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The author's studies in astroelasticity are reviewed, covering the dynamics of coupled systems of dynamic solids, the vibrations of a paraboloidal antenna, the thermal flutter of spacecraft boom and the effect of large structural deflection on control stability. A method proposed by Popov in nonlinear automatic control theory (1961) is used as the basis of the studies.
The results of a one year study to develop a dynamic response model for the Space Shuttle Solid Rocket Motor (SRM) propellant are presented. An extensive literature survey was conducted, from which it was concluded that the only significant variables affecting the dynamic response of the SRM propellant are temperature and frequency. Based on this study, and experimental data on propellants related to the SRM propellant, a dynamic constitutive model was developed in the form of a simple power law with temperature incorporated in the form of a modified power law. A computer program was generated which performs a least-squares curve-fit of laboratory data to determine the model parameters and it calculates dynamic moduli at any desired temperature and frequency. Additional studies investigated dynamic scaling laws and the extent of coupling between the SRM propellant and motor cases. It was found, in agreement with other investigations, that the propellant provides all of the mass and damping characteristics whereas the case provides all of the stiffness.
This report consists of the following sections: a list of the NASA DOSE (Dynamics of the Solid Earth) Program Global Positioning System (GPS)-based campaigns supported by the UNAVCO (University Navstar Consortium) Boulder Facility; a list of NASA DOSE GPS permanent site installations supported by the UNAVCO Boulder Facility; and example science snapshots indicating the research projects supported with equipment and technical support available to DOSE Principal Investigators via the UNAVCO Boulder Facility.
This paper discusses the effect of pressure on the dynamics of pre-stiffened structures such as the Advanced Solid Rocket Motor (ASRM). Previous work in which the stiffness terms resulting from constant pressure were derived has been extended to enable modeling of nonconstant pressure applied over nonenclosed volumes. These conditions will result in nonsymmetric terms in the global stiffness matrix which will not cancel out. Three new pressure stiffness elements incorporating these nonsymmetric terms have been implemented as dummy elements in COSMIC NASTRAN and have been tested on various simple examples as well as an existing ASRM NASTRAN finite element model. The results indicate that for all load cases of practical interest to the ASRM program, the nonsymmetric terms have very little effect on the dynamic characteristics. In addition, the pressure stiffness elements developed in the previous work which assumed constant pressure gave virtually the same results as the new elements even for problems in which the pressures are not constant. The original elements appear to work well as long as the pressure gradient across any individual element is no larger than about 0.75 psi/inch. The new elements are therefore most useful for determining the conditions under which the original pressure stiffness elements can be used.
Relationship between dynamic contact angle and velocity of liquid front along solid surface
Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.
The dynamic response properties of the space shuttle solid rocket moter (TP-H1148) propellant were characterized and the expected limits of propellant variability were established. Dynamic shear modulus tests conducted on six production batches of TP-H1148 at various static and dynamic strain levels over the temperature range from 40 F to 90 F. A heat conduction analysis and dynamic response analysis of the space shuttle solid rocket motor (SRM) were also conducted. The dynamic test results show significant dependence on static and dynamic strain levels and considerable batch-to-batch and within-batch variability. However, the results of the SRM dynamic response analyses clearly demonstrate that the stiffness of the propellant has no consequential on the overall SRM dynamic response. Only the mass of the propellant needs to be considered in the dynamic analysis of the space shuttle SRM.
An extension is proposed of the classical theory of fracture to viscoelastic and elastic-plastic materials in which the plasticity effects are confined to a narrow band encompassing the crack front. It is suggested that the Griffith-Irwin criterion of fracture, which requires that the energy release rate computed for a given boundary value problem equals the critical threshold, ought to be replaced by a differential equation governing the slow growth of a crack prior to the onset of rapid propagation. A new term which enters the equation of motion in the dissipative media is proportional to the energy lost within the end sections of the crack, and thus reflects the extent of inelastic behavior of a solid. A concept of apparent surface energy is introduced to account for the geometry dependent and the rate dependent phenomena which influence toughness of an inelastic solid. Three hypotheses regarding the condition for fracture in the subcritical range of load are compared. These are: (1) constant fracture energy (Cherepanov), (2) constant opening displacement at instability (Morozov) and (3) final stretch criterion (Wnuk).
Combustion instability - response of solid propellant combustion zone to normally incident one-dimensional pressure waves
During the last decade, there has been an unprecedented improvement in both the accuracy and the temporal resolution of Earth rotation measurements. Determination of the position of the Earth's rotation axis both in inertial space and with respect to the crust with accuracies of about 0.3 milliarcseconds (mas) are now routine. In recent years, there has been an emphasis on the determination of short-period (daily and less) variations in Earth rotation. Two space based geodetic systems, very long baseline interferometry (VLBI) and the global positioning system (GPS) have proved to be very successful in this endeavor. Results for the tidally coherent part of the subdaily Earth rotation variations determined from the analysis of VLBI data are discussed. The magnitude of other subdaily variations are also considered.
The work performed under this contract provides for the improvement of modeling of troposphere propagation delay in very long base interferometry (VLBI) data, defining of required accuracy of ancillary data type(s) to measure tropospheric behavior and to develop a clear correspondence between tropospheric behavior and the quality of geodetic VLBI measurements.
This final report summarizes the accomplishments during the contract period. Under the contract NVI, Inc. provided support to the VLBI group at NASA's Goddard Space Flight Center. The contract covered a period of approximately eight years during which geodetic and astrometric VLBI evolved through several major changes. This report is divided into four sections which correspond to major task areas in the contract: A) Coordination and Scheduling, B) Field System, C) Station Support, and D) Analysis and Research and Development.
This final report summarizes the accomplishments during the contract period. Under the contract NVI, Inc. provided support to the VLBI group at NASA's Goddard Space Flight Center. The contract covered a period of approximately eight years during which geodetic and astrometric VLBI evolved through several major changes. This report is divided into four sections which correspond to major task areas in the contract: A) Coordination and Scheduling, B) Field System, C) Station Support, and D) Analysis and Research and Development.
This final report summarizes the accomplishments during the contract period. Under the contract Nepal, Inc. provided support to the VLBI group at NASA's Goddard Space Flight Center. The contract covered a period of approximately eight years during high geodetic and astrometric VLBI evolved through several major changes. This report is divided into five sections that correspond to major task areas in the contract: A) Coordination rid Scheduling, B) Field System, CN Station Support, D) Analysis and Research and Development, and E) Computer Support.
This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.
Liquid surface and liquid-solid interface dynamic responses to acceleration changes
Numerical simulations are used to model the dynamics of solid fragments in the high-pressure fuel turbopump of the Space Shuttle Main Engine (SSME HPFTP). The simulations are conducted in a probabilistic structure in order to simulate the variance in the geometrical configuration, material properties and initial conditions of the solid fragments. The results of the particle dynamics simulations are presented in the form of the probability of surface impacts, and probability distributions of the impacting velocity and impingement angle.