bluuebunny/crossref_metadata_2025 huggingface dataset:
Intelligent Automatic Mesh Generation for Multichip Modules
Authors: Jog Anagha G. , Grosse Ian R. , Corkill Daniel D.
Published: March 2021

Currently, the pre-processing stage of finite element analysis is a major stumbling block towards automation of the entire finite element modeling and analysis (FEMA) process. The lack of complete automation of FEMA greatly limits its impact as a design tool. This paper presents a blackboard-based, object-oriented modeling system for intelligent a-priori automatic three dimensional mesh generation. The modeling system enables the user to define the physical system at a natural domain-specific high level of abstraction and automatically derives lower-level finite element model representations. Knowledge sources interact with the blackboard to make modeling idealizations and select optimal meshing strategies. An example application in the domain of finite element modeling of multi-chip module microelectronic devices is presented.
Determination of Air Temperature Distribution in the Annular Space Using Finite Difference Method
Authors: Kosasih Engkos Achmad , Koestoer Raldi Artono
Published: March 2021

This papers discusses air temperature distribution in the annular space on forced convection of turbulent air flow, which have been determined using numerical method, and compares the result with experimental data.

Partial Differential Equations are presented in the final formulation, whereas turbulent flow model applied the simple algebraic model. These equations are changed into numerical equations by means of Finite Difference Method, in the form of explicit equation systems. The steps for solving these systems will be discussed.

The comparison between numerical solutions and experimental data shows a good result especially in the fully developed region of the air flow.
Towards a Symbolic Math CAD/CAM System
Authors: Trias Tom , Kyaw Myo , Thompson Darren , Leff Laurence , Malik Z.
Published: March 2021

We have written two pieces of software that are necessary for mechanical engineering design and analysis. These are a CAD-CAM system using Constructive Solid Geometry and a finite element analysis system. Both are unique in that they are written in the symbolic math system MAPLE. All entities in each of these programs are entered symbolically. For example, in the CSG system, we talk about a square whose dimensions are a, b and side1. In the finite element analysis, we talk about a symbolic representation for a regular grid. This scheme has advantages over conventional finite element analysis and Constructive Solid Geometry approaches.
Finite Element Analysis of Magnetohydrodynamic Pump Flow
Authors: Berry K. J. , Cameron T. M.
Published: March 2021

A Finite Element Analysis (FEA) parametric study of 2D Magnetohydrodynamic (MHD) pump flow is presented. The analysis assumes steady, viscous, incompressible fluid flow in the presence of a magnetic field applied normal to the plane of motion. The fluid is electrically conducting and the analysis is applicable to the design and performance evaluation of DC electromagnetic MHD pumps.

The primitive variable Galerkin finite element approach is used to discretize the complete Navier-Stokes equations governing fluid motion which are coupled to both the Maxwell’s equations governing electromagnetic fields, and the conservation of energy equation governing the temperature field. Analysis variables include: velocity; pressure; temperature; voltage; electric field; magnetic flux; current density and pump efficiency. These variables are evaluated for low to moderate values of the magnetic interactive parameter. The velocity field distortion is compared to other numerical results and insight into solution convergence difficulties is presented.
Mathematical Resolution of MBTI Creativity Data Into Personality Type Components
Authors: Wilde Douglass J.
Published: March 2021

A novel approach to the quantitative analysis of psychological issues in design is formulated. It treats any quadruple of Myers-Briggs Personality Index (MBTI) scores as a four-dimensional vector decomposable into components in the usual manner of vector analysis. To make the MBTI scores more understandable to the engineer untrained in psychology, new coordinate systems are proposed in which the component axes point toward human personality types such as “Strategist” rather than the usual idealized psychological concepts such as “Introvert”. Also presented as a semantic aid to understanding is a tentative matrix of oversimplified word labels serving as a bridge between terse psychological designators such as “INTJ” and their corresponding detailed personality type descriptions. The methods are used to analyze results from two American Society for Engineering Education (ASEE) faculty workshops on creativity in design education.
Wavelet Transforms in Fractal-Based Form Tolerancing
Authors: Srinivasan R. S. , Wood Kristin L.
Published: March 2021

Tolerancing is a crucial problem for mechanical designers, as it has quality and cost implications on product design. Research in tolerancing has addressed specific areas of the problem. Building upon previous research, a unified approach for geometric tolerancing with fractal-based parameters has been recently proposed. This paper explores an alternative error profile analysis and synthesis method, based on wavelets, that maintains and extends the use of fractals for surface error abstraction. An overview of the theory of wavelets is provided, and the link between fractals and wavelets is established. Experimental data are used to illustrate the application of wavelet theory to surface profile reconstruction and synthesis. The synthesis methods are then implemented in the design of ball-bearing elements, demonstrating the utility of fractal-based tolerancing. Plans for further study and implementation conclude the paper.
A Designer’s Spreadsheet
Authors: Ramaswamy Rajan , Ulrich Karl
Published: March 2021

We have observed that many designers use spreadsheet programs for preliminary parametric design calculations. The primary reason for this appears to be the flexibility and ease of use of spreadsheets as compared to more advanced analysis tools. However, current commercially available spreadsheets were originally designed for finance and accounting and do not naturally support the analytical techniques used in design and engineering. Attempts to adapt spreadsheets for engineering have largely been limited to adding features such as support for trigonometric functions. In this paper, we propose a fundamentally different kind of spreadsheet for use in preliminary parametric design. We describe the features of this spreadsheet that make it especially suitable for preliminary parametric design, discuss the theoretical basis for implementing it and present the results of preliminary user tests.
Measurement Foundations for Design Engineering Methods
Authors: Otto Kevin N.
Published: March 2021

Among the many tasks designers must perform, evaluation of concepts based on performance criteria is fundamental. A formal evaluation of a design defines a measurement of the design: an assessment reflected by real valued numbers. A measurement requires some basic a-priori information from the designer. In particular, a base-point design is required from which the remaining designs are relatively measured. Also, a metric reference design is required to compare the deviation of each remaining design from the base point design. Given these two reference designs, any other design can be evaluated numerically. Such engineering methods as concept selection charts, QFD, optimization, and many current research methods in engineering design use these measurement fundamentals to evaluate designs. Measurement theory provides a common framework to discuss solution evaluation within all of these methods. Further, the minimum formalization needed to make evaluations among design configurations is also demonstrated.
The Method of Imprecision Compared to Utility Theory for Design Selection Problems
Authors: Otto Kevin N. , Antonsson Erik K.
Published: March 2021

Two methods have been proposed for manipulating uncertainty reflecting designer choice: utility theory and the method of imprecision. Both methods represent this uncertainty across decision making attributes with zero to one ranks, higher preference modeled with a higher rank. The two methods can differ, however, in the combination metrics used to combine the ranks of the incommensurate design attributes. Utility theory resolves the multi-attributes using various well proven additive metrics. In contrast, the method of imprecision resolves by also considering non-additive metrics, such as ranking by the worst case performance or by multiplicative metrics. The axioms of utility theory are appropriate for designs where it is deemed the attributes can always be traded off, even to the point of achieving zero preference in some attributes. In the case of a design with attributes which cannot have zero preference, such as stress limits or maximum allowed cost, the method of imprecision is more appropriate: it trades off attribute levels without permitting any of them to be traded off to zero performance.
Non-Intrusive Protocol Study of Design Idea Generation
Authors: Shah Jami J. , Nico Jill A. , Kraver Theodore C.
Published: March 2021

An experiment involving a protocol study of design idea generation is described in this paper. Two designers were used as subjects in a co-operative environment for design. This is less obtrusive to the design process than a single subject thinking out aloud. A framework for macroscopic analysis of cognitive processes in idea generation was developed. It includes identification of activity objects, generation of state diagrams, and statistical analysis of interaction densities. The role of experience and analogies in idea generation was identified and studied. Although the analysis is based on limited data, the idea of non-intrusive protocol study, and the modeling techniques developed could be used for future experiments.
Nonlinear Dynamics of an Oilless Reciprocating Compressor
Authors: Minas Constantinos
Published: March 2021

Two modeling methodologies of the dynamics of a motor-compressor system are presented. The first approach considered only the mechanical system subjected to a sinusoidal input force with the pressure term in the equation of motion treated as a nonlinear stiffness term. The second methodology consisted of a mathematical model that couples the electromagnetic and thermodynamic equations to the dynamic equations that describe the motion of the piston. The mathematical model which consisted of a set of four first order simultaneous nonlinear time varying differential equations, was solved by numerical integration routines that use the Adams-Moulton method with an adaptive integration step. The two methodologies are illustrated through an example. Steady-state operation was shown to be reached rapidly after a 0.13s transient. An analysis at various amplitudes and frequencies of the input voltage in the driver-coil of the motor, showed the amplitude dependence of the resonant frequency of the mechanical system, and a heavily damped system when operating at the design amplitude. The most efficient frequency of operation was also determined for a variety of required mass flow rates.
Dynamic Stability of Free Piston Stirling Engines
Authors: Ulusoy Necati , McCaughan Frances
Published: March 2021

A Stirling engine develops work output from a thermal input. It is a quiet pollution free engine, which can use any heat source, including solar power. The piston-displacer mechanism is essentially a vibrating spring mass system and can be dynamically modelled, leading to a set of coupled nonlinear ordinary differential equations. The inadequacies of previous linear approaches are discussed and it is shown that the inclusion of a nonlinear load will lead to stable periodic motion as desired.
Parameter Estimation Techniques Based on Optimizing Goodness-of-Fit Statistics for Structural Reliability
Authors: Starlinger Alois , Duffy Stephen F. , Palko Joseph L.
Published: March 2021

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell’s numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper’s nonlinear regression algorithm.
The Effect of Fiber Type on the Level of Stress Concentration Created by U-Notches in Long-Fiber Composite Plates
Authors: Turgut A. , Arsian N. , Sancaktar Erol
Published: March 2021

The effect of fiber type on the level of stress concentration created by u-notches were investigated for unidirectional and symmetric cross-ply laminates loaded on or off-axis. The finite element method was used for this purpose utilizing triangular elements under plane stress conditions. Analyses were performed for three different fiber reinforcements of epoxy matrix: glass, graphite and boron. Typical material properties reported in the literature for glass/epoxy, boron/epoxy and graphite/epoxy were used in calculations. The accuracy of the finite element code utilized was first checked by calculating the u-notch stress concentration factors for an isotropic steel plate.
MMC Life System Development (Phase I): A NASA/Pratt & Whitney Cooperative Program
Authors: Zaretsky Erwin V. , deLaneuville Robert E.
Published: March 2021

Pratt & Whitney Aircraft and NASA Lewis Research Center studied a silicon-carbide-fiber-reinforced, titanium-metal-matrix (MMC) composite designated SiC(SCS-6)/Ti-15V-3Cr-3Al-3Sn. Fracture tests of three nominal 15.24-cm (6-in.) diameter SCS–6/Ti-15-3 rings at 427 °C (800 °F) and room temperature resulted in failure at internal pressures of 0.172 GPa (25 ksi) (average) and 0.235 GPa (34.1 ksi), respectively. Predictions of internal pressure to failure varied from 0.140 to 0.276 GPa (20.3 to 40.1 ksi) at 427 °C (800 °F). Nondestructive evaluation revealed that the rings’ MMC cores had varying density and were not uniformly distributed inside the monolithic casing. Analytical predictions of ring cyclic life at 0.154-GPa (22.4-ksi) internal pressure varied from 1000 to 15 000 cycles. No fatigue life data were obtained with the MMC rings for comparison with theory.
A Life Prediction Method for Matrix Dominated Fatigue Failures of SCS-6/Ti-15-3 MMC
Authors: Gravett Phillip W.
Published: March 2021

This paper presents a method for determining the matrix dominated cyclic fatigue capability of continuous fiber reinforced SCS-6, Ti-15-3 metal matrix composites (MMC). The basis of the fatigue life prediction system relies on the matrix material dominating the fatigue behavior of the MMC. This assumption has been supported by test data and failure mechanisms identified in unidirectional isothermal and out-of-phase thermomechanical fatigue (TMF) specimens which typically show an area of matrix cracking before failure. Since the matrix fatigue capabilities dominate the fatigue behavior of the composite, an MMC thick cylinder model with an anisotropic coefficient of thermal expansion is used to characterize the state of stress in the matrix. The Smith-Watson-Topper fatigue stress damage parameter is applied to the calculated matrix stresses to determine a “corrected” matrix fatigue stress which is isolated from laminate geometry and laminate stress. This method correlates well to room and high temperature SCS-6/Ti-15-3 MMC test data. Since the “corrected” matrix stress fatigue response is independent of fiber volume, stress ratio, and load history, this MMC Life Prediction System can be used to predict the fatigue behavior of any reasonable laminate and loading in which the failure is matrix dominated. With this life system, life analyses can be performed for laminate geometries and loadings at which no test data exists, which will prove valuable when designing engine components where optimization of MMC capabilities are required but testing is limited.
Elastic Plastic Analysis of Bimaterial Beams With Strain Hardening
Authors: Eischen J. W. , Reagan S. W.
Published: March 2021

Considerable attention has been paid to the bimaterial thermostat stress analysis problem as regards applications in microelectronic packaging. When a bimaterial beam is subjected to a temperature change, internal stress is developed that generates curvature. The present paper generalizes previous idealizations whereby a linear elastic material response has been assumed. We treat each of the beam materials as elastic-plastic with a bilinear response. A solution is obtained for the stress and deformation in the bimaterial structure following a “strength of materials” approach. While the solution is imperfect in that the stress free boundary conditions at the ends of the strip are not satisfied exactly, it does capture the overall behavior of the bimaterial beam but for the well-known end effect. Several numerical examples are presented using design data for materials commonly encountered in microelectronics applications.
Response Analysis of Discretized Plates Under In-Plane and External Nonstationary Random Excitations
Authors: To C. W. S. , Wang B.
Published: March 2021

Responses of panel structures on board ships and aerospace systems under point and in-plane intensive transient excitations, originating, primarily, from near-mixed explosion and impact upon the ships are investigated and presented in this paper. The panel structures are idealized by finite elements while the intensive transient in-plane and point loads are modelled as nonstationary random processes. The latter are treated as products of modulating functions and Gaussian white noise processes. The focus of the paper is the comparison of results obtained by employing the three nodes, eighteen degree-of-freedoms (DOF) triangular bending plate element (the explicit element stiffness, mass and stability matrices of which have been derived by the authors) and the four nodes, twelve DOF Melosh-Zienkiewicz-Cheung (MZC) rectangular bending plate element. The isssues addressed are: (a) convergence and reduction of computational time by applying the eighteen DOF plate element in comparison to the MZC element, (b) the contribution of the in-plane nonstationary random excitation on the response of the discretized structures, and (c) the influence of the number of modes included in the response computation.
Nonstationary Vibrations of a String With Time-Varying Length and a Mass-Spring System Attached at the Lower End
Authors: Terumichi Y. , Ohtsuka M. , Fukawa Y. , Yoshizawa M. , Tsujioka Y.
Published: March 2021

The purpose of this paper is to study the nonstationary vibrations of a string with time-varying length, and a mass-spring system attached at the lower end. The string is excited sinusoidally by the horizontal displacement at its upper end and the mass-spring system has two-degrees-of-freedom vertically and horizontally. It is clarified analytically that the moving velocity of the string influences the peak amplitude of the string vibration at the passage through resonances. Moreover it is shown numerically that the amplitudes of both the string and the mass vibrations depend on the sign of the moving velocity, in the case where the natural frequency of the mass-spring system is close to the frequency of the excitation. The above two theoretical results are confirmed experimentally with a simple experimental setup.
Parametric Stability of Belt-Driven Slider-Crank Mechanisms With Flexible Coupler
Authors: Chivate Pramod N. , Farhang Kambiz
Published: March 2021

Two mathematical models are presented for investigating parametric vibration stability of high-speed slider-crank mechanisms. Both models account for flexibility in the connecting rod and the drive system. The drive system is assumed to comprise a motor, pulleys and flexible drive belt. A combination of Newtonian and Lagrangian formulations is used to derive a system of nonlinear partial differential equations with position-periodic coefficients. Applying Galerkin’s method and performing appropriate linearizations, these equations are reduced to a system of linear ordinary differential equations with position-periodic coefficients.

The above two formulations are employed along with the Floquet theory to investigate parametric stability of slider-crank mechanisms with flexible connecting rod and drive system.
Nonconservative Stability of Gyroscopic Rotor Systems
Authors: Chen Hwang-Kuen , Ku Der-Ming , Chen Lien-Wen
Published: March 2021

The stability behavior of a cantilevered shaft, rotating at a constant speed and subjected to a follower force at the free end, is studied by the finite element method. The equations of motion for such a gyroscopic system are formulated by using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moments, bending and shear deformations are included. In order to determine the critical load of the present nonconservative system more quickly and efficiently, a simple and direct method that utilizes the eigenvalue sensitivity with respect to the follower force is introduced. The numerical results show that for the present nonconservative system, the onset of flutter instability occurs when the first and second backward whirl speeds are coincident. And also, due to the effect of the gyroscopic moments, the critical flutter load decreases as the rotational speed increases.
Analysis of Nonlinear Oscillators by Wavelet Transform Lyapunov Exponents
Authors: Lamarque C.-H. , Malasoma J.-M.
Published: March 2021

In this paper we give the definition of exponents which look like to Lyapunov exponents in the cases of non-smooth flows of differential equations or iterated maps, and carry back Lyapunov exponents in smooth cases. We test our definition by using some simple examples examples.
Analytical Prediction of Nonlinear System Response to Non-Stationary Excitations
Authors: Raman Arvind , Davies Patricia , Bajaj Anil K.
Published: March 2021

The study of the non-stationary response of systems has many applications in problems related to transition through resonance in rotating machinery, aerospace structures and other physical systems.

In this paper, we present methods to analytically predict the response of some weakly nonlinear systems to slowly varying parameter changes. We consider systems which can be averaged and represented as two first order equations. The evolution of the solutions of such systems through critical (jump or bifurcation) points is studied using the method of matched asymptotic expansions. As an example, the method is used to predict the response of the forced Duffing’s oscillator during passage through resonance.

Starting with a general system of two, first-order equations, we set up a slowly varying equilibrium or ‘outer’ solution as an asymptotic expansion about the stationary solution. This solution is seen to be invalid in a small neighborhood of the critical points — the ‘inner’ region. In this inner layer, the system of equations is transformed into the Jordan canonical form, which is easier to study. Using approximations from the center manifold theory, the problem is reduced to one first-order equation. By making appropriate scale changes, an ‘inner’ solution is developed. This solution is asymptotically matched with the outer expansion to yield a unified solution valid for all time.
Dynamic Responses of Plates With Viscoelastic Damping Treatment
Authors: Yi Sung , Ahmad M. Fouad , Hilton Harry H.
Published: March 2021

Dynamic transient responses of plates with free damping layers are studied in order to evaluate free layer damping treatment performances. The effects of forcing frequencies and temperatures on free-layer viscoelastic damping treatment of plates are investigated analytically. Young’s modulus ratio of structures to viscoelastic damping materials and the damping layer thickness effects on the damping ability are also explored.
A Comparison of Continuum and Lumped-Mass Models for Hyper-Redundant Manipulator Mechanics
Authors: Chirikjian Gregory S.
Published: March 2021

The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator degrees-of-freedom. Furthermore, these methods are not fully parallelizable. For ‘hyper-redundant’ manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an ‘infinite degree-of-freedom’ (or continuum) problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.
Impact Control of Flexible Robots Using Sliding Mode Technique
Authors: Chen Eming
Published: March 2021

In the flexible robot force control situations, if there exists a discontinuity between the robot tip sensor and the work-piece, the robot contact process becomes a nonlinear system control problem. The control tasks require the robot hand to switch from free motion control to contact motion control. The inevitable high impact force tends to let the system become unstable. The purpose of this paper is to investigate the control of the manipulator during this process. In this paper, dynamic models of the flexible link manipulator in both non-contacted and contacted modes are first derived. Due to the fact that the arm vibration shape functions are changed between the two modes, a transform matrix will be used to transform the controlled state variables, such as generalized position and velocity. A nonlinear sliding mode control technique has been implemented in an attempt to extinguish the chatter phenomenon and settle quickly to the desired setpoint.
Closed Form Modeling of Continuous Parameter Robotic Systems-Contact/Impact and Wave Propagation
Authors: Barhorst Alan A.
Published: March 2021

The high fidelity modeling of robotic systems is addressed. The operation of a robot usually consists of a free-flight regime, a contact/impact regime, and a constrained motion regime. Presented in this paper is a demonstration of a systematic method for modeling the complete motion of a manipulator. The model is complete in the sense that all motion regimes are seamlessly handled and the inherently distributed nature of elasticity and mass are rigorously modeled. Since the model properly integrates the distributed parameters with the discrete parameters (boundary conditions too), the effects of disturbance waves propagating in the robotic chain of bodies can be studied.

The methodology demonstrated in this work is a recent development. The methodology is based in variational principles but its operational aspects hide the variational calculus. The method seamlessly handles holonomic and nonholonomic motion constraints. The method also allows the determination of post impact velocities and pointwise velocity fields for hybrid parameter multiple body (HPMB) systems. Exact relationships used to determine when the separation of colliding bodies has occurred are also readily generated. For analysts familiar with Kane’s form of the Gibbs-Appell equations, the method will be affable.

The system modeled in this paper will allow all the curious HPMB system dynamics to be studied. That is: a two flexible link planar manipulator undergoing all three motion regimes mentioned above. The flexible beams are taken as Euler-Bernoulli beams with large deflections. The modeling technique will be demonstrated by deriving the complete model of this system.

Some of the advantages of the technique demonstrated herein include: a) closed form hybrid parameter models, b) automatic boundary conditions, c) holonomic and nonholonomic motion, d) wave propagation, and e) rapid regeneration of system models.
Simulated Behavior of a System With Base Excitation Using an Electrorheological Fluid Damper
Authors: Rieder Paul N. , Tichy John A.
Published: March 2021

The flow properties of electrorheological (ER) fluids change with the application of an electric field. Presently, these materials are a novelty with few direct applications, but they have drawn considerable interest. Proposed applications include lubricants, dampers, clutches, brakes, etc.

Existing ER fluids are best described by the Bingham fluid model. The Bingham material is described by two parameters, a yield shear stress and a viscosity. When the shear stress magnitude exceeds the yield shear stress, quasi-Newtonian flow results; otherwise the material is rigid. For many ER fluids, the yield shear stress is proportional to the square of the applied electric field. In the present study, the Bingham model is applied to a rectangular flow channel. A rigid core forms midway across the film, the core thickness being proportional to the yield shear stress. The damper force is predicted as a function of a dimensionless parameter which depends on the yield shear stress, the flow rate, and channel geometry.

Calculations are performed for a simple vibration isolation system. Such a system may represent a smart shock absorber to minimize vibration response to oscillation input from a bumpy road. The ER damper is shown to be effective in isolating vibration within a band of linear behavior.
Active Optimum Control of Orthotropic Plates Using Piezoelectric Stiffeners
Authors: Birman Victor , Adali Sarp
Published: March 2021

Active control of orthotropic plates subjected to an impulse loading is considered. The dynamic response is minimized using in-plane forces or bending moments induced by piezoelectric stiffeners bonded to the opposite surfaces of the plate and placed symmetrically with respect to the middle plane. The control forces and moments are activated by a piece-wise constant alternating voltage with varying switch-over time intervals. The magnitude of voltage is bounded while the switch-over time intervals are constantly adjusted to achieve an optimum control. Numerical examples presented in the paper demonstrate the effectiveness of the method and the possibility of reducing the vibrations to very small amplitudes within a short time interval which is in the order of a second.
Free and Forced Localization in a Nonlinear Periodic Lattice
Authors: Vakakis Alexander F. , King Melvin E. , Pearlstein Arne J.
Published: March 2021

Free and forced localized periodic motions in an infinite nonlinear periodic lattice are analytically investigated. The lattice consists of weakly coupled identical masses, each connected to the ground by a nonlinear stiffness. In order to study the localized motions of the discrete system a continuoum approximation is assumed, and the ordinary differential equations of motion are replaced by a single nonlinear partial differential equation. The time-periodic solutions of this equation are then obtained by an averaging method, and their stability is examined using an analytic linearized method. It is shown that localized periodic motions of the lattice correspond to standing solitary solutions of the partial differential equation of the continuous approximation. For the free lattice, localized free motions occur when the coupling stiffnesses forces are much smaller than the nonlinear effects of the grounding stiffnesses. Moreover, these free localized motions are detected in the perfectly periodic nonlinear lattice, i.e., even in the absence of structural disorder (a feature which is an essential prerequisite for linear mode localization). When harmonic forcing is applied to the chain, localized, non-localized, and chaotic motions occur, depending on the spatial distribution and the magnitude of the applied loads. A variety of spatially distributed harmonic loads and analytic expressions for the resulting localized motions of the chain are derived.
On Eigenmode Statistics and Power Variances in Randomly Shaped Membranes
Authors: Weaver Richard L.
Published: March 2021

The eigenmodes and eigenfrequencies of finite differenced membranes with rough boundaries are obtained numerically. Such systems are approximations to reverberation rooms. The statistics of the eigenfrequencies are found to be identical to those of the Gaussian Orthogonal Ensemble (GOE) of random matrices. The Wigner conjecture that the modes may be understood to be uncorrelated random superpositions of plane waves with no significant inter-modal correlations is also corroborated. The consequences of these eigen-statistics upon the statistics of responses are discussed.
Localization of Vibration in Disordered Multi-Span Beams With Damping
Authors: Bouzit Djamel , Pierre Christophe
Published: March 2021

The combined effects of disorder and structural damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.
Vibration Localization in Dual-Span, Axially Moving Beams: Formulation and Results
Authors: Al-jawi A. A. N. , Pierre Christophe , Ulsoy A. G.
Published: March 2021

An investigation of the vibration localization phenomenon in dual-span, axially moving beams is presented. The effects of a tension difference among the spans, also referred to as disorder, on the natural modes of free vibration are studied in terms of interspan coupling and transport speed. The equations governing the transverse vibration of the two-span, axially moving beam are derived through Hamilton’s principle and solution methods are developed. Results demonstrate that normal mode localization indeed occurs for both stationary and translating disordered two-span beams, especially for small interspan coupling. The occurrence of localization is characterized by a peak deflection much greater in one span than in the other. In the stationary disordered case, localization becomes more pronounced as interspan coupling decreases, i.e., as the span axial tension increases. In the axially moving disordered case, the transport speed has a significant influence on localization, and generally speaking localization becomes stronger with increasing speed. For a moving beam with identical spans, the two loci of each pair of natural frequencies may exhibit one or more crossing(s) (depending on the value of tension) when plotted against the axial transport speed. These crossings become veerings when the beam is disordered, and localization is strongest at those speeds where the eigenvalue veerings occur.
An Experimental Study of the Influence of Disk Flexibility and Rubbing on Rotordynamics
Authors: Wu Fangsheng , Flowers George T.
Published: March 2021

This study is an experimental investigation of the influence of disk flexibility and rubbing on rotordynamics. The rotor rigs used in the experiments were designed to have included disk flexibility and a rubbing mechanism. The governing equations of motion are similar to those studied in analytical investigations. The system responses to imbalance were recorded and orbit trajectories were plotted at a set of different rotating speeds. The results show the rubbing response development from light forward bouncing, mixed forward bouncing, to high amplitude backward whirling heavy rubbing. The results also show that the flexible-disk rotor has the tendency of having a high frequency component at the upper rotor speed range of mixed bouncing. These agree very well with the results from an earlier analytical study.
Whirling of Composite-Material Driveshafts Including Bending-Twisting Coupling and Transverse Shear Deformation
Authors: Bert Charles W. , Kim Chun-Do
Published: March 2021

A simplified theory for predicting the first-order critical speed of a shear deformable, composite-material driveshaft is presented. The shaft is modeled as a Bresse-Timoshenko beam generalized to include bending-twisting coupling. Numerical results are compared with those for both thin and thick walled shell theories and generalized Bernoulli-Euler theory.
A New Damper Seal for Turbomachinery
Authors: Vance John M. , Schultz Richard R.
Published: March 2021

A new type of labyrinth seal for damping vibration and whirl in turbomachinery has been invented and tested at Texas A&M University (TAMU). Test results of the prototype, along with a conventional labyrinth seal, show that the new design has fifteen times more direct damping than the conventional bladed seal. The design also has a feature that blocks swirl of the working fluid, which is known to be destabilizing in machines with conventional seals. This paper shows how the new design is different from conventional bladed seals and honeycomb seals, describes the test apparatus and results, describes a theory which explains the test results, and explains how the seal can be much more effective than a bearing damper for reducing vibration in turbomachines with a compressible working fluid.
Theory Versus Experiment for Short (L/D = 1/6) Honeycomb and Smooth Annular Pressure Seals
Authors: Childs Dara W. , Kleynhans George F.
Published: March 2021

A study which compares theoretical predictions of experimental rotordynamic and leakage results is presented for short (L/D = 1/6) honeycomb and smooth annular pressure seals. A computer code used in this comparison has been developed from a theory that employs a perturbation analysis of the governing equations flow and uses Moody’s pipe friction relationship for the surface friction of the rotor and stator. This study was undertaken to investigate how well an existing code could predict these characteristics with input provided from recorded test data and independent flat-plate tests. The results examine the effect that the following independent test parameters have on the experimental measurements and theoretical predictions: inlet preswirl, rotor speed, inlet pressure, pressure ratio across seal, seal clearance, and honeycomb cell width. Experimental results show that leakage is reduced by decreasing the honeycomb cell width. Rotordynamically, the short seals are stabilizing over all test parameter ranges. However, the short seals did not perform as favorably as longer (L/D = 1/3) seals. In general, the theory overpredicts rotordynamic coefficients and leakage.
A Theoretical Approach to Determine Angular Stiffness and Damping Coefficients of an Axial Spline Coupling in High-Speed Rotating Machinery
Authors: Ku C.-P. Roger , Walton James F. , Lund Jorgen W.
Published: March 2021

This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. A unique test methodology and data reduction procedures were developed. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a non-rotating shaft was excited by an external shaker. A rotordynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. In addition, sensitivity analyses were performed to demonstrate that the accuracy of the dynamic coefficients do not rely on the accuracy of the data reduction procedures.
Crack Detection in Turbo Rotors Vibrational Analysis and Fault Detection
Authors: Söffker Dirk , Bajkowski Jozef , Müller Peter C.
Published: March 2021

Applying the theory of Lyapunov exponents for nonsmooth dynamical systems, chaotic motions and strange attractors are found in the case of a cracked rotor. To detect the crack and establish a clear relation between shaft cracks in turbo rotors and induced phenomena in vibrations measured in bearings, a model-based method is applied. Based on a fictitious model of the time behaviour of the nonlinearities, a state observer of an extended dynamical system is designed resulting in estimates of the nonlinear effects.
Explicit Solution of LQG Compensator Design Problem for Flexible Structures With Collocated Rate Sensors
Authors: Balakrishnan A. V.
Published: March 2021

We present an explicit solution to a stochastic control problem generally referred to as the LQG (Linear Quadratic Gaussian) or Stochastic Regulator problem for continuum models of flexible structures with collocated rate sensors, which holds a fortiori for FEM or truncated modal models. Robustness properties accruing from the positive realness of the optimal compensator transfer function are described, and convergence of modal approximations is proved. Preliminary experimental results on the NASA LaRC SCOLE testbed are included.
An Application of Active Dynamic Absorber to the Milling Process and its Experimental Verification
Authors: Liu K. J. , Rouch Keith E.
Published: March 2021

In order to reach the inside surfaces of some workpieces, a prototype for milling extension is developed. The milling extension has a low static stiffness and is prone to machine tool chatter, therefore vibration control in this type of machining is of importance. The paper proposes the application of an active dynamic absorber to the milling process. A finite element model for the milling extension with consideration of the cutting dynamics is developed. An annular ring serving as the dynamic absorber mass is connected to the main system through active force generating systems which are piezoelectric translators functioning as actuators. The annular ring and the actuators are functioning as an active dynamic absorber in the theory to suppress the vibration of the milling system. Optimal control algorithms are used to calculate the Kalman feedback control for the equivalent lumped-mass milling structure model. Transient responses of the system are obtained. Oscillation of the milling extension equipped with the active dynamic absorber is attenuated appreciably, therefore the surface finish of a workpiece is improved. Harmonic responses are also obtained with and without the feedback control to show the superiority of the active control technique. A proof-of-concept experiment is designed and conducted to verify the theoretical prediction. Comparisons between the simulation and experimental results are made.
A Brief Study of Passive Viscous Damping for the SPICE Bulkhead Structure
Authors: Thompson Thomas J. , Baumgarten Joseph R.
Published: March 2021

The SPICE Testbed at Phillips Laboratory is being used to evaluate the effects of structural vibration on line-of-sight error for this strut built structure. A design incorporating active control and passive damping techniques is suggested to reduce the optical path distortion created in the vibrating structure. The passive viscous damping applied to the structure serves to aid the active control system stability in the cross-over and spill-over frequency range by producing a specified magnitude of damping in specified critical modes. This magnitude of damping is to be achieved by replacing the standard filament wound undamped struts with optimally placed D-struts which contain series and parallel combinations of springs and viscous dampers and produce damped vibration response from in-line strut deflection. This D-strut must replace standard struts in a tear-down of the bulkhead. The present study proposes to provide the requisite damping by adding on viscous damping at diagonal nodal locations in the bulkhead, circumventing the need to disassemble the SPICE bulkhead. The study shows specific increase in loss factor and improved damping ratio provided by the diagonal dampers when compared to in-line D-struts for specific modes and frequencies.
Combined Piezoelectric-Hydraulic Actuator Based Active Vibration Control for Rotordynamic System
Authors: Tang Punan , Palazzolo Alan , Kascak Albert , Montague Gerald , Li Wenduan
Published: March 2021

Previous research by the authors concentrated on using piezoelectric actuators for active vibration control (AVC) of rotating machinery. The current work extends this by positioning the piezoactuator remotely from the controlled structure and transmitting the control force via a hydraulic line and two pistons. Liquid plastic is employed as a transmission “fluid” to obtain a high bulk modulus and low leakage. The paper presents results for bulk moduli measurement, and bench and rig tests for the entire actuator system. These results show the high effectiveness of the hybrid actuator for controlling vibrations on a laboratory rotor test rig.
Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method
Authors: Rao Mohan D. , Gorrepati Krishna M.
Published: March 2021

This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.