the theoretical curves for the extremes of simple support and rigid clamping.

Levy, Samuel↗

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

Subrahmanyam, K. B.↗

Non-linear dynamic response of a wind turbine blade

The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

Chopra, I.↗

Full potential unsteady computations including aeroelastic effects

A unified formulation is presented based on the full potential framework coupled with an appropriate structural model to compute steady and unsteady flows over rigid and flexible configurations across the Mach number range. The unsteady form of the full potential equation in conservation form is solved using an implicit scheme maintaining time accuracy through internal Newton iterations. A flux biasing procedure based on the unsteady sonic reference conditions is implemented to compute hyperbolic regions with moving sonic and shock surfaces. The wake behind a trailing edge is modeled using a mathematical cut across which the pressure is satisfied to be continuous by solving an appropriate vorticity convection equation. An aeroelastic model based on the generalized modal deflection approach interacts with the nonlinear aerodynamics and includes both static as well as dynamic structural analyses capability. Results are presented for rigid and flexible configurations at different Mach numbers ranging from subsonic to supersonic conditions. The dynamic response of a flexible wing below and above its flutter point is demonstrated.

Shankar, Vijaya↗