The Third International Workshop on Jointed Structures was held from August 16th to 17th, 2012, in Chicago Illinois, following the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Thirty two researchers from both the United States and international locations convened to discuss the recent progress of mechanical joints related research and associated efforts in addition to developing a roadmap for the challenges to be addressed over the next five to ten years. These proceedings from the workshop include the minutes of the discussions and follow up from the 2009 workshop [1], presentations, and outcomes of the workshop. Specifically, twelve challenges were formulated from the discussions at the workshop, which focus on developing a better understanding of uncertainty and variability in jointed structures, incorporating high fidelity models of joints in simulations that are tractable/efficient, motivating a new generation of researchers and funding agents as to the importance of joint mechanics research, and developing new insights into the physical phenomena that give rise to energy dissipation in jointed structures. The ultimate goal of these research efforts is to develop a predictive model of joint mechanics.
Random vibration under preload is important in multiple endeavors, including those involving launch and re-entry. There are some methods in the literature to begin to address this problem, but there is nothing that accommodates the existence of preloads and the necessity of making probabilistic statements about the stress levels likely to be encountered. An approach to achieve to this goal is presented along with several simple illustrations.
A systematic approach to defining margin in a manner that incorporates statistical information and accommodates data uncertainty, but does not require assumptions about specific forms of the tails of distributions is developed. This approach extends to calculations underlying validation assessment and quantitatively conservative predictions.
The SNL/AWE joint mechanics workshop, held in Dartington Hall, Totnes, Devon, UK 26-29 April 2009 was a follow up to another international joints workshop held in Arlington, Virginia, in October 2006. The preceding workshop focused on identifying what length scales and interactions would be necessary to provide a scientific basis for analyzing and understanding joint mechanics from the atomistic scale on upward. In contrast, the workshop discussed in this report, focused much more on identification and development of methods at longer length scales that can have a nearer term impact on engineering analysis, design, and prediction of the dynamics of jointed structures. Also, the 2009 meeting employed less technical presentation and more break out sessions for developing focused strategies than was the case with the early workshop. Several 'challenges' were identified and assignments were made to teams to develop approaches to address those challenges.
The nonlinear behavior of mechanical joints is a confounding element in modeling the dynamic response of structures. Though there has been some progress in recent years in modeling individual joints, modeling the full structure with myriad frictional interfaces has remained an obstinate challenge. A strategy is suggested for structural dynamics modeling that can account for the combined effect of interface friction distributed spatially about the structure. This approach accommodates the following observations: (1) At small to modest amplitudes, the nonlinearity of jointed structures is manifest primarily in the energy dissipation - visible as vibration damping; (2) Correspondingly, measured vibration modes do not change significantly with amplitude; and (3) Significant coupling among the modes does not appear to result at modest amplitudes. The mathematical approach presented here postulates the preservation of linear modes and invests all the nonlinearity in the evolution of the modal coordinates. The constitutive form selected is one that works well in modeling spatially discrete joints. When compared against a mathematical truth model, the distributed dissipation approximation performs well.
This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.
Advanced computing hardware and software written to exploit massively parallel architectures greatly facilitate the computation of extremely large problems. On the other hand, these tools, though enabling higher fidelity models, have often resulted in much longer run-times and turn-around-times in providing answers to engineering problems. The impediments include smaller elements and consequently smaller time steps, much larger systems of equations to solve, and the inclusion of nonlinearities that had been ignored in days when lower fidelity models were the norm. The research effort reported focuses on the accelerating the analysis process for structural dynamics though combinations of model reduction and mitigation of some factors that lead to over-meshing.
The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transform leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Coupling with a linearized structural dynamics model is made possible through the solid wall boundary condition. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using piecewise-smooth finite element bases. Stability of the coupled fluid/structure system is examined for the case of uniform flow past a thin plate. Stability of the reduced order model for the fluid is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation.
The NSF/SNL joint mechanics workshop, held in Arlington, Virginia, 16-18 October, 2006, attempted to assess the current state of the art for modeling joint mechanics for the purpose of structural dynamics calculation, to identify the underlying physics issues that must be addressed to advance the field, and to propose a path forward. Distinguished participants from several countries representing research communities that focus on very different length and time scales identified multiple challenges in bridging those scales. Additionally, two complementary points of view were developed for addressing those challenges. The first approach - the 'bottom-up' perspective - attempts to bridge scales by starting from the smallest length scale and working up. The other approach starts at the length scale of application and attempts to deduce mechanics at smaller length scales through reconciliation with laboratory observation. Because interface physics is a limiting element of predictive simulation in defense and transportation, this issue will be of continuing importance for the foreseeable future.
A relatively new concept in the field of mechanical shock analysis has been introduced whereby an analysis is made on the work done on structures by the excitation force. The energy imparted to a structure by the excitation can then be divided into various storage and loss mechanisms within the structure. These energies can be used to both evaluate shock response severity and characterize the underlying excitation. Previous work has illustrated the many advantages of the energy methods over traditional shock response spectrum techniques. This work will show that the energy delivered to a MDOF system is uncoupled between modes. Therefore, the total deformational energy delivered to a MDOF system is a weighted sum of the uncoupled modal contributions. This leads to the ability to compute input energy on a modal basis using uncoupled, SDOF calculations. Further, the internal storage and loss energies are also uncoupled. When the input excitation is broadband, the energy input into a MDOF structure by ground motion is dominated by that mode with the largest fraction of participating mass, often the fundamental mode of the system. This leads to the justification for treating complex structures as SDOF oscillators when using energy methods to evaluate both the underlying excitation and the structural response.
It is shown that for any material or structural model expressible as a Masing model, there exists a unique parallel-series (displacement-based) Iwan system that characterizes that model as a function of displacement history. This poses advantages both in terms of more convenient force evaluation in arbitrary deformation histories as well as in terms of model inversion. Characterization as an Iwan system is demonstrated through the inversion of the Ramberg-Osgood model, a force(stress)-based material model that is not explicitly invertible. An implication of the inversion process is that direct, rigorous comparisons of different Masing models, regardless of the ability to invert their constitutive relationship, can be achieved through the comparison of their associated Iwan distribution densities.
A technique published in SAND Report 2006-1789 ''Model Reduction of Systems with Localized Nonlinearities'' is illustrated in two problems of finite element structural dynamics. That technique, called here the Method of Locally Discontinuous Basis Vectors (LDBV), was devised to address the peculiar difficulties of model reduction of systems having spatially localized nonlinearities. It's illustration here is on two problems of different geometric and dynamic complexity, but each containing localized interface nonlinearities represented by constitutive models for bolted joint behavior. As illustrated on simple problems in the earlier SAND report, the LDBV Method not only affords reduction in size of the nonlinear systems of equations that must be solved, but it also facilitates the use of much larger time steps on problems of joint macro-slip than would be possible otherwise. These benefits are more dramatic for the larger problems illustrated here. The work of both the original SAND report and this one were funded by the LDRD program at Sandia National Laboratories.
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Structural assemblies often include bolted connections that are a primary mechanism for energy dissipation and nonlinear response at elevated load levels. Typically these connections are idealized within a structural dynamics finite element model as linear elastic springs. The spring stiffness is generally tuned to reproduce modal test data taken on a prototype. In conventional practice, modal test data is also used to estimate nominal values of modal damping that could be used in applications with load amplitudes comparable to those employed in the modal tests. Although this simplification of joint mechanics provides a convenient modeling approach with the advantages of reduced complexity and solution requirements, it often leads to poor predicted responses for load regimes associated with nonlinear system behavior. In this document we present an alternative approach using the concept of a "whole-joint" or "whole-interface" model [1]. We discuss the nature of the constitutive model, the manner in which model parameters are deduced, and comparison of structural dynamic prediction with results for experimental hardware subjected to a series of transient excitations beginning at low levels and increasing to levels that produced macro-slip in the joint. Further comparison is performed with a traditional "tuned" linear model. The ability of the whole-interface model to predict the onset of macro-slip as well as the vast improvement of the response levels in relation to those given by the linear model is made evident. Additionally, comparison between prediction and high amplitude experiments suggests areas for further work.
The presence of mechanical joints--typified by the lap joint--in otherwise linear structures has been accommodated in structural dynamics via ad hoc methods for a century. The methods range from tuning linear models to approximate non-linear behavior in restricted load ranges to various methods which introduce joint dissipation in a post-processing stage. Other methods, employing constitutive models for the joints are being developed and their routine use is on the horizon.
The generalized momentum balance (GMB) methods, explored chiefly by Shabana and his co-workers, treat slap or collision in linear structures as sequences of impulses, thereby maintaining the linearity of the structures throughout. Further, such linear analysis is facilitated by modal representation of the structures. These methods are discussed here and extended. Simulations on a simple two-rod problem demonstrate how this modal impulse approximation affects the system both directly after each impulse as well as over the entire collision. Furthermore, these simulations illustrate how the GMB results differ from the exact solution and how mitigation of these artifacts is achieved. Another modal method discussed in this paper is the idea of imposing piecewise constant forces over short, yet finite, time intervals during contact. The derivation of this method is substantially different than that of the GMB method, yet the numerical results show similar behavior, adding credence to both models. Finally, a novel method combining these two approaches is introduced. The new method produces physically reasonable results that are numerically very close to the exact solution of the collision of two rods. This approach avoids most of the non physical, numerical artifacts of interpenetration or chatter present in the first two methods.
The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Pade rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.
The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured adequately through direct simulation of the contact mechanics within a structural dynamics analysis. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. This document discusses a road-map for developing such constitutive models.
The structural dynamics modeling of engineering structures must accommodate the energy dissipation due to microslip in mechanical joints. Given the nature of current hardware and software environments, this will require the development of constitutive models for joints that both adequately reproduce the important physics and lend themselves to efficient computational processes. The exploration of the properties of mechanical joints--either through fine resolution finite element modeling or through experiment--is itself an area of research, but some qualitative behavior appears to be established. The work presented here is the presentation of a formulation of idealized elements due to Iwan, that appears capable of reproducing the important joint properties as they are now understood. Further, methods for selecting parameters for that model by joining the results from experiments in regimes of small and large load are developed. The significance of this work is that a reduced order model is presented that is capable of reproducing the important qualitative properties of mechanical joints using only a small number of parameters.
Frictional energy dissipation in joints is an issue of long-standing interest in the effort to predict damping of built up structures. Even obtaining a qualitative understanding of how energy dissipation depends on applied loads has not yet been accomplished. Goodman[l] postulated that in harmonic loading, the energy dissipation per cycle would go as the cube of the amplitude of loading. Though experiment does support a power-law relationship, the exponent tends to be lower than Goodman predicted. Recent calculations discussed here suggest that the cause of that deviation has to with reshaping of the contact patch over each loading period.
The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. While computing the von Mises stress distribution in a structural system due to a deterministic load condition may be straightforward, difficulties arise when considering random vibration environments. As a result, alternate methods are used in practice. One such method involves resolving the random vibration environment to an equivalent static load. This technique, however, is only appropriate for a very small class of problems and can easily be used incorrectly. Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the input is another method used to address this problem. This technique proves computationally inefficient and provides no insight as to the character of the distribution of von Mises stress. This tutorial describes a new methodology to investigate the design reliability of structural systems in a random vibration environment. The method provides analytic expressions for root mean square (RMS) von Mises stress and for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution. A brief overview of the theoretical development of the methodology is presented, followed by detailed instructions on how to implement the technique on engineering applications. As an example, the method is applied to a complex finite element model of a Global Positioning Satellite (GPS) system. This tutorial presents an efficient and accurate methodology for correctly applying the von Mises stress criterion to complex computational models. The von Mises criterion is the traditional method for determination of structural reliability issues in industry.
Salinas provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of weapons systems. This document provides a users guide to the input for Salinas. Details of input specifications for the different solution types, output options, element types and parameters are included. The appendices contain detailed examples, and instructions for running the software on parallel platforms.
I have recently become involved in the ABET certification process under the new system - ABET 2000. This system relies heavily on concepts of Total Quality Management (TQM). It encourages each institution to define its objectives in terms of its own mission and then create a coherent program based on it. The prescribed steps in setting up the new system at an engineering institution are: o identification of constituencies G definition of mission. It is expected that the department's mission will be consistent with that of the overall institution, but containing some higher resolution language appropriate to that particular discipline of the engineering profession. o statement of objectives consistent with the mission 3G~~\vED " enumeration of desired, and preferably measurable, outcomes of the process that would ~ `=. verify satisfaction of the objectives. ~~~ 07 !398 o establish performance standards for each outcome. o creation of appropriate feedback loops to assure that the objectives are still consistent with Q$YT1 the mission, that the outcomes remain consistent with the objectives, and that the curriculum and the teaching result in those outcomes. It is my assertion that once the institution verbalizes a mission, enumerated objectives naturally flow from that mission. (We shall try to demonstrate by example.) Further, if the mission uses the word "engineer", one would expect that word also to appear in at least one of the objectives. The objective of producing engineers of any sort must -by decree - involve the presence of the ABET criteria in the outcomes list. In other words, successful satisfaction of the ABET items a-k are a necessary subset of the measure of success in producing engineers. o We shall produce bachelor level engineers whose training in the core topics of chemical (or electrical, or mechanical) engineering is recognized to be among the best in the nation. o We shall provide an opportunity for our students to gain a significant exposure to biomedical topics and the integration of those topics with chemical (electrical or mechanical) engineering. o We shall provide unique opportunities for our students to work with clinicians and researchers in hospitals and other medical institutions. combined criteria a-k of ABET and 1-6 of AICHE (or IEEE or ASME) in some sensible manner. Here I have just estimated the number of distinct criteria that would be extracted from the AICHE paragraphs. These criteria are necessarily included because of the objective to producing chemical (electrical or mechanical) engineers. every student who desires an internship or independent study at a medical institution will be placed. a majority of our students will take either the FE exam or the M-CAT exam. demonstrating a commitment to professionalism and to life-long learning. a majority of our students will go on to graduate school or other post-graduate school. (I do not assert that this sort of outcome is appropriate to all excellent schools. In the case of this hypothetical school though, this outcome might be a reasonable expectation.) medical schools will rank our school as among the best from which to admit
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 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.
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.
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.