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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A finite micro-rotation material point method for micropolar solid and fluid dynamics with three-dimensional evolving contacts and free surfaces

This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. Additionally we also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.

42 ENGINEERING↗
NASA NTRS1940

The frequencies of cantilever wings in beam and torsional vibrations

Methods are described for calculating the period and frequency of vibration of cantilever wings and similar structures in which the weight and moment of inertia vary along the span. Both the beam and torsional frequencies may be calculated by these methods. The procedure is illustrated by examples. It is shown that a surprisingly close approximation to the beam frequency may be obtained by a very brief calculation in which the curvature of the wing in vibration is assumed to be constant. A somewhat longer computation permits taking account of the true curvature of the beam by a series of successive approximations which are shown to be strongly convergent. Analogous methods are applied to calculations of the torsional frequency. For the first approximation it is assumed that the angle of twist varies linearly alone the semispan. True variation of the twist is computed by successive approximations which are strongly convergent, as in the case of beam vibrations.

Burgess, C P↗
NASA NTRS1985

Finite difference analysis of torsional vibrations of pretwisted, rotating, cantilever beams with effects of warping

Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.

Subrahmanyam, K. B.↗
NASA NTRS1985

Vibration and buckling of rotating, pretwisted, preconed beams including Cooriolis effects

The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams were studied. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: (1) one based upon a finite-difference approach using second order central differences for solution of the equations of motion, and (2) based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. The individual and collective effects of pretwist, precone, setting angle, thickness ratio and Coriolis forces on the natural frequencies and the buckling boundaries are presented. It is shown that the inclusion of Coriolis effects is necessary for blades of moderate to large thickness ratios while these effects are not so important for small thickness ratio blades. The possibility of buckling due to centrifugal softening terms for large values of precone and rotation is shown.

Subrahmanyam, K. B.↗
NASA NTRS1985

Vibration and buckling of rotating, pretwisted, preconed beams including Coriolis effects

The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams were studied. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: (1) one based upon a finite-difference approach using second order central differences for solution of the equations of motion, and (2) based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. The individual and collective effects of pretwist, precone, setting angle, thickness ratio and Coriolis forces on the natural frequencies and the buckling boundaries are presented. It is shown that the inclusion of Coriolis effects is necessary for blades of moderate to large thickness ratios while these effects are not so important for small thickness ratio blades. The possibility of buckling due to centrifugal softening terms for large values of precone and rotation is shown.

Subrahmanyam, K. B.↗
NASA NTRS1985

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.↗
NASA NTRS1995

Advanced Modeling of Micromirror Devices

The flexure-beam micromirror device (FBMD) is a phase only piston style spatial light modulator demonstrating properties which can be used for phase adaptive corrective optics. This paper presents a complete study of a square FBMD, from advanced model development through final device testing and model verification. The model relates the electrical and mechanical properties of the device by equating the electrostatic force of a parallel-plate capacitor with the counter-acting spring force of the device's support flexures. The capacitor solution is derived via the Schwartz-Christoffel transformation such that the final solution accounts for non-ideal electric fields. The complete model describes the behavior of any piston-style device, given its design geometry and material properties. It includes operational parameters such as drive frequency and temperature, as well as fringing effects, mirror surface deformations, and cross-talk from neighboring devices. The steps taken to develop this model can be applied to other micromirrors, such as the cantilever and torsion-beam designs, to produce an advanced model for any given device. The micromirror devices studied in this paper were commercially fabricated in a surface micromachining process. A microscope-based laser interferometer is used to test the device in which a beam reflected from the device modulates a fixed reference beam. The mirror displacement is determined from the relative phase which generates a continuous set of data for each selected position on the mirror surface. Plots of this data describe the localized deflection as a function of drive voltage.

Michalicek, M. Adrian↗
NASA NTRS1992

Flexure-torsion behavior of sheat-deformable beams with applications to aircraft wing sections

The flexure-torsion behavior of a tip-loaded cantilever beam with an arbitrary cross-section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross-sections, the calculated coefficients represent a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-section properties including: the torsion constant, shear deformation coefficients, shear correction factors, and the shear center location. A new linear relation is developed for locating the shear center using the Saint-Venant flexure and torsion solutions, where the twist rate is zero about the line of shear centers (not the centroidal axis). Numerical results are presented for a triangular cross-section and different NACA airfoils.

Kosmatka, J. B.↗
NASA NTRS1990

Improved DMD configurations for image correlation

Two novel deformable mirror structures have been developed for spatial light modulators: an 'AM torsion beam' and a 'phase-mostly single-quadrant cantilever' beam. Both devices are well-suited to optical correlator input and filtering functions. Which the optical modulation characteristic of the torsion-beam modulator is essential amplitude only, which is well suited for use as the input modulator of the optical correlator, the characteristic of the one-quadrant modulator is a phase-mostly modulation whose amplitude changes are coupled to the phase changes; this renders it operable in the Fourier plane of the optical correlator as the filtering device.

Florence, James M.↗
NASA NTRS1989

A comparison of two trusses for the space station structure

The structural performance of two truss configurations, the orthogonal tetrahedral and a Warren-type, are compared using finite element models representing the November Reference Phase 1 Space Station. The truss torsional stiffness properties and fundamental torsion frequency are determined using cantilever truss-beam models. Frequencies, mode shapes, transient response, and truss strut compressive loads are compared for the two space station models. The performance benefit resulting from using a high modulus truss strut is also presented. Finally, assembly and logistics characteristics of the two truss configurations are evaluated.

Sutter, Thomas R.↗
NASA NTRS1993

Flexure-torsion behavior of prismatic beams. I - Section properties via power series

The behavior of a tip-loaded cantilever beam with an arbitrary cross section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross sections, the calculated coefficients represented a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-sectional properties (torsion constant, shear correction factors, shear deformation coefficients, and shear center location). A new linear relation is developed for locating the shear center, where the twist rate is zero about the line of shear centers. Moreover, the kinematic relations for a new fully compatible one-dimensional beam theory are developed. Numerical results are presented first to verify the approach and second to provide section data on NACA four-series airfoils not currently found in the literature.

Kosmatka, J. B.↗
NASA NTRS1995

Silicon Micromachining in RF and Photonic Applications

Texas Instruments (TI) has developed membrane and micromirror devices since the late 1970s. An eggcrate space membrane was used as the spatial light modulator in the early years. Discrete micromirrors supported by cantilever beams created a new era for micromirror devices. Torsional micromirror and flexure-beam micromirror devices were promising for mass production because of their stable supports. TI's digital torsional micromirror device is an amplitude modulator (known as the digital micromirror device (DMD) and is in production development, discussed elsewhere. We also use a torsional device for a 4 x 4 fiber-optic crossbar switch in a 2 cm x 2 cm package. The flexure-beam micromirror device is an analog phase modulator and is considered more efficient than amplitude modulators for use in optical processing systems. TI also developed millimeter-sized membranes for integrated optical switches for telecommunication and network applications. Using a member in radio frequency (RF) switch applications is a rapidly growing area because of the micromechanical device performance in microsecond-switching characteristics. Our preliminary membrane RF switch test structure results indicate promising speed and RF switching performance. TI collaborated with MIT for modeling of metal-based micromachining.

Lin, Tsen-Hwang↗
NASA NTRS2014

Mechanical Behavior of Microelectromechanical Microshutters

A custom micro-mechanical test system was constructed using off-the-shelf components to characterize the mechanical properties of microshutters. Microshutters are rectangular microelectromechanical apertures which open and close about a narrow torsion bar hinge. Displacement measurements were verified using both capacitive and digital image correlation techniques. Repeatable experiments on Si3N4 cantilever beams verified that the test system operates consistently. Using beam theory, the modulus of elasticity of the low stress Si3N4 was approximately 150 GPa, though significant uncertainty exists for this measurement due primarily to imprecise knowledge of the cantilever thickness. Tests conducted on microshutter arrays concluded that reducing the Si3N4 thickness from 250 nm to 500 nm reduces the torsional stiffness by a factor of approximately four. This is in good agreement with analytical and finite element models of the microshutters.

silicon nitride↗
NASA NTRS1985

Influence of rotation and pretwist on cantilever fan blade flutter

The fundamental and lowest frequency natural modes in a cantilever fan blade exhibit significant amounts of flexure and torsion coupled by pretwist and operation in a rotational force field. Consequently the flutter estimation of such blades requires an accurate structural description that incorporates these two effects, amongst others. A beam-type finite element model is used in this study with up to six spanwise elements, each element being pretwisted. Coalescence-type flutter is found with subsonic aerodynamics. Evidence of the aerodynamic resonance phenomenon is exhibited and the importance of including radially varying aerodynamic forces is brought out.

Sisto, F.↗