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A probabilistic approach is used to obtain an analytical solution to the Fokker-Planck equation used in the transient analysis of the phase-locked loop phase error process of the first-order phase-locked loop. The solution procedure, which is based on the Girsanov transformation, is described.
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
This report describes the user's manual for 'HPTAM,' a two-dimensional Heat Pipe Transient Analysis Model. HPTAM is described in detail in the UNM-ISNPS-3-1995 report which accompanies the present manual. The model offers a menu that lists a number of working fluids and wall and wick materials from which the user can choose. HPTAM is capable of simulating the startup of heat pipes from either a fully-thawed or frozen condition of the working fluid in the wick structure. The manual includes instructions for installing and running HPTAM on either a UNIX, MS-DOS or VMS operating system. Samples for input and output files are also provided to help the user with the code.
Transient Response Analysis Program, TRAP aids in analysis of frequency response of force-transmission and shock-damping devices. Devices analyzed with TRAP include hydraulic actuators, automotive shock absorbers and electromechanical actuators.
Antimony surface segregation during Si(100) molecular beam epitaxy (MBE) was investigated at temperatures T(sub s) = 515 - 800 C using concentration transient analysis (CTA). The dopant surface coverage Theta, bulk fraction gamma, and incorporation probability sigma during MBE were determined from secondary-ion mass spectrometry depth profiles of modulation-doped films. Programmed T(sub s) changes during growth were used to trap the surface-segregated dopant overlayer, producing concentration spikes whose integrated area corresponds to Theta. Thermal antimony doping by coevaporation was found to result in segregation strongly dependent on T(sub s) with Theta(sub Sb) values up to 0.9 monolayers (ML): in films doped with Sb(+) ions accelerated by 100 V, Theta(sub Sb) was less than or equal to 4 x 10(exp -3) ML. Surface segregation of coevaporated antimony was kinematically limited for the film growth conditions in these experiments.
A fuze assembly, which consists of three major parts, nose, collar and sleeve, was designed to survive severe transverse impact giving a maximum base acceleration of 20.000 G. It is shown that hoop failure occurred in the collar after the impact. They also showed that by bonding the collar to the nose, the collar was able to survive the same impact. To find out the effectiveness of the bonding quantitatively, axisymmetric solid elements TRAPAX and TRIAAX were used in modelling the fuze and direct transient analysis was performed. The dynamic stresses in selected elements on the bonded and unbonded collars were compared. The peak hoop stresses in the unbonded collar were found to be up to three times higher than those in the bonded collar. The NASTRAN results explained the observed hoop failure in the unbonded collar. In addition, static and eigenvalue runs were performed as checks on the models prior to the transient runs. The use of the MPCAX cards and the existence and contributors of the calculated first several nearly identical natural frequencies are addressed.
The aircraft engine design process seeks to achieve the best overall system-level performance, weight, and cost for a given engine design. This is achieved by a complex process known as systems analysis, where steady-state simulations are used to identify trade-offs that should be balanced to optimize the system. The steady-state simulations and data on which systems analysis relies may not adequately capture the true performance trade-offs that exist during transient operation. Dynamic Systems Analysis provides the capability for assessing these trade-offs at an earlier stage of the engine design process. The concept of dynamic systems analysis and the type of information available from this analysis are presented in this paper. To provide this capability, the Tool for Turbine Engine Closed-loop Transient Analysis (TTECTrA) was developed. This tool aids a user in the design of a power management controller to regulate thrust, and a transient limiter to protect the engine model from surge at a single flight condition (defined by an altitude and Mach number). Results from simulation of the closed-loop system may be used to estimate the dynamic performance of the model. This enables evaluation of the trade-off between performance and operability, or safety, in the engine, which could not be done with steady-state data alone. A design study is presented to compare the dynamic performance of two different engine models integrated with the TTECTrA software.
Personal computers can now do many jobs that formerly required a large mainframe computer. An example is NASA Lewis Research Center's program Analysis of RotorDynamic Systems (ARDS), which uses the component mode synthesis method to analyze the dynamic motion of up to five rotating shafts. As originally written in the early 1980's, this program was considered large for the mainframe computers of the time. ARDS, which was written in Fortran 77, has been successfully ported to a 486 personal computer. Plots appear on the computer monitor via calls programmed for the original CALCOMP plotter; plots can also be output on a standard laser printer. The executable code, which uses the full array sizes of the mainframe version, easily fits on a high-density floppy disk. The program runs under DOS with an extended memory manager. In addition to transient analysis of blade loss, step turns, and base acceleration, with simulation of squeeze-film dampers and rubs, ARDS calculates natural frequencies and unbalance response.
A study of the steady-state and transient response of the squeeze film damper bearing is presented. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived. The bearing equivalent stiffness and damping coefficients are determined by steady-state equations. These coefficients are used to find the bearing configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The transient analysis of rotor-bearing systems is performed by coupling the bearing and journal equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included in the analysis. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed with emphasis on solving the system characteristic frequency equation and on producing stability maps. It is shown that for optimum stability and low force transmissability the squeeze bearing should operate at an eccentricity ratio epsilon 0.4.
Two transient operational modes of the X-34 pressurization system were analyzed using the ROCket Engine Transition Simulation (ROCETS) program. The first operational mode considers the normal operation. For the engine burn period, the required helium mass and pressure of each propellant tank were calculated. In the second case, the possibility of failure of the pressurization system solenoid valves, its consequence on the over-pressurization, and simultaneous operation of pressurization and vent/relief systems were evaluated.
Undamped modes approximate dynamic behavior of rotors and bearings. Application of modal analysis to uncouple equations of motion simplifies stability, steady-state unbalance response, and transient response analysis of system; nonlinear stability is predicted from calculated frequency spectra. Analysis provides designers with complete information without involving large-scale computational costs. Programs are written in FORTRAN IV for use on CDC 6600 computer.
Alternative techniques for finite element models for transient analyses are explored, using as an example a pinned-pinned beam. Attention is given to the relationships between desired accuracy and the available computer resources. Stiffness, mass, damping, and loading components approximations are examined with note taken of optimization methods. Generation of regular grid results indicates a linear relationship between the number of elements or degrees of freedom and the number of eigenvalues for a given accuracy. Comparisons of the finite element models in terms of accuracy/element or accuracy/degree of freedom were found to be inaccurate for determining model efficiency. Higher accuracies were available from lumped mass and damping models than assumptions of consistent loading, which was preferred to statically equivalent loading.
X-33 is an advanced technology demonstrator vehicle for the Reusable Launch Vehicle (RLV) program. The thermal protection system (TPS) for the X-33 is composed of complex layers of materials to protect internal components, while withstanding severe external temperatures induced by aerodynamic heating during high speed flight. It also serves as the vehicle aeroshell in some regions using a stand-off design. MSC/NASTRAN thermal analysis capability was used to predict transient temperature distribution (within the TPS) throughout a mission, from launch through the cool-off period after landing. In this paper, a typical analysis model, representing a point on the vehicle where the liquid oxygen tank is closest to the outer mold line, is described. The maximum temperature difference between the outer mold line and the internal surface of the liquid oxygen tank can exceed 1500 F. One dimensional thermal models are used to select the materials and determine the thickness of each layer for minimum weight while insuring that all materials remain within the allowable temperature range. The purpose of working with three dimensional (3D) comprehensive models using MSC/NASTRAN is to assess the 3D radiation effects and the thermal conduction heat shorts of the support fixtures.
Many methods have been developed to aid analysts in identifying component modes which contribute significantly to component responses. These modes, typically targeted for dynamic model correlation via a modal survey, are known as target modes. Most methods used to identify target modes are based on component global dynamic behavior. It is sometimes unclear if these methods identify all modes contributing to responses important to the analyst. These responses are usually those in areas of hardware design concerns. One method used to check the completeness of target mode sets and identify modes contributing significantly to important component responses is mode participation. With this method, the participation of component modes in dynamic responses is quantified. Those modes which have high participation are likely modal survey target modes. Mode participation is most beneficial when it is used with responses from analyses simulating actual flight events. For spacecraft, these responses are generated via a structural dynamic coupled loads analysis. Using MSC/NASTRAN DMAP, a method has been developed for calculating mode participation based on transient coupled loads analysis results. The algorithm has been implemented to be compatible with an existing coupled loads methodology and has been used successfully to develop a set of modal survey target modes.
The transient performance of two concepts for control of vertical takeoff aircraft remote lift fans is analyzed and discussed. Both concepts employ flow transfer between pairs of lift fans located in separate parts of the aircraft in order to obtain attitude control moments for hover and low-speed flight. The results presented are from a digital computer, dynamic analysis of the YJ97/LF460 remote drive turbofan. The transient responses of the two systems are presented for step demands in lift and moment.
Fokker-Planck boundary value solutions to transient phase error response of nonlinear phase locked tracking systems
The transient response of a single cell of a typical phase change material type thermal capacitor has been modeled using numerical conductive heat transfer techniques. The cell consists of a base plate, an insulated top, and two vertical walls (fins) forming a two-dimensional cavity filled with a phase change material. Both explicit and implicit numerical formulations are outlined. A mixed explicit-implicit scheme which treats the fin implicity while treating the phase change material explicitly is discussed. A band algorithmic scheme is used to reduce computer storage requirements for the implicit approach while retaining a relatively fine grid. All formulations are presented in dimensionless form thereby enabling application to geometrically similar problems. Typical parametric results are graphically presented for the case of melting with constant heat input to the base of the cell.
The use of the NASTRAN conical shell element in static, eigenvalue, and direct transient analyses is demonstrated. The results of a NASTRAN static solution of an externally pressurized ring-stiffened cylinder agree well with a theoretical discontinuity analysis. Good agreement is also obtained between the NASTRAN direct transient response of a uniform cylinder to a dynamic end load and one-dimensional solutions obtained using a method of characteristics stress wave code and a standing wave solution. Finally, a NASTRAN eigenvalue analysis is performed on a hydroballistic model idealized with conical shell elements.