Penalty finite element models for nonlinear dynamic analysis
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Noor, A. K.↗
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A three-dimensional dynamic analysis and libration study of a tethered satellites system
By a three-dimensional Lagrangian formulation, an exact set of ten coupled nonlinear second-order differential equations has been derived for a system with an extensible tether connecting two end satellites of distributed mass. The effects of tether mass, small orbital eccentricity, central body oblateness, aerodynamic drag force, and solar radiation pressure are also included in the formulation. By linearizing the exact differential equations, the in-plane (orbital plane) differential equations are found to be decoupled from the out-of-plane ones. The characteristic equation of the in-plane differential equations is derived and some associated stability constraints are shown.
Tang, C. C. H.↗
Modeling of joints for the dynamic analysis of truss structures
An experimentally-based method for determining the stiffness and damping of truss joints is described. The analytical models use springs and both viscous and friction dampers to simulate joint load-deflection behavior. A least-squares algorithm is developed to identify the stiffness and damping coefficients of the analytical joint models from test data. The effects of nonlinear joint stiffness such as joint dead band are also studied. Equations for predicting the sensitivity of beam deformations to changes in joint stiffness are derived and used to show the level of joint stiffness required for nearly rigid joint behavior. Finally, the global frequency sensitivity of a truss structure to random perturbations in joint stiffness is discussed.
Belvin, W. Keith↗
Formulation of numerical procedures for dynamic analysis of spinning structures
The paper presents the descriptions of recently developed numerical algorithms that prove to be useful for the solution of the free vibration problem of spinning structures. First, a generalized procedure for the computation of nodal centrifugal forces in a finite element owing to any specified spin rate is derived in detail. This is followed by a description of an improved eigenproblem solution procedure that proves to be economical for the free vibration analysis of spinning structures. Numerical results are also presented which indicate the efficacy of the currently developed procedures.
Gupta, K. K.↗
Dynamic analysis and experiment methods for a generic space station model
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Belvin, W. Keith↗
SRB combustion dynamics analysis computer program (CDA-1)
A two-dimensional numerical model is developed for the unsteady oscillatory combustion of the solid propellant flame zone. Variations of pressure with low and high frequency responses across the long flame, such as in the double-base propellants, are accommodated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition for the gaseous phase with no condensed phase reaction. Numerical calculations are carried out using the Galerkin finite elements, with perturbations expanded to the zeroth, first, and second orders. The numerical results indicate that amplification of oscillatory motions does indeed prevail in high frequency regions. For the second order system, the trend is similar to the first order system for low frequencies, but instabilities may appear at frequencies lower than those of the first order system. The most significant effect of the second order system is that the admittance is extremely oscillatory between moderately high frequency ranges.
Chung, T. J.↗
Dynamic analysis of an unrestrained, rotating structure through nonlinear simulation
An alternate derivation based on Hamilton's principle of equations of motion of a flexible body for use in nonlinear simulation modeling is presented. The equations include terms representing variation in the inertial properties of the body resulting from flexibility as well as terms coupling rigid body and flexible momenta that arise from satisfaction of only the linear part of the mean axis conditions. An approximate method for including the centrifugal stiffening in a way that permits a variable spin vector is given. The equations are exercised in a simulation program on an example structure initially spinning about its unstable principal axis in a gravity-free vacuum.
Zeiler, Thomas A.↗
Stability and dynamic analysis of a slender column with curved longitudinal stiffeners
The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.
Lake, Mark S.↗
Dynamic analysis of the joint dominated beam
A method for determining the vibrational modes of the joint dominated beam is presented with reference to space erectable structures. Mathematical models with and without joint imperfection are developed. Joint imperfection is represented by a simple flexibility, k, in the axial direction of the chord members only. An interactive computer program is used to obtain eigenvalue characteristics and mode shapes of the system. Results are presented on frequencies of the given truss beam with and without joint imperfections for three-panel and 10-panel models. Also presented are results of parametric studies of the beam truss models of three and 10 panels with k = 0.05, 0.10, 0.50, and 1.0 x 10 to the -7th.
Abu-Saba, Elias G.↗
Dynamic analysis of flexible mechanical systems using LATDYN
A 3-D, finite element based simulation tool for flexible multibody systems is presented. Hinge degrees-of-freedom is built into equations of motion to reduce geometric constraints. The approach avoids the difficulty in selecting deformation modes for flexible components by using assumed mode method. The tool is applied to simulate a practical space structure deployment problem. Results of examples demonstrate the capability of the code and approach.
Wu, Shih-Chin↗
Dynamic analysis of rotor blade undergoing rotor power shutdown
A rigid flap-lag blade analysis was developed to simulate a rotor in a wind tunnel undergoing an emergency power shutdown. Results show that for a rotor at a nonzero shaft tilt angle undergoing an emergency power shutdown, the oscillatory lag response is divergent. The mean lag response is large when tested at high collective pitch angles. Reducing the collective pitch during the emergency shutdown reduces the steady lag response. Increasing the rotor shaft tilt angle increases the oscillatory lag response component. The blade lag response obtained by incorporating a nonlinear lag damper model indicates that in this case the equivalent linear viscous damping is lower than originally expected. Simulation results indicate that large oscillatory lag motions can be suppressed if the rotor shaft is returned to the fully vertical position during the emergency power shutdown.
Nguyen, Khanh Quoc↗
Computational fluid dynamic analysis of liquid rocket combustion instability
The paper presents a computational analysis of liquid rocket combustion instability. Consideration is given to both a fully nonlinear unsteady calculation as well as a new CFD-based linearized stability analysis. An analytical solution for the linear stability problem in a constant area combustion chamber with uniform mean flow is developed to verify the numerical analyses.
Venkateswaran, Sankaran↗
Modeling of composite beams and plates for static and dynamic analysis
A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.
Hodges, Dewey H.↗
A discrete momentum-conserving explicit algorithm for multibody dynamics analysis
A discrete momentum-conserving, explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid-point implicit formula for integrating the Euler parameters and a second-order discrete momentum-conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.
Park, K. C.↗
Modeling of composite beams and plates for static and dynamic analysis
The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.
Hodges, Dewey H.↗
Dynamic analysis to evaluate viscoelastic passive damping augmentation for the Space Shuttle Remote Manipulator System
The effectiveness of constrained viscoelastic layer damping treatment designs is evaluated separately as passive control measures for low frequency joint dominated modes and higher frequency boom flexure dominated modes using a NASTRAN finite element analysis. Passive damping augmentation is proposed which is based on a constrained viscoelastic layer damping treatment applied to the surface of the manipulators's flexible booms. It is pointed out that even the joint compliance dominated modes can be damped to some degree through appropriate design of the treatment.
Alberts, Thomas E.↗
Dynamic analysis of pretwisted elastically-coupled rotor blades
This paper addresses the accuracy of using a one-dimensional analysis to predict frequencies of elastically-coupled highly-twisted rotor blades. Degrees of freedom associated with shear deformation are statically condensed from the formulation, so the analysis uses only those degrees of freedom associated with classical beam theory. The effects of cross section deformation (warping) are considered, and are shown to become significant for some types of elastic coupling. Improved results are demonstrated for highly-coupled blade structures through account of warping in a local cross section analysis, without explicit inclusion of these effects in the beam analysis. A convergence study is also provided which investigates the potential for improving efficiency of elastically-coupled beam analysis through implementation of a p-version beam finite element.
Nixon, Mark W.↗
A discrete momentum-conserving explicit algorithm for rigid body dynamics analysis
A discrete momentum-conserving explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid-point implicit formula for integrating the Euler parameters and a second-order discrete momentum-conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.
Park, K. C.↗