bluuebunny/crossref_metadata_2025 huggingface dataset:
Component Minimum Life Estimation Based on Life Testing Suspended Prior to Failure
Authors: Ehrich Fredric F.
Published: March 2021

One possible approach to life extension of aerospace components is to take those parts or subsystems that have run the limited initial life estimate and been removed from service, and to operate them in simulated service for periods of time beyond the initial life estimate. It is often the case that such testing must be suspended before the part reaches the point of actual failure. A need therefore exists to use such suspended test data to infer a life limit.

The standard deviation of the estimated life can generally be reliably quantified by applying results from laboratory material tests and information on the variability of the unit’s dimensions. The derived life estimate must therefore be consistent with the known standard deviation.

The problem is structured as a variational one, that is, a problem of finding the values of a set of variables — the hypothetical duration of the individual suspended tests if they had been continued to failure — subject to the constraints that the period of continuation must be equal to or greater that zero, and that the standard deviation of the average value of the life of the sample set be equal to the known, predetermined value. The problem is made determinate by applying the conservative requirement that calculated average life of the sample set be the lowest possible value.

Although the problem is nonlinear and not amenable to traditional linear programming solution, a very simple pair of algorithms have been identified which permit exact solution for all ranges of objective standard deviation. Solutions to typical problems are given to illustrate the utility of the procedure.
Firmware Design Capture
Authors: Viste Michael J. , Cannon David M.
Published: March 2021

One of Allen-Bradley’s goals is leveraging — taking better advantage of existing resources. We are developing a methodology and supporting tools that help engineers share and reuse (i.e., leverage) their firmware design and development work. Writing reusable firmware source code is especially difficult due to the tight constraints in most embedded systems — code must usually be written for product specific hardware needs and resources. Reuse of engineering work at the design level is a more effective approach.

With this in mind, we have been working with Allen-Bradley Power Products engineers and managers to pilot a Firmware Design Capture (FDC) system. In a FDC system, engineers work in their own paper or electronic workbooks compiling descriptions of their domains’ technologies and algorithms in loosely structured electronic document sets called technology books. Product-specific information is placed in complementary document sets called product books. Engineers can access this growing body of ‘Strategic Design Information’ that they and others have created; freely drawing from, commenting on, or adding to it. Key characteristics of this FDC system are:

• A focus on collecting reusable and accessible design information

• Incremental, small-grained development of documents during design activity

• Electronic format of documents, for ease of refinement and access

• Unobtrusive tools and methods, determined through frequent user feedback

We expect this methodology to help engineers improve schedule predictability and reduce the firmware development life cycle, better retain vital technologies and product data, and increase product quality. Feedback from our initial work supports these expectations.
The Creation of a Taxonomy for Manufacturability Design Requirements
Authors: Gershenson John A. , Stauffer Larry A.
Published: March 2021

In this paper, we present a taxonomy of manufacturing issues used in the design process. The purpose of this taxonomy is to serve as a checklist of issues about manufacturing that can be considered during the product definition process. Such a taxonomy helps designers to incorporate manufacturing considerations in conceptual and detail design. In this paper, we also present the taxonomy’s development. A study was conducted to improve our initial taxonomy by soliciting reviews from experienced, practicing engineers. In this way, we hope to assure that the taxonomy is useful in an industrial design context.
A Model of Information Exchange in the Design Process
Authors: Christian Andrew D. , Seering Warren P.
Published: March 2021

This paper describes a method of modeling the engineering design process and a simulation that implements the model. The model explicitly represents the communication requirements of interdependent design projects and the assigned roles of individuals. The simulation uses computer agents to represent individuals working within a design environment, exchanging information, and making decisions based on a limited rationality model of human behavior. This paper describes how the model and simulation can be used to make predictions about design team performance.
Modeling Uncertainty in Preliminary Design: A Short Review
Authors: Butler A. C. , Coates G. R. , Rao S. S. , Sadeghi F. , LeClair S. R.
Published: March 2021

Several mathematical theories exist for modeling uncertainty, and this paper explores the use of three different techniques for modeling judgment in preliminary engineering design. The relative advantages and disadvantages of each theory are discussed from an applied perspective based on experience with prototype systems. These techniques include the Dempster-Shafer theory, Bayesian Belief Networks, and Fuzzy Systems. Additionally, the relative merits and limitations of each technique are discussed in a qualitative manner drawing on experience gained with each model. Conclusions are drawn about the effectiveness of these techniques for representing uncertainty in preliminary engineering design.
Design for Product Variety: Key to Product Line Structuring
Authors: Ishii Kosuke , Juengel Cheryl , Eubanks C. Fritz
Published: March 2021

This study develops a method to capture the broadest customer preference in a product line while minimizing the life-cycle cost of providing variety. The paper begins with an overview of product variety and its importance in overhead costs: supply chain, equipment and tooling, service, and recycling. After defining the product structure graph as a representation of variety, the paper introduces an approximate measure for the customer importance and life-cycle cost of product variety The cost measure utilizes the concept of late point identification which urges standardization early in the manufacturing process and differentiation at the end of the process. The variety importance-cost map allows engineers to identify cost drivers in the design of the product or the manufacturing system and seek improvements. The refrigerator door example illustrates the concept. On-going work seeks to validate and enhance the method with several companies from different industries.
Designing Student-Centered Learning Into a Multimedia Classroom: One Small Step
Authors: Heidler Jeffrey S. , Thompson John C. , Hrinyak Matthew J. , Mistree Farrokh
Published: March 2021

Courses today are instructor-centered in that students rely on the instructor and textbook as knowledge sources and offer themselves as “empty vessels” to be filled with facts and skills. We are interested in exploring student-centered learning using multimedia technology. We want to determine how multimedia can be used to empower students to controltheir own learning. In this paper, we report on a small part of our investigation, namely, the development of a framework for implementing engineering case studies in multimedia to facilitate student-centered learning.
Life Algorithm: Its Concept and Application
Authors: Fukuda Shuichi , Konishi Fumikazu
Published: March 2021

Recently an autonomous system that meets the growing demand for solving a problem in adiversifying environment has been desired, in order to secure more robustness and flexibility. As a first step towards establishing such an autonomous system, we developed Life Algorithm (LA). Life Algorithm is fundamentally an extension of Genetic Algorithm (GA). While the conventional GA approach is based on genes and is homogeneous in its essence, LA is something more like a genome and realizes more diversity. A group of genes with different evaluation function is considered and these constitute agents. Thus, more individuality and more interaction between these agents can be taken into account and more robustness to cope with the widely and quickly changing environment can be realized. This paper demonstrates the usefulness of an LA approach by illustrating the example of power plant operation through simulation and an experiment of a solar cell system.
Direct and Intuitive Input Device for 3-D Shape Design
Authors: Murakami Tamotsu
Published: March 2021

Standard input tools such as the mouse and keyboard do not provide users with a direct and intuitive means of 3-D shape manipulation. This study proposes a new concept of interface system for 3-D shape deformation using a deformable real object as an input tool. By deforming the tool with bare hands with a tactile feedback, users can manipulate a 3-D shape modeled and displayed on a computer screen directly and intuitively. A prototype with a cubical input tool made of electrically conductive polyurethane foam demonstrates the effectiveness and promise of the concept.
Section CAD: A Tool for Rapid Prototyping
Authors: Fukuda Shuichi , Suzuke Daisuke
Published: March 2021

This paper proposes a new methodology for a geometric design. While a conventional 3-D CAD directly treats an object in a 3-D space, Section CAD, which we propose in this paper, treats the object as a set of several discrete sections. Therefore, editing only 2-D information, Section CAD enables a designer to design a topologically complex object more intuitively than conventional ones at the earlier stages of design.

Because Section CAD can interpolate between a few distant sections properly, the designer does not have to edit all sections of the object. In this way, Section CAD provides a very flexible tool for rapid prototyping by generating the whole shape of an object using discrete partial sections.
A Study on Topological Optimization of Structure Using Cantor Function As Teaching Function
Authors: Arakawa Masao , Ohkubo Naoto , Yamakawa Hiroshi
Published: March 2021

In order to obtain better structural designs, it is important to carry out optimization from primary parts of those designs. Especially, designs of topologies of structures were depended on intuition of the designers and they were not always best fitted to the requirements of the structure. These days, designs of topologies of the structures become important to meet those purposes. In this study, we will propose a new method to obtain optimum topology of the structure to satisfy their requirements by growth and degeneration tutored by Cantor function as teaching function. Cantor function is the one which is very famous as an introduction of the fractal. By operating its order, it is very easy to manipulate its division among 0 and 1. We set skipping and restarting rules of growth and degeneration, and criteria of convergence. We applied the proposed method to the problem similar to the one well-known as Mitchell truss problem to compare the results obtained by the proposed method. From these numerical examples, we can obtain quite similar topological results to the homogenization method in small number of iteration. There, the proposed method has advantages in computational time, cost and memory. More over, we can see the growth of the topology. Although we demonstrate the proposed method in a few examples, we can say that the proposed method can derive optimum oriented topology even with this simple scheme efficiently.
Japanese Product Development: Today and Tomorrow
Authors: Fukuda Shuichi
Published: March 2021

The task of creating a common basis among different people becomes more and more important with the increasing complexities and diversification of product, since collaboration becomes inevitable. But Japanese have to develop some new technologies for assisting them, since we communicate non-verbally rather than verbally. Japanese could work together as a team up to now, since there were a clear goal from the first. To cope with the diversification, goal finding will be most important.

VR and multimedia technologies would be very promising, but they have tobe adapted to the Japanese way, where the atmosphere or the sense of sharing the same way of thinking plays a much important role than true production of the real world.

If such technologies could be developed, they will also serve a great deal for attaching values to the processes of design and production. The conventional approach considered values in terms of the performances of the final products alone and the processes to realize them were regarded only as cost inreasing factors. But this situation will surely change if such technologies can be realized.
A New Concept in Mechanical Design Education: The Mechanical Systems Engineering at the University of Technology of Compiegne (France)
Authors: Ramond Bruno
Published: March 2021

This paper presents the Mechanical Systems Engineering at the University of Compiegne. After a description of the education system at UTC, we examine some particular aspects of MSE and the main ideas we had in mind when we have developed this project.
Design for Maintenance by Constrained Motion Planning
Authors: Li Tsai-Yen , Chang Hsuan
Published: March 2021

In designing an assembly product, maintainability is a crucial issue that determines whether certain parts can be accessed for routine maintenance. In the past its study has been largely manual and labor intensive. Either by using physical mockup or computer animation with CAD models of a design, the task relies on human to provide an access path for the part. In this paper we present an automated system that replaces the traditional manual process. By applying results from and developing extensions to the motion planning research in robotics, we demonstrate that this automated system is an effective addition to CAD systems. We specifically describe the extension that accounts for special motion constraints imposed by designers. We also present experimental results from applying such a system to problems in industrial applications. The results show that such an system can not only reduce the turn-around time for checking maintainability of a product but also provide more accurate feedback to the designers on potential maintenance problems.
A Virtual Reality Environment for Synthesizing Spherical Four-Bar Mechanisms
Authors: Osborn Scott W. , Vance Judy M.
Published: March 2021

This paper describes the development of a virtual reality environment which facilitates the design of spherical four-bar mechanisms. The virtual environment allows the user to naturally interact with the input data and specify the design parameters while operating in a three-dimensional environment. We see this development as a logical extension of existing graphics-based spatial design software. The need for a three-dimensional design space is driven by the difficulty in specifying design inputs and constraints for a spatial problem using a two-dimensional interface. In addition, once the mechanism has been created, the virtual environment provides the opportunity for the user to visually verify that the mechanism will perform the desired three-dimensional motion.
Shape Similarity Assessment of Mechanical Parts Based on Solid Models
Authors: Sun Tien-Lung , Su Chuan-Jun , Mayer Richard J. , Wysk Richard A.
Published: March 2021

Previous research toward part similarity assessment has been based on two kinds of symbolic part representation schemes, i.e., GT coding schemes and form feature based descriptions. The performance of these approaches is limited because the symbolic part representation is information incomplete and ambiguous. A solid model, on the other hand, is an unambiguous and information complete computer representation for 3D objects. In this work, the shape similarity between two polyhedra is formalized based on isomorphic subgraphs of graph representations extracted from their boundary models. A novel approach is proposed to match subgraphs. Input to the proposed methodology consists of two types of solid models, i.e., the boundary model and a CSG representation called the TO tree. The TO tree is used to derive a set of major sweep directions for a part. Using the matched major sweep directions as probes, a generate-and-test strategy is applied to find the matched subgraphs. A prototype system based on the proposed methodology has been implemented. The prototype system was programmed in AutoLisp© and is interfaced to the AME© solid modeler of AutoCAD©. Shape similarity comparison between various mechanical parts with intersecting features has been successfully accomplished by the system.
Multibody Modeling of Vehicles in a Virtual Prototyping Environment
Authors: Vejju Kishore Sai , Freeman Jeffrey S.
Published: March 2021

This paper presents concepts involved in the theory and implementation of a vehicle body and suspension modeling tool as part of the software development for the National Advanced Driving Simulator (NADS). The NADS will be a state-of-the-art, operator-in-the-loop ground vehicle simulator, which can be applied to both human factors and vehicle virtual prototyping studies. By applying the modeling tool developed in this study, vehicle kinematic models can be easily created and tested, either using off-line engineering analysis packages or using operator-in-the-loop simulators, such as the NADS.

Vehicles are complex systems containing multiple bodies, joints and force generating elements. Manually modeling these systems for kinematic and/or dynamic analysis is tedious and prone to errors. This creates a need for a modeling tool which reduces modeling time, increases modeling accuracy and is easy to use. This paper discusses the concepts involved in developing a modeling tool for the topology analysis and assembly of the multibody vehicle model. Suspension system modeling is briefly described, along with an example employing the US Army HMMWV vehicle.
Consistency Management in Feature-Based Parametric Design
Authors: Vieira Ana Sofia
Published: March 2021

One of the main problems to be solved in design-by-features is to preserve the semantic correctness of feature-based models. Currently, feature-based parametric design (FbPD) is being used as one of the most powerful approaches for solving this problem. In this paper, a fundamental principle of this approach is introduced. Three aspects stated, are: FbPD deals with functional design primitives, it solves the automatic generation of model variations, and it offers the basis for the development of a mechanism to check the semantic correctness of feature-based models. Several concepts for the definition of semantic constraints are presented. They instigate the classification of semantic constraints in four different categories, based on the constraint evaluation-time, purpose, behaviour, and representation. Sinfonia, a system for feature-based parametric design, is presented as a testbed environment for design-by-features applications. One of its modules, the Consistency Handler, uses the constraint concepts introduced in order to preserve the semantic consistency of the models. Several examples illustrate the different types of constraints. In addition, an algorithm applied for the process of a consistent feature modification is presented.
Joint Optimization of Functional Performance and Production Costs Based Upon Mechanical Features and Tolerances
Authors: Xue D. , Rousseau J. H. , Dong Z.
Published: March 2021

A method for jointly evaluating and optimizing the functional performance and production costs of a design is introduced to produce high quality designs with better life-cycle performance and shorten product development lead-times. Various design approaches considering both functional performance and production costs are investigated. A method for associating performance with costs based upon a combined feature, tolerance and production process model is introduced. The methods are illustrated using a typical design example of the hole feature. The study contributes to optimal design theory, and forms the basis for integrated concurrent engineering design.
Gravitational Effects on Two Link. Flexible Multibody Systems
Authors: Smart David W. , Wiens Gloria J.
Published: March 2021

Few flexible multibody studies have been conducted in which gravity is included in the analysis and of these, none include the axial component of the gravitational loading. However, as multibody systems become increasingly more flexible, the axial loads induced by gravity are playing an increasingly more important role in the elastic characteristics of multibody systems, especially in the ground testing of those for space applications. In an effort to minimize the unreliable aspects in ground testing, the research presented here provides a relatively simple theoretical model based on the quasi-dynamics of two link multibody systems with an arbitrary orientation within the gravitational field. The theoretical model has shown gravity does play a significant role in predicting accurate first and second frequencies and the static deflections of such systems. Experimental verification of the theoretical results is presented.
Elastic Robot Arms With Variable Length: Part I — A Systematic Nonlinear Modeling Approach
Authors: Söffker Dirk
Published: March 2021

In this paper modeling of a geometric nonlinear beam and the corresponding matrix representation of the model of 3rd order is considered. Especially in the case of lightweight robots for space applications undergoing large reference motion, the nonlinear dynamic behaviour of the beam should be modeled as exact as possible. Here coupling effects betweeen the elastic variables due to the geometric nonlinear beam kinematic are important. ‘Stiffning effects’ and parametrically excited effects between longitudinal and bending vibrations e.g., should also be considered.

Starting with the nonlinear beam kinematics, all equations up to terms of second order are considered. Using the principal of virtual work, nonlinear equations are given, which are discretized by Hermite polynomials in the next step. Considering also terms of second order in the elastic variables, a special technique handling this equations in the usual structural dynamics matrix representation is developed to preserve the couplings of higher order in contrast to the usual linearization. Additionally, the length-variability is considered. So the clearness and effectiveness of matrix methods is combined with beam theory of 3rd. order, this means quadratic terms for the elastic variables axe considered building up state-dependend matrices. The importance of the effects of those couplings axe shown by two simulation examples of a planar and a spatial lightweight, very flexible telescopic robot arm for space operations. It can be shown clearly, that beside the known stiffning effects due to nominal axial loads, effects of higher order may weaken the structure up to failure of the structure.
Numerical Study of an Impact Oscillator
Authors: Marudachalam Kannan , Bursal Faruk H.
Published: March 2021

Systems with discontinuous dynamics can be found in diverse disciplines. Meshing gears with backlash, impact dampers, relative motion of components that exhibit stick-slip phenomena axe but a few examples from mechanical systems. These form a class of dynamical systems where the nonlinearity is so severe that analysis becomes formidable, especially when global behavior needs to be known. Only recently have researchers attempted to investigate such systems in terms of modern dynamical systems theory.

In this work, an impact oscillator with two-sided rigid constraints is used as a paradigm for studying the characteristics of discontinuous dynamical systems. The oscillator has zero stiffness and is subjected to harmonic excitation. The system is linear without impacts. However, the impacts introduce nonlinearity and dissipation (assuming inelastic impacts). A numerical algorithm is developed for studying the global dynamics of the system. A peculiar type of solution in which the trajectories in phase space from a certain set of initial conditions merge in finite time, making the dynamics non-invertible, is investigated. Also, the effect of “grazing,” a behavior common to constrained systems, on the dynamics of the system is studied.

Based on the experience gained in studying this system, the need for an efficient general-purpose numerical algorithm for solving discontinuous dynamical systems is motivated. Investigation of stress, vibration, wear, noise, etc. that are associated with impact phenomena can benefit greatly from such an algorithm.
Impacts With Friction
Authors: Pfeiffer Friedrich , Glocker Christoph
Published: March 2021

Mechanically impacts with friction include questions of relative kinematics and of constraint dynamics both in normal and in tangential directions. In addition both directions are of course coupled because impulses in one direction influence the behaviour in the other direction, especially when considering the normal impulses stored at the end of the compression phase. Together with the stored tangential impulses it governs the expansion phase. Paper presents a model of such impacts with friction considering a compression and an expansion phase. Some examples illustrate the practical relevancy of the theory.
Experimental Investigation of the Dynamics and Bifurcations of an Impacting Spherical Pendulum
Authors: Garza S. , Ertas A.
Published: March 2021

An experimental investigation was performed to determine the dynamics of an inverted, impacting spherical pendulum with large deflection and vertical parametric forcing. The pendulum system was studied with nine different bob and two different base configurations, for twenty times the natural frequency at shaker powers of 0 to 125 mm-hz. It was found that sustained conical motions did not naturally occur. The spherical pendulum system was analyzed to determine under what conditions the onset of Type I and sustainable Type II responses occurred.
Frictional Impact of an Elastic Body
Authors: Marghitu Dan B.
Published: March 2021

A model is presented for the impact with friction of a flexible beam in translational and rotational motions. This model enables one to predict the rigid body motion as well as the elastic after the impact. The system of equations is written in the Lagrangean formalism using a set of coupled reference position and local elastic generalized coordinates. The model uses an experimental dynamic coefficient of friction and an experimental co-efficient of restitution. We introduce a finite number of vibrational modes to take into account the vibrational behavior of the beam during impact.
Control of Nonlinear Parametrically Excited Beam Vibrations
Authors: Schlacher Kurt , Irschik Hans , Kugi Andreas
Published: March 2021

A straight composite beam under the action of a harmonic axial support motion is considered. Piezoelectric layers are used to control the parametrically excited vibrations. A nonlinear initial-boundary-value problem for the deflection is derived, which is approximated by a set of nonlinear ordinary differential equations. The controller design is based on the differential geometric approach by extending the method of input output linearization to the time variant case. Controllers with different zero dynamics are presented to show that the approximating system can be stabilized by a proper choice of the virtual output function.
Techniques for Periodic Control of Flapping of a Helicopter Blade
Authors: Pandiyan R. , Sinha S. C.
Published: March 2021

The primary objective of this paper is to present new periodic control strategies for the control of flapping motion of an individual helicopter rotor blade in forward flight which is represented by a differential equation with periodic coefficients. First, an algebraic procedure based on Chebyshev polynomial expansion is employed to control the periodic flapping motion. In this approach, the state vector and the elements of the periodic system matrix have been expanded in terms of shifted Chebyshev polynomials of the first kind over the principal period. Later, optimal control theory in conjunction with Floquet Theory has been used to design full state and observer state feedback controllers. In the second method, the feedback controllers have been designed in the time-invariant domain through an application of a linear, invertible, periodic transformation known as Liapunov-Floquet (L-F) transformation to the periodic system model. It is shown that by using both the methods the periodic control gains can be obtained as explicit functions of time and therefore, a control scheme more suitable for real-time implementation can be achieved. The design procedures have been found to be much simpler in character when compared to those techniques that have been appeared in the literature.
In-Plane Vibration of High-Speed Spur Gear Webs
Authors: Arakere Nagaraj K. , Nataraj C.
Published: March 2021

High cycle fatigue loading of gear webs due to in-plane stresses, caused by forced excitation resulting from centrifugal loading and dynamic tooth loads, has been known to cause radial fatigue cracks. This is especially prevalent in high-speed gears used in aerospace applications, with small web thickness, for weight reduction. Radial cracks have also been observed to originate at the outer edge of lightening holes machined in gear webs for weight reduction. This paper presents an analytical treatment of the in-plane vibration of high-speed gear webs resulting from rotational effects and periodic excitation from dynamic tooth loading. Dynamic tooth loads result from the combined effect of inertia forces of gear wheels which are significant at high speeds, the periodic variation of gear mesh stiffness, and involute tooth profile errors.

The gear web is modeled as a thin rotating disc and the governing differential equations of motion and the associated boundary conditions are derived from first principles. A comprehensive tooth stiffness model for spur gears is used that accounts for periodic variation of mesh stiffness. The dynamic tooth loads are obtained by solving the pertinent equations of motion, using a collocation method, that yields a closed-form expression for the periodic excitation, that is used as an input for the in-plane vibration problem. The in-plane vibration equations are solved by an approximate method of weighted residuals. It is found that the displacement fields and the resulting stresses can be significant under certain speeds and loading conditions. The in-plane stresses leading to high cycle fatigue loading, and frequency components of the resulting response are discussed in detail.
Dynamics of a Free Play Type of Nonlinearity System Under Deterministic and Random Excitations
Authors: Orabi Ismail I.
Published: March 2021

The dynamics of nonlinear structures under harmonic and random excitations is studied. The harmonic excitation is modeled by periodic loadings while the random excitations is modeled by segments of stationary Gaussian white noise processes. Transient responses of a single-degree-of-freedom model is studied to illustrate the characteristic of nonlinear responses. A free play type of nonlinearity is considered. The effects of nonlinearities on the overall dynamics of structure is investigated. The linearization technique is used to calculate the response statistics. To check the accuracy of the linearization technique, the results are compared with Monte-Carlo digital simulations and good agreement are observed.
Parametric Vibrations in a Magneto-Thermo-Elastic Layer of Finite Thickness
Authors: Wauer Jörg
Published: March 2021

The dynamic behavior of a magneto-thermo-elastic planar layer subjected to a bias magnetic field is examined. The magnetic field acts parallel to the layer surfaces and is composed of a constant and a harmonically oscillating part. In particular, the small coupled magneto-thermo-elastic vibrations superimposed on the basic steady state response due to the stationary magnetic excitation are analyzed. Attention is focused on the influence of the pulsating part of the bias magnetic field on the governing variational equations to prove the stability of the basic state. In general, the stability equations describing the perturbations of the magnetic, thermal and elastic field properties are coupled in a special form and also the parametric excitation acts in a non-classical manner. Hence the variety of possible parametric resonances seems to be limited.
Dynamic Analysis of Non-Uniform Beams With Time Dependent Elastic Boundary Conditions
Authors: Lee Sen Yung , Lin Shueei Muh
Published: March 2021

The dynamic response of a non-uniform beam with time dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. The time dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third order degree, instead of the fifth order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.
The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques
Authors: Tong X. , Tabarrok B.
Published: March 2021

In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.
Development and Application of Interpolated Cell Mapping to the Lorenz Equations
Authors: Tongue Benson H. , White Matt T.
Published: March 2021

The Interpolated Cell Mapping strategy is extended to allow an analysis of the Lorenz equations. Both cell size and mapping time are varied in order to identify optimal solutions. A higher-order interpolation method for Interpolated Cell Mapping is developed and compared to numerical integration. Regions of state space with high levels of spatial deformation are found and are seen to correspond to areas that are dense with basin boundaries.
Smoothing Technique for Rub or Looseness-Related Rotor Dynamic Problems
Authors: Goldman Paul , Muszynska Agnes
Published: March 2021

The lateral vibration response of a rotor, experiencing periodic contact with a nonrotating machine component, is considered. In the case of an inelastic impact, this causes a piecewise, step-changing stiffness of the system. Applying to the rotor model a specially developed variable transformation which smooths discontinuities, and applying then an averaging technique, a variety of imbalance-related resonant regimes of rotor lateral motion are obtained, and their stability is analyzed. The developed analytical algorithm has a high potential as a valuable research tool for investigating local nonlinear effects in rotor systems.
Nonlinear Vibration Characteristics With Large Unbalance of Turbogenerators Rotor Systems
Authors: Lu Songyuan , Wei Gao
Published: March 2021

Some catastrophic vibration failures of turbogenerators shaft system have occurred in China and abroad. But, since the researches on nonlinear vibration characteristics of real engineering rotor-bearing system were not thoroughgoing in the past years, so the accurate and quantity analysis on particular accidents is still impossible. However, to understand the nonlinear vibration characteristics with large unbalance is engineering important for accident analysis, investigation and for precautions against the failures.

This paper employed a new transfer matrix-time marching approach, and made researches on calculation for nonlinear vibration caused by large vibration at the generator rotor and low pressure rotor of 200MW turbogenerators made in China.

By this study, some new and important conclusions concerned transient process while much mass escaped from turbogenerators rotor at operation condition have been obtained. They can provide valuable suggestions to the accident analysis, the design of large turbogenerators shaft and operation technology of the power plants, and these conclusions will be the foundation for the further researches on the destruction mechanism of turbogenerators forced by nonlinear vibration.
Effects of Experimental Procedures on Narmax Model Estimation
Authors: McCabe Sarah A. , Davies Patricia
Published: March 2021

The nonlinear autoregressive moving average model with exogenous inputs (NARMAX model) is a convenient digital representation that can be used to simulate a large class of nonlinear vibratory systems. However, the process of identifying the model structure and estimating the model term coefficients can be prohibitively computationally intensive. Most identification techniques start with a model structure containing all possible terms and then use an algorithm to determine the significance of each term and reduce the model size by eliminating insignificant terms. For many physical systems of interest (such as those with high order dynamics or multi-inputs/multi-outputs), the size of the model can exceed the available computational resources. It therefore becomes necessary to apply all available knowledge of the physical system to eliminate terms from the initial model structure and reduce this task to manageable proportions. To explore the utility of this identification method, it was used to identify the NARMAX model for a numerically generated single degree of freedom system. The identified model was used to simulate the system; a comparison is made between the numerically integrated response and the NARMAX simulated response. However, it is one thing to test system identification techniques by applying them to numerically generated data and quite another to use data which has been measured from a physical system. Not only are there differences between the ideal model of the system and the physical system, the measurement process introduces other changes to the data such as sampling effects, quantization effects, filtering effects, and measurement induced noise. In order to determine what effects on the model identification process are introduced by each step in the measurement process, the numerically integrated data was successively modified to simulate the effects of filtering and quantization (which introduces measurement noise) and the model identification process was performed on this altered data. These newly identified models were again used to simulate the system for purposes of comparison. Finally, the model identification process is applied to data measured from a physical system and the resulting model is evaluated for the purpose of simulation.
Identification of Nonlinear Systems Parameters Using Polyspectral Measurements and Analysis
Authors: Hajj Muhammad R. , Nayfeh Ali H. , Popovic Pavol
Published: March 2021

Experimental and analytical techniques that characterize nonlinear modal interactions in structures are used to quantify parameters in representative nonlinear systems. The subject of the experimental study is a three-beam frame. Subharmonic resonances and interaction between widely spaced modes are exploited to determine nonlinear parameters in models that represent these interactions. The phases of the auto-bispectra of the response of this structure appear in the analytical solutions of the representative models. Values of these phases could thus aid in determining other unknown parameters of nonlinear systems.
Applications of Time-Frequency Analysis to Structures With Internal Resonance
Authors: Dippery Kyle D. , Smith Suzanne Weaver
Published: March 2021

Time-frequency analysis is an approach to characterizing the nature of signals whose frequency content changes over time. Although the primary applications of this field have, to date, been in the area of communications and signal analysis, it is becoming known in the field of structural dynamics. This paper explores the application of two straightforward time-frequency techniques to several structures that exhibit internal resonance. In particular, the systems analyzed exhibit simple modal interactions and, in one case, a transition to chaos. While other methods exist for analysis of these types of behaviors, larger systems with more complex resonances maybe better analyzed with time-frequency techniques.
The Nonlinear Vibration Analysis of a Clamped-Clamped Beam by a Reduced Multibody Method
Authors: Kovacs A. P. , Ibrahim R. A.
Published: March 2021

The nonlinear response characteristics for a dynamic system with a geometric nonlinearity is examined using a multibody dynamics method. The planar system is an initially straight clamped-clamped beam subject to high frequency excitation in the vicinity of its third natural mode. The model includes a pre-applied static axial load, linear bending stiffness and a cubic in-plane stretching force. Constrained flexibility is applied to a multibody method that lumps the beam into N elements for three substructures subjected to the nonlinear partial differential equation of motion and N-1 linear modal constraints. This procedure is verified by d’Alembert’s principle that leads to a discrete form of Galerkin’s method. A finite difference scheme models the elastic forces. The beam is tuned by the axial force to obtain fourth order internal resonance that demonstrates bimodal and trimodal responses in agreement with low and moderate excitation test results. The continuous Galerkin method is shown to generate results conflicting with the test and multibody method. A new checking function based on Gauss’ principle of least constraint is applied to the beam to minimize modal constraint error.
A Study of Bifurcations in Periodic Systems
Authors: Guttalu Ramesh S. , Flashner Henryk
Published: March 2021

An approach for analysis of stability and bifurcations of multivariable nonlinear systems with periodically varying coefficients is formulated using the notion of point mapping (period to period mapping). Analytical expressions of the point mapping and its dependence on system’s parameters are obtained using a recursive procedure. The procedure yields coefficients of a multinomial expansion of the point mapping up to an arbitrary order of state variables and parameters. Analytical stability and bifurcation conditions can be then expressed as functional relations between system parameters. In addition, parametric expressions for bifurcated solutions of different periods are also obtained. The proposed approach is demonstrated in a study of parametric stability and bifurcation of a nonlinear Mathieu’s equation. Analytical conditions for bifurcation as well as expressions for bifurcation to harmonic and subharmonic solutions are derived. The results are compared to direct integration computation that are considered to be an “exact solution”. It is shown that, unlike perturbation analysis, the proposed method provides very accurate solution even for large values of the parameters. Moreover, unlike most existing methods, the approach presented here is applicable to multiple degree-of-freedom systems with multiple parameters. Most existing analysis methods apply mainly to single degree-of-freedom systems and their extension to higher dimensions is difficult and computationally cumbersome.
Experiments on a Rocking Block
Authors: Fielder William T. , Virgin Lawrence N. , Plaut Raymond H.
Published: March 2021

A rigid, slender, rectangular block is an apparently simple example of a stability problem. In a static sense, the upright position remains stable providing the restoring moment due to gravity is sufficient to offset any applied overturning moment. Rotated about either corner, the block will overturn if a critical angle is exceeded. However, if the (quiescent) block is subjected to a horizontal (dynamic) base excitation, and assuming that no sliding, bouncing, or out-of-plane motion occurs, a typical block may either: (i) remain stationary relative to the base, (ii) rock, or (iii) overturn.

The conditions under which overturning occurs are of particular interest here, i.e., the boundary between categories (ii) and (iii) above. Combinations of forcing parameters, i.e., magnitude and frequency of the sinusoidal excitation, are categorized according to whether, and how quickly, overturning occurs. The transition when the block changes from rotation about one corner to the other, the energy loss at impact, and large-angle geometric effects are the sources of nonlinearity in this problem.

Based on numerical integration, and taking great care to accurately model the impact condition, it is shown that transient rocking prior to overturning exhibits an extreme sensitivity and dependence on certain system parameters. A number of counter-intuitive features are observed. Some elementary experiments conducted on a relatively slender, rigid block placed on a shake table confirm some of the simulation results, but also point out the modeling difficulties encountered in such inherently sensitive systems.
On Integrating Factors and a Perturbation Method
Authors: van Horssen W. T.
Published: March 2021

In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.
Optimal Structural Control: A Reliability-Based Approach
Authors: Kaspari D. C. , Spencer B. F. , Sain M. K.
Published: March 2021

This paper develops probabilistically-based optimal control strategies which focus on minimizing the extreme responses of a structure subject to stochastic excitation. A performance function is chosen that is directly related to the failure probability for the structure. Optimization is performed over a parameterized class of controllers, subject to a probabilistic constraint on the available control effort. System uncertainty is modelled parametrically and is incorporated into the optimization algorithm. First and second order reliability methods (FORM/SORM) are employed for calculation of the required probabilities. A numerical example using a two story structure subject to seismic excitation is provided to illustrate the approach. The probability estimates based on the FORM/SORM approach are compared with Monte Carlo simulation (MCS) to demonstrate the efficiency and accuracy of the FORM/SORM approach.
Fuzzy Control of Nonlinear Systems in the Presence of Noise
Authors: Casciati F. , Faravelli L.
Published: March 2021

Imprecise linguistic descriptions of system conditions can be used as the basis for activating control forces. In this paper, one discusses the aspects of the application of fuzzy control to civil engineering problems. Attention is focused on the presence of noise in the sensor reading and in the time delay. The results of numerical examples studying nonlinear systems subjected to random excitations are presented to illustrate some peculiar features of fuzzy control.