Publications

The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. For deterministic loads, both static and dynamic, the calculation of von Mises stress is straightforward, as is the resulting calculation of reliability. For loads modeled as random processes, the task is different; the response to such loads is itself a random process and its properties must be determined in terms of those of both the loads and the system. This has been done in the past by Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the problem. Here, we present a method that provides analytic expressions for the probability distributions of von Mises stress which can be evaluated efficiently and with good precision numerically. Further, this new approach has the important advantage of

An efficient method is presented for calculation of RMS von Mises stresses from stress component transfer functions and the Fourier representation of random input forces. An efficient implementation of the method calculates the RMS stresses directly from the linear stress and displacement modes. The key relation presented is one suggested in past literature, but does not appear to have been previously exploited in this manner.

The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

Applications where O-rings are used to isolate atmospheric environments within a structure are critical to weapon reliability. Failure occurs when gases are able to travel from one side of the O-ring to the other. The anticipated cause of failure is the relaxation of the rubber over decades, the reduction in closure force, and the O-ring`s consequent inability to offer a barrier to gas transport. A predictive model with tractable complexity has been developed to predict the time over which an O-ring is able to maintain an acceptable value of closure force.

Though the theme of System Engineering is integration, and it is normal to attempt in integration to ignore the lines between disciplines, there are distinct characteristics of the mechanical design portion of any major system design project that make this difficult. How these characteristics compound the difficulty of integration is discussed and means to minimize the associated obstacles are suggested.

No abstract available.

A novel approach to mitigating chatter vibrations in machine tools is presented. Encountered in many types of metal removal processes, chatter is a dangerous condition which results from the interaction of the cutting dynamics with the modal characteristics of the machine-workpiece assembly. Tool vibrations are recored on the surface of the workpiece during metal removal, imposing a waviness which alters the chip thickness during subsequent cutting passes. Deviations from the nominal chip thickness effect changes in the cutting force which, under certain conditions, can further excite vibrations. The chatter mitigation strategy presented is based on periodically altering the impedance of the cutting tool assembly. A cyclic electric (or magnetic) field is applied to the spindle quill which contains an electro-rheological (or magneto-rheological) fluid. The variable yield stress in the fluid affects the coupling of the spindle to the machine tool structure, changing the natural frequency of oscillation. Altering the modal characteristics in this fashion disrupts the modulation of current tool vibrations with previous tool vibrations recorded on the workpiece surface. Results from a simulated milling process reveal that significant reductions in vibration amplitude can be achieved through proper selection of fluid and excitation frequency.

A strategy is presented to develop computationally efficient models for a class of structures containing nonlinearities. Those structures are ones for which the predominant nonlinearity is in the interfaces of linear subsystems. In those cases, one hopes to achieve low order models for the linear subsystems coupled with simplistic models for the interfaces. The theme of this paper is that of deducing the properties of the nonlinear interfaces by examining the properties of the full nonlinear structure in light of the known properties of the linear subsystems. Situations where such problems arise include those where the nonlinearity derives from sliding friction or stick-slip friction. Those conditions can seriously compromise system performance if not addressed adequately, occasionally leading to either sloppy control or complete loss of stability. It is the problem of identifying those nonlinear subsystems that is addressed here.

No abstract available.

Polyelectrolyte (PE) gels are swollen polymer/solvent networks that undergo a reversible volume collapse/expansion through various types of stimulation. Applications that could exploit this large deformation and solvent expulsion/absorption characteristics include robotic {open_quotes}fingers{close_quotes} and drug delivery systems. The goals of the research were to first explore the feasibility of using the PE gels as {open_quotes}smart materials{close_quotes} - materials whose response can be controlled by an external stimulus through a feedback mechanism. Then develop a predictive capability to simulate the dynamic behavior of these gels. This involved experimentally characterizing the response of well-characterized gels to an applied electric field and other stimuli to develop an understanding of the underlying mechanisms which cause the volume collapse. Lastly, the numerical analysis tool was used to simulate various potential engineering devices based on PE gels. This report discusses the pursuit of those goals through experimental and computational means.

The primary difficulty of computing the vibration of spinning inflated membranes arises from the low natural frequencies of such systems. When such systems are rotated near their own natural frequencies the dynamics equations must account for higher order kinematics than is necessary for more rigid structures. These complications results from the membrane loads that develop within the bodies in reaction to the accelerations of the overall body. When second order kinematics act against these membrane loads, the resulting energies become of the same order as the potential and kinetic energies of the vibrations that would be calculated by first order kinematics. These complications apply to the problem addressed here. Here we consider a spin-stabilized, inflated membrane, spinning around its minor axis. This structure is very flexible and somewhat viscoelastic, so vibrations excited by the overall motion of the structure will dissipate energy of the system, thus reducing the kinetic energy. A reduction in kinetic energy consistent with a conservation of angular momentum results in coning and, eventually, tumbling. Here we must address the excitation of vibration by the rigid-body motion and then we must address the retarding effect of the energy dissipation on the rigid-body motion.

The first portion of this paper proposes a method of fabricating a material whose modulus can be changed substantially through the application of a specified stimulus. The particular implementation presented here indirectly exploits the large deformation associated with shape memory alloys to achieve the desired modulation of stiffness. The next portion of this paper discusses a class of vibration problems for which such materials have a serious potential for vibration suppression. These are problems, such as the spinning up of rotating machinery, in which the excitation at any time lies within a narrow frequency band, and that band moves through the frequency spectrum in a predictable manner. Finally, an example problem is examined and the utility of this approach is discussed.

The problem of calculating the vibrations of rotating structures has challenged analysts since the observation that use of traditional modal coordinates in such problems leads to the prediction of instability involving infinite deformation when rotation rates exceed the first natural frequency. Much recent published work on beams has shown that such predictions are artifacts of incorporating incomplete kinematics into the analysis, but that work addresses analysis of only simple structures such as individual beams and plates. The authors present a new approach to analyzing rotating flexible structures that applies to the rotation of general linear (unjointed) structures, using a system of nonlinearly coupled deformation modes. This technique is called a Method of Quadratic Modes. 37 refs., 5 figs., 1 tab.

A computer code, PREGO, has been developed to perform calculations for three related problems: reflection of an acoustic wave against a layered viscoelastic medium: (water/medium); transmission of an acoustic wave through such a medium (water/medium/water); and radiation of an acoustic wave through such a medium: (medium/water). This code draws an experience gained in writing and using a predecessor code, IMPEDE, which was devised to calculate the steady state reflection of an acoustic wave impinging on a layered substrate of elastic or viscoelastic materials. That code employed a finite element formulation to discretize the complex-valued, second order ordinary differential equations for monochromatic steady state acoustics. The principles of numerical analysis that underlie PREGO are different and less subject to discretization error than those used in IMPEDE. The formulation used in PREGO is similar to that of higher dimensional boundary integral formulations in that it uses closed form expressions for the complex velocity fields in each layer, given in terms of the velocities at the boundary of that layer. The solutions for each layer are coupled together by requiring that stresses and velocities be continuous across interfaces. 5 refs., 4 figs.

When the boundary integral equation method is applied to exterior acoustics problems, singularities occur in the resulting algebraic equations at various frequencies associated with the eigenvalues of an interior problem. These frequencies are referred to as forbidden,'' and various methods have been devised to overcome the computational difficulties presented at these frequencies. The work presented here is an extension to the CHIEF method in that higher derivatives, in addition to the function itself, are constrained to be zero at selected points in the interior domain. Whereas the relative success of either method depends on the quantity and selection of interior points, the SuperCHIEF method requires fewer interior points and is less sensitive to point selection, resulting in improved robustness without significant increase in computational complexity. 3 refs., 14 refs.