bluuebunny/crossref_metadata_2025 huggingface dataset:
A Class of Forms From Function: The Case of Parts Moving in Contact
Authors: Ilieş Horea T. , Shapiro Vadim
Published: November 2020

We consider the general problem of designing mechanical parts moving in contact under the influence of externally applied loads. Geometrically, the problem may be characterized in terms of a conjugate triplet which is formed by the two shapes moving in contact and their relative motion. We show that every such triplet belongs to at least two classes of functionally equivalent designs that may be represented uniquely by maximal triplets, corresponding respectively to the two largest contact shapes that are guaranteed to contain all other possible solutions to the contact design problem.

In practical terms, the proposed characterization of the contact problem enables the systematic exploration of the design space using fully defined representatives of the functionally equivalent class of parts. Furthermore, such exploration may be performed using standard tools from geometric modeling, and without assuming any particular parametrization that necessarily restrict both the design space and possible computational techniques for exploring feasible designs. Because it supports generation of an essentially unlimited space of design solutions for a given contact problem, the proposed approach is particularly effective at the conceptual design stage.
Orchestrating Learning in a Graduate Engineering Design Course
Authors: Chamberlain Matthew K. , Williams Christopher B. , Cowan F. Scott , Mistree Farrokh
Published: November 2020

ME6101: Engineering Design is a graduate level course offered by The George W. Woodruff School of Mechanical Engineering at the Georgia Institute of Technology. The course is orchestrated to achieve three objectives, namely, to have students internalize the Pahl and Beitz design method, to help them “reinvent” the Pahl and Beitz design method to meet the challenges of the future, and most importantly, to learn how to continue learning about design. The course was given during the Fall 2000 semester to a class of nineteen students — most in their first semester of graduate school — in addition to six practicing engineers via a distance-learning program. In this paper, the techniques utilized to foster learning in ME6101 are described. Excerpts from students’ essays are presented as anecdotal evidence that the concerted use of these methods aids students both in the internalization of course content and the development of personal practices that will serve them well in and beyond their engineering careers.
The Influence of Product Modularity During Concept Selection of Consumer Products
Authors: Mattson Christopher A. , Magleby Spencer P.
Published: November 2020

The design of modular products, or modular-product design, is a powerful design strategy that can boost the competitive edge of a company that employs its benefits. We introduce in this paper an approach for managing the influence of product modularity during concept selection of consumer products. We propose a process that consists of four steps. The first step is to define the business strategy and associated objectives for the product, based on an expanded definition of modularity. The second step is to prioritize the objectives using an objective tree. The third step is to establish design metrics and the final step is to weigh each metric by the design objectives. The outcome of the process is an overall objective metric (composite score) that is used for concept selection and is a measure of the balance of design objectives affected by modularity. Finally, three product concepts of varying modularity are analyzed using various design objectives to show that the selection of the best (most suitable) concepts depend fully on the design objectives and that the most modular designs are not necessarily the best.
Towards Biomimetic Concept Generation
Authors: Vakili V. , Shu L. H.
Published: November 2020

This paper describes efforts towards generalizing biomimetic concept generation in engineering design. Biomimetic design fully or partially imitates or evokes some biological phenomenon. Nature has often inspired solutions to engineering problems. While biological phenomena hold a vast amount of ideas, a method for finding and using these ideas would make biomimetic innovation faster, easier and more accessible. The paper begins with a brief review of related research, recognition of engineering ideas in biological phenomena and advantages of the natural brand. Next presented are strategies for finding potential analogies in biological phenomena, including searching functionally across multiple levels of organization, from the molecule to the biosphere. Initial efforts at finding appropriate analogies are documented using an example in design for remanufacture.
A Real-Time Multibody Vehicle Dynamics Model Using a Subsystem Synthesis Method
Authors: Kim Sung-Soo , Oh Young-Seok
Published: November 2020

A real-time multibody vehicle dynamics model has been developed using a subsystem synthesis method in a PC-based workstation. The subsystem synthesis method produces 6 × 6 matrix form of equations of motion for the chassis and small size each of suspension subsystem equations of motion separately. Simulations such as, bump-run, stop-and-go, and brake-in-turn have been carried out. Solutions have been validated to compare with those from the model with the conventional recursive formulation. CPU times taken for simulations have been also measured to verify the real-time simulation capability of the proposed vehicle model.
A Precise and Stiffly Stable Time Integration Method for Vibration Equations
Authors: Fujikawa Takeshi , Imanishi Etsujiro
Published: November 2020

A method of time integration algorithm is presented for solving stiff vibration and motion problems. It is absolutely stable, numerically dissipative, and much accurate than other dissipative time integration methods. It achieves high-frequency dissipation, while minimizing unwanted low-frequency dissipation. In this method change of acceleration during time step is expressed as quadratic function including some parameters, whose appropriate values are determined through numerical investigation. Two calculation examples are demonstrated to show the usefulness of this method.
A Control Method for Non-Linear Time-Varying System Using Mixed H2/H∞ Control: Position and Force Control of 2-Link Manipulator
Authors: Kajiwara Itsuro , Yambe Katsuhiro , Nishidome Chiaki
Published: November 2020

Dynamics of multi-link manipulators are highly nonlinear and depend on the time varying configuration. This paper presents a method of gain scheduling which consists in designing a linear time invariant (LTI) controller for each operating point and in switching controller when the operating conditions change. Each LTI controller is designed based on LMI approach in which an optimization problem is defined as a mixed H2/H∞ control problem with pole placement. The performance of the force and the position controls is defined by the H2 norm, and the robust stability according to gain scheduling is evaluated with the H∞ norm and the pole placement of the closed-loop system. The effectiveness and the practicability of the proposed method are verified by both simulations and experiments with 2-link manipulator system.
Influence of Reference Conditions in the Analysis of the Impact of Flexible Bodies
Authors: Escalona José L. , Mayo Juana , Domínguez Jaime
Published: November 2020

In this paper, the floating frame of reference approach is applied to the dynamics of the impact of flexible bodies, while component mode synthesis is used to describe deformation. The influence of the reference conditions, that indicate the type of attachment between the body fixed frame of reference and the flexible bodies, is investigated. Rigid and free attachments allow the use of fixed interface and free interface normal modes, respectively. A finite number of fixed interface modes does not fulfil the natural boundary condition at the attachment point. Free interface normal modes cannot describe the compressive forces at the contact surface. However, it is shown that both set of modes are able to describe the impact-induced elastic waves. In the evaluation of the kinematic coefficient of restitution, these two approaches differ significantly. When free attachment is considered, the derivatives of the reference co-ordinates coincide with the equivalent rigid body velocities of the flexible bodies, remaining constant after the impact. However, if the body frame of reference is rigidly attached, the equivalent rigid body velocities of the flexible body have to be evaluated as a linear combination of the derivative of reference and elastic co-ordinates. The axial impact of a rigid body on a flexible rod and the transverse impact of a flexible pendulum with a fixed stop are simulated to illustrate these facts. Hertzian contact forces are assumed to occur during impact.
Efficient Direct Differentiation Sensitivity Analysis for General Multi-Rigid-Body Dynamic Systems
Authors: Hsu Yuhung , Anderson Kurt S.
Published: November 2020

Sensitivity analysis plays an important role in modern engineering applications where design optimization is desired. A computationally efficient sensitivity analysis scheme is presented in this paper in an effort to facilitate design optimization as it pertains to general, complex multi-rigid-body dynamic systems. Based on the underlying velocity space projection, state space formulation, and direct differentiation approach, the first-order sensitivity information can be efficiently determined in a fully recursive manner for general multi-rigid-body dynamic systems involving an arbitrary number of closed loops. The overall computational expense of this method is bilinear in the number of design variables and the number of system generalized coordinates. The solution accuracy and the computational performance are demonstrated by several numerical examples.
Plastic Deformation of Steel Safety Guardrails
Authors: Neuenhaus Detlef , Kammel Christian , Geßler Urs Joachim , Sedlacek Gerhard
Published: November 2020

In case of contact between two colliding bodies various force interactions in the contact area occur. Therefore, the virtual power for contact zones has to comprise impulse or contact in normal direction and friction in tangential direction of the common plane depending on the way of relative movement. Within this paper a sophisticated algorithm for the description of the virtual power in contact zones is presented. Hence, the implementation of this algorithm to the MEPHISTO (Multibody systems with ElasticPlastic HInges and changeable STructure Organization) multibody program code is successfully proved in the particular case of vehicle impact on a safety barrier system.
The Automatic Stabilization Algorithm for Euler-Lagrange Equations With Holonomic/Nonholonomic Constraints in Multibody System Dynamics
Authors: Pan Zhenkuan , Zhao Weijia
Published: November 2020

A new automatic constraint violation stabilization algorithm for numerical integration of Euler-Lagrange equations of motion of multibody system dynamics based on Baumgarte constraint violation stabilization method and Taylor expansion of constraint functions is presented. The constraint equations may be holonomic or nonholonomic. The parameters α, β, σ used in Baumgarte’s method are determined automatically according to integration step. Some numerical examples compare the accuracy between the traditional method and the one suggested in this paper are presented finally.
Stochastic Analysis of a Fractionally Damped Beam
Authors: Agrawal Om P.
Published: November 2020

This paper presents a general analytical technique for stochastic analysis of a continuous beam whose damping characteristic is described using a fractional derivative model. In this formulation, the normal-mode approach is used to reduce the differential equation of a fractionally damped continuous beam into a set of infinite equations each of which describes the dynamics of a fractionally damped spring-mass-damper system. A Laplace transform technique is used to obtain the fractional Green’s function and a Duhamel integral type expression for the system’s response. The response expression contains two parts, namely zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for White noise. The approach can be extended to all those systems for which the existence of normal modes is guaranteed.
Jorgen Lund: A Perspective on His Contributions to Modern Rotor Bearing Dynamics
Authors: Smalley Anthony J.
Published: November 2020

This paper presents a perspective on the work of Dr. J. W. Lund, in the field of rotor-bearing dynamics. Dr. Lund died on November 16, 2000 — indisputably the father of modern rotor-dynamic analysis. The perspective is somewhat personalized, and supplemented by personal knowledge, coming from someone who has known Dr. Lund for over 30 years, who has benefited from the insights of Dr. Lund, and whose career has been measurably advanced as a result of Dr. Lund’s personal and public contributions.

The paper traces what the author considers to be the most influential work of Dr. Lund, both in published journals, in the software which has shaped the design and problem solution for modern turbomachinery, and in data published in various manuals, government reports, and course notes. It addresses, in particular, his work in oil bearings, gas bearings, unbalance response of flexible rotors, stability of flexible rotors, squeeze-film dampers, rotor balancing, and modal testing of rotors. It provides a road map for those who would revisit the knowledge base, which has shaped the design of high performance turbomachinery for industrial applications. It shows how the work of Dr. Lund has permeated the practice of today’s suppliers of turbomachinery, the users of turbomachinery, and the consultants to the industry. Some of the publications addressed specifically by the paper are the report volumes on rotor-dynamics prepared under contract by MTI, authored by Dr. Lund, and sponsored by the U.S. Air Force in the mid-1960’s, the RPI-MTI short course notes on gas bearings, software documentation, and major papers.
The Scientific Work of Jorgen Lund and a Personal Assessment of its Significance
Authors: Rieger Neville F.
Published: November 2020

A selection of the more important works of Jorgen Lund, are described. The industrial features of the periods in which specific developments in rotordynamics took place are discussed, together with these developments themselves and the investigators who made them. Lund’s contributions are included within the latter part of this framework.

The comparative value of Lund’s work is considered in terms of several criteria, which are judged to apply to the work of investigators generally. These criteria are used to examine the characteristics of three important pioneers of vibration technology, to demonstrate the validity of these criteria. Lund’s contributions are shown to be of high caliber when judged by the same criteria.
Application of Lund’s Stability Analysis Program in Design of Modern Turbomachinery
Authors: De Choudhury Pranabesh
Published: November 2020

The analytical tool developed by Lund has aided in the design and manufacture of modern turbomachinery operating at relatively high speeds, under severe operating conditions, with high gas pressure, and gas density. The purpose of this paper is to show, by means of selected problems, as a practicing engineer in the design of high speed turbomachinery, how the methods developed by Lund aided in the design and problem diagnostics of such turbomachinery.
Theoretical Study on Instability Boundary of Rotor-Hydrodynamic Bearing Systems: Part II — Rotor With External Flexible Damped Support
Authors: Guo Zenglin , Kirk R. Gordon
Published: November 2020

The situation of a rotor-hydrodynamic bearing system in external flexible damped support is more complicated than that discussed before in Part I but it can become an alternative means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is built first. Then, the analytical study on the vertical rotor is conducted. The results show that there might be up to four threshold speeds in this configuration that form a consecutive regional pattern taken turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results of the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of value for support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.
A New Finding on the Dynamic Stiffness Matrices of Asymmetric and Axisymmetric Shafts
Authors: Raffa Francesco A. , Vatta Furio
Published: November 2020

In this paper the dynamic stiffness method is developed to analyze a rotating asymmetric shaft, i.e. a shaft whose transverse section is characterized by dissimilar principal moments of inertia.

The shaft is modeled according to the Rayleigh beam theory including the effects of both translational and rotational inertia, and gyroscopic moments.

The mathematical description is carried out in a reference system rotating at the shaft speed and is based on the exact solution of the governing differential equations of motion. The exact expressions of the shaft displacements are utilized for deriving the 8 × 8 complex dynamic stiffness matrix of the shaft.

A new relationship is obtained which links the dynamic stiffness matrix of the asymmetric shaft to the 4 × 4 real dynamic stiffness matrix of the axisymmetric shaft.
Modal Control of Flywheel Motion in Magnetic Bearings
Authors: Gosiewski Zdzislaw , Sawicki Jerzy T.
Published: November 2020

Satellite flywheels utilize the solar energy when the satellite is on the Sun side of Earth. When the satellite is in the Earth shadow, the flywheel supplies the inboard instruments with electric energy. This regime of operation causes that angular velocity of the flywheel changes over the wide range. The magnetic bearings are suitable to suspend the flywheel in the vacuum environment. In addition, they can realize other tasks, like for example automatic balancing, diagnostics, or sensor run-out compensation. The control system of magnetic bearings should account for variable plant dynamics, with parameters dependent on angular velocity. The modal approach to control flywheel motion is presented. The control scheme is developed separately for translatory and for rotary motion. The generated results demonstrate that the developed approach is correct and straightforward.
Influence of a Synchronized Self-Shifting Clutch in a Single-Shaft Plant on the Torsional Behaviour of the Shaft Train in Case of Electrical Faults
Authors: Klocke Meinolf , Verstege Stefan
Published: November 2020

Synchro-self-shifting clutches allow the construction of combined gas- and steam power plants as single-shaft systems, which are economically advantageous due to enhanced efficiency and the use of only one generator for gas- and steam turbines.

However, problems occur concerning the question, how to calculate torsional stresses and take into account the operation of the clutch in case of electrical faults.

The article presents calculations of shaft and coupling torques as functions of time carried out by different methods in one exemplary case of faulty operation for a 351MW/228MW combined gas and steam single-shaft plant The clutch is modelled by a nonlinear torsional stiffness.

The calculations show extremely strong impacts of torque inside the clutch due to intermittend engagement and disengagement processes. However, taking additionally into account damping influences inside the clutch one obtains no significant deviations from the results of a calculation for rigid couplings instead of the clutch.
Active Control of Rotor Vibrations by Means of Piezoelectric Actuators
Authors: Carmignani Costantino , Forte Paola , Rustighi Emiliano
Published: November 2020

This work deals with the development of an adaptive hydrodynamic bearing made of a mobile housing mounted on piezoelectric actuators. The device is placed near one of the two bearings supporting a slender shaft. Imposing a harmonic displacement on the mobile bearing, in two orthogonal directions, a rotating force, and hence a correcting moment, can be produced on the shaft so as to reduce the bending caused by the unbalance. The first tests carried out are encouraging and the agreement of experimental and numerical results is satisfactory.
Forced Response of Disks due to Distributed Pressure Fields
Authors: Mohamad A. H. , Ravoux J. , Jacquet-Richardet G.
Published: November 2020

The shape and the frequency of excitation, induced by distributed pressure fields, have both a major influence on the associated response of bladed disks. The way those pressure fields are considered by finite element models have then to be as accurate as possible. In this paper, an analytical model, adapted to the prediction of the forced response of clamped-free circular plates, due to distributed pressure fields, is first derived. This model is considered as a reference in order to assess the effectiveness of different finite element modeling.
A System Identification Technique Using Pseudo-Wavelets for General Linear Systems
Authors: Hou Zhikun , Hera Adriana
Published: November 2020

A concept of pseudo-wavelet is proposed based on shifting and scaling of conventional wavelets and a related pseudo-wavelet transform (PWT) is defined. The paper presents two special pseudo-wavelets defined based on the frequency response functions of the first- and the second-order linear dynamic systems, respectively. A PWT-based system identification technique is developed to estimate the system parameters, including the time constant associated with a single real pole of the system and the natural frequency and the damping ratio associated with a pair of conjugate complex poles of the system. The proposed approach is illustrated for representative linear dynamic systems of up to the third-order and good estimates are obtained in all studied cases. Noise effects on the accuracy are also investigated. The paper presents a preliminary study of the PWT-based system identification technique for general linear dynamic systems.
Nonlinear Parametric Identification of Oscillating Cables Using Wavelets
Authors: Romeo Francesco , Gattulli Vincenzo , Benedettini Francesco
Published: November 2020

In the present study a wavelet-based procedure is applied for the parametric identification of a nonlinear discrete cable model on the basis of experimental data obtained from free-vibration dynamic tests. The 3D cable dynamics is described by two partial integro-differential equations in the transversal planar and nonplanar displacement components. By expanding such variables in series of linear eigenfunctions, a discrete model is obtained by applying a classical Galerkin procedure. The resulting set of nonlinear ODEs contains quadratic and cubic coupling terms. The core of the identification technique is the discretization of such nonlinear differential equations by means of orthogonal Daubechies scaling functions. The Wavelet-Galerkin solution of the nonlinear equation involving the scaling function expansion of nonlinear terms leads to an algebraic problem that has to be inverted in order to solve for the vector of unknown parameters. A sdof model able to describe the in-plane unimodal oscillations is considered. Numerical and experimental identification tests are presented. Accurate estimates of the linear and quadratic parameters are achieved from the moderate oscillation amplitude response of an experimental discrete cable-mass model. The accuracy of the cubic parameter estimate is shown to depend on the level of both the oscillation amplitude and noise.
Computationally Efficient Time-Domain Modeling of Fluid Transmission Lines
Authors: Manhartsgruber Bernhard
Published: November 2020

The behavior of laminar, liquid pipe flow can be simulated with Zielke’s method using a convolution integral for computing the wall friction from past velocity changes and a method of characteristics. The major drawback of Zielke’s method is the large consumption of computation time and computer memory due to the increasing sequence of past velocity values. The Zielke-Suzuki method replaces the convolution integral by a system of linear difference equations saving both memory and computation time. This paper shows how to formulate the Zielke-Suzuki method as a standard, discrete time linear system. The application of order reduction methods to this standard form gives a reduced system with identical input output behavior. Thus, a further improvement of the Zielke-Suzuki method with respect to both computation time and memory consumption has been reached.
Failure Prognosis Using Nonlinear Short-Time Prediction and Multi-Time Scale Recursive Estimation
Authors: Chelidze David , Cusumano Joseph P. , Chatterjee Anindya
Published: November 2020

In this paper we describe a new, general purpose machinery diagnostic/prognostic algorithm for tracking and predicting evolving damage using only available “macroscopic” observable quantities. The damage is viewed as occurring in a hierarchical dynamical system consisting of a directly observable, “fast” subsystem coupled with a hidden, “slow” subsystem describing damage evolution. This method provides damage diagnostics and failure prognostics requiring only the measurements from the fast subsystem and a model of the slow subsystem. Damage tracking is accomplished by a two-time-scale modeling strategy based on phase space reconstruction using the measured fast-time data. Short-time predictive models are constructed using the reconstructed phase space of the reference (undamaged) fast subsystem. Later, fast-time data for the damaged system is collected and used to estimate the short-time reference model prediction error, or a tracking function. An average value of the tracking function over a given data record is used as a tracking metric, or measure of the current damage state. Recursive, nonlinear filtering is used to estimate the actual damage state based on the tracking metric input. Estimates of remaining useful life are obtained recursively using a linear Kalman filter. This method is applied to an experimental nonlinear oscillator containing a beam with a crack which propagates to complete failure. We demonstrate the ability to track the evolving damage state of the beam using only strain time series data. We also give accurate predictions of remaining useful life, in real time, beginning well in advance of the final complete fracture at the end of experiment.
Structure-Excitation Modal Decoupling by Modification of the Involved Acoustic Modes of the Sound Insulating Enclosure
Authors: Papadopoulos Christos I. , Georgiou Ioannis T.
Published: November 2020

Several noise sources such as machinery with rotating or reciprocating parts routinely produce high levels of noise in narrow frequency ranges lying in the neighbourhood of the rotating or reciprocating frequency and their harmonics. When enclosures are used to isolate such noise sources, peak response might be observed at these frequency ranges due both to increased excitation amplitude and resonating phenomena caused by the interaction of the excitation with the acoustic modes of the enclosure. Especially in the low frequency range and for low or intermediate wall absorption, the acoustic response of the enclosure is modal and these peak responses can be intense. This paper proposes a methodology to minimize the effect of narrow-frequency-band noise by redistribution of the acoustic modes of the insulating enclosure. This can be achieved by shifting the enclosure acoustic modes away from the excitation frequency so as to make superimposed resonating phenomena less intense. For that, several variable geometric modifications of the enclosure walls are introduced. The magnitude of those modifications that will lead to sparse mode distribution in the neighbourhood of the excitation frequency is estimated by means of a combined finite element-optimisation method. The above methodology is applied to an orthogonal enclosure and two different narrow-band loads in the neighbourhood of 90 and 120 Hz are studied. It is shown that, for each frequency load, a feasible set of geometric modifications can be found so as for the neighbouring modes to be shifted and, consecutively, for resonating effects to be made less intense. Furthermore it is shown that feasible solution to the problem of simultaneous control of noise having two or more intense excitation frequencies is also attainable.
Quasi-Periodic Motions of Articulated Pipes Conveying Flowing Fluid
Authors: Szabó Zsolt
Published: November 2020

In this paper two nice examples are investigated where a ‘chain’ of n = (1, 2) pieces of rigid pipes contains incompressible and frictionless flowing fluid. We give an overview about the linear and nonlinear analysis of the autonomous system, i.e. when the pipes contain steady flow. Assuming pulsatile flow, the system becomes time-periodic. The stability charts of the linearized system are generated applying a numerical method based on Chebyshev polynomials. Finally, we analyze the effect of the nonlinear part in some critical points of the obtained stability charts and the dynamic behaviour of the original nonlinear periodic system is simulated numerically. The results are shown in Poincaré maps and bifurcation diagrams.
Geared Rotordynamic Systems on Hydrodynamic Bearings
Authors: Theodossiades S. , Natsiavas S.
Published: November 2020

The present study investigates response and stability characteristics of gear-pair systems supported on oil journal bearings. The systems examined are driven by a motor providing a known torque, which is transferred to a load element through shafts and a gear-box. Here, the emphasis is placed on the gear-pair action, by assuming that the interconnecting shafts are rigid. This results in mechanical models with strongly nonlinear characteristics, whose long time dynamics are then effectively studied by applying appropriate numerical methodologies. In this way, useful information is obtained for the influence of the loading, the gear mesh and the journal parameters on the system dynamic behavior, including periodic, quasiperiodic and chaotic response. Efforts are also directed towards predicting the onset of oil whirl instability and investigating its effects on the gear-pair dynamics.
Grazing Bifurcations of Initially Quasi-Periodic System Attractors
Authors: Dankowicz Harry J. , Piiroinen Petri T. , Nordmark Arne B.
Published: November 2020

This paper discusses the dramatic changes in system dynamics that arise as parameter variations lead to the appearance of grazing intersections between periodic and quasi-periodic attractors and state-space discontinuities. In particular, a method based on the discontinuity-mapping approach is employed to predict the effects of near-grazing interactions with the discontinuity surface solely based on information about the discontinuity and the pre-grazing trajectory and requiring no knowledge of the impacting system. An example from the study of legged locomotion is used to illustrate the significance of such grazing bifurcations on the presence of sustained gait in simple anthropomorphic mechanisms. The predictive power of the discontinuity-mapping approach is illustrated on a low-dimensional model example.
Steady State Vibrations of a Piecewise Linear System
Authors: Jazar G. Nakhaie , Golnaraghi M. F. , Swanson D. A.
Published: November 2020

In this paper we examine the dynamics of a mechanical system with a piecewise linear damping and stiffness, which is characterized as a strongly nonlinear system. Searching for the exact steady state periodic response of piecewise linear systems for harmonic excitations, lead to a set of transcendental equations which should be solved numerically. The strong nonlinear characteristic of the system is the reason for failure of most traditional perturbation methods in providing an approximated frequency response. In this paper we show that the averaging method of Krylov-Bogoliobuv-Mitropolsky (or multiple time scale method) may be used to find the behavior of this type of system.

Optimization of linear vibration isolators and engine mounts has a straightforward solution: the stiffness should be as soft as possible. Static deflection and maximum allowable relative mount displacement (rattle space) determine the limit of mount softness. Dividing the travel space into two (or more) stages enables us to use an isolator with a different stiffness for each stage. This is a simple method to have a more advanced passive mount isolator. However, this also makes the system piecewise linear, which has a strongly nonlinear behavior if the ratio of the two stages are far from unity.

Asymmetrical bilinear systems, with different stiffness and damping values for compression and tension, are used when the relative motion in negative direction is more (or less) critical than in positive direction. Sensitivity analysis of the system shows that the difference in the damping plays a more important role than the stiffness difference in these systems.

In this paper, using averaging method, we examine the nonlinear behavior of piecewise linear mounts at resonance, and provide a comprehensive analysis which may be used to better design for these kind of vibration isolators.
Semi-Discretization of Delayed Dynamical Systems
Authors: Insperger Tamás , Stépán Gábor
Published: November 2020

An efficient numerical method is presented for the stability analysis of linear retarded dynamical systems. The method is based on a special kind of discretization technique with respect to the past effect only. The resulting approximate system is delayed and time-periodic in the same time, but still, it can be transformed analytically into a high dimensional linear discrete system. The method is especially efficient for time varying delayed systems, including the case when the time delay itself varies in time. The method is applied to determine the stability charts of the delayed Mathieu equation with damping.
Analysis of Bifurcations and Chaos in Three Coupled Physical Pendulums With Impacts
Authors: Awrejcewicz Jan , Kudra Grzegorz , Lamarque C.-H.
Published: November 2020

In this work the triple pendulum with damping, external forcing and with impacts is investigated. The extension of a coefficient restitution rule and a special transition condition rule for perturbation (linearized system in the Lyapunov exponents algorithm) in each discontinuity point are applied. Periodic, quasi-periodic, chaotic and hyperchaotic motions are observed using Poincaré maps and bifurcational diagrams, which are verified by the Lyapunov exponents. In additon basins of attraction of some coexisting regular and irregular attractors are illustrated and discussed.
Application of the Harmonic Balance Method to Ground Moling Machines Operating in Periodic Regimes
Authors: Woo Ko-Choong , Rodger Albert A. , Neilson Richard D. , Wiercigroch Marian
Published: November 2020

The paper describes current research into mathematical modelling of a novel vibro-impact ground moling system. Experimental and theoretical studies suggest periodic responses are required to achieve the optimal penetrating conditions for the ground moling process, as this results in reduced soil penetration resistance. Therefore, there is a practical need for a robust and efficient methodology to calculate periodic responses for a wide range of operational parameters. Due to the structural complexity of a real vibro-impact moling system, the dynamic response of an idealised impact oscillator has been investigated in the first instance. This paper presents a detailed study of periodic responses of the impact oscillator under harmonic forcing using alternating frequency-time harmonic balance method. Recommendations of how to effectively adapt the alternating frequency-time harmonic balance method for a stiff impacting system are given. The periodic motion is represented algebraically by a truncated Fourier series and the systematic methodology employed allows for convergence. The idea central to this procedure is that the linear oscillator is explicitly solvable analytically, and this allows for the initial set of Fourier coefficients. The clearance value is then adjusted so that contact with the secondary stiffness is slight and the nonlinearity is weak. The solution to this subsequent system is obtainable as the initial guess is close to the required solution.
Periodic and Nonperiodic Thermomechanical Responses of Shape-Memory Oscillators
Authors: Lacarbonara Walter , Bernardini Davide , Vestroni Fabrizio
Published: November 2020

Nonlinear responses of shape-memory oscillators are investigated systematically using a numerical procedure and a modified Ivshin-Pence model for the restoring force. Due to the discontinuities in the tangent stiffness, classical gradient-based shooting techniques for determining periodic responses are not applicable. Herein the implemented algorithm searches the periodic solutions as fixed points of the Poincaré map. The Jacobian of the map is calculated via a central finite-difference scheme and its eigenvalues are computed to ascertain the stability of the solutions and the associated codimension-one bifurcations. A number of frequency-response curves are constructed for some meaningful shape-memory oscillators (characterized by different hysteresis loops) and for various excitation levels in the primary and superharmonic frequency ranges. The investigations are conducted both in isothermal and non-isothermal conditions. A rich class of solutions and bifurcations — including jump phenomena, pitchfork, period doubling, complete or incomplete bubble structures with a variety of nonperiodic responses — is found and discussed.
Analysis of Piecewise Linear Systems With Boundaries in Displacement and Velocity Using Vector Fields
Authors: Nakai Mikio , Hagio Seiji , Mizutani Kazuki , Zahid Hossain Md.
Published: November 2020

A generalized solution methodology based on piecewise linear vector fields has been proposed for piecewise linear systems with boundaries for both displacement and time. In this paper, this methodology is applied in analyzing dynamic responses of torsional vibration through bilinear spring stiffness with changing hysteretic torque in the rotating machinery system, which has boundaries for both displacement and velocity. For asymmetric torque with hysteresis, two cases exist when restoring torque changes smoothly and discontinuously. Period-one and period-two solutions are sought in two cases and compared with ones obtained by the numerical method. Our present method can be applied to dynamic responses of piecewise linear systems having velocity and displacement boundaries.
Experimental Investigation of Control Logic for State-Switched Dampers
Authors: Larson Gregg D. , Cunefare Kenneth A.
Published: November 2020

Recently, significant interest has been generated by the possibilities of active vibration control through the implementation of state switching, or piezoceramic shunting. A state-switched absorber (SSA) is a vibration absorber that has the unique ability to change its resonant state amongst multiple distinct resonant states while in motion, thereby increasing the effective bandwidth over that of a single frequency device and allowing control of multi-frequency and transient disturbances. In contrast, a switch-shunted damper (SSD) is a variant of an SSA that is used to increase the damping of the structure to which the damper is applied. A prototype SSD has been built and tested to experimentally investigate switching control logic. For this prototype, the results indicate that switching states at a condition of maximum strain yields enhanced damping effectiveness but also leads to the generation of potentially undesirable mechanical transients.
Constrained-Layer Damping of Torsional Vibration of Thin-Walled Tubes
Authors: Nayfeh Samir A.
Published: November 2020

In this paper, we take up the problem of damping torsional vibration of thin-walled tubes with closed sections. Assuming that the deformation obeys the Saint-Venant hypotheses, we develop a model suitable for predicting the complex stiffness per unit length in tubes with constrained viscoelastic layers over part or all of their perimeter. For some basic cross-sectional shapes, we solve the warping problem and thence obtain closed-form expressions for the complex stiffness per unit length. Finally, we provide some guidelines for the design of tubes with high damping in torsion.
Vibration Confinement via Optimal Eigenvector Assignment and Piezoelectric Networks
Authors: Tang J. , Wang K. W.
Published: November 2020

The underlying principle for vibration confinement is to alter the structural modes so that the corresponding modal components have much smaller amplitude in concerned areas than the remaining part of the structure. In this research, the state-of-the-art in vibration confinement technique is advanced in two correlated ways. First, a new eigenstructure assignment algorithm is developed to more directly suppress vibration in regions of interest. This algorithm is featured by the optimal selection of achievable eigenvectors that minimizes the eigenvector components at concerned areas by using the Rayleigh Principle. Second, the active control input is applied through an active-passive hybrid piezoelectric network. With the introduction of circuitry elements, which is much easier to implement than changing or adding mechanical components, the state matrices can be reformed and the design space in eigenstructure assignment can be greatly enlarged. The merit of the proposed system and scheme is demonstrated and analyzed using a numerical example.
Modal Control for Piezo-Coupled Elastic Beams and Plates
Authors: Murray John J. , Knowles Gareth J.
Published: November 2020

The potential advantages of lightweight, compact and easily attacheable or embeddable induced strain actuators can be quickly overshadowed by the bulky power supplies, electronics and controls necessary to drive them. Previous work in power and control has used circuit-theoretic concepts to combine the control system design process with energy flow analysis. This is extended here to encompass thin plates with multiple attached piezoelectric devices, providing the basis for an integrated theory of high-efficiency active control with piezoelectric elements. A major result is that, while good broadband vibration suppression and damping require active control, this does not imply that the control consumes net energy. In addition to the usual division into passive and active control, therefore, a third possibility of active, zero-energy control (termed quasi-active control) arises.
Vibration Control of Parallel Identical Flexible Structures Using Interactive Force
Authors: Kougo Shigeru , Fujihara Hiroshi , Yoshida Katsuhiko , Tanaka Hiroyuki , Watanabe Toru , Seto Kazuto , Tan Andy C. C.
Published: November 2020

This paper deals with active vibration control of two identical flexible structures arranged in parallel. One of the authors had presented a vibration control mechanism so that two or more structures are connected via non-contact actuators in which one structure is utilized as a reaction wall for another structure’s control mutually. However, in such a mechanism, the control performance reduces as the natural frequencies of structures become closer. In this report, authors present a modified mechanism in which actuators are connected to the structures with long arms so that the direction of vibration in a mode differs on each structure. In this way, the reaction force from the actuator on structure is introduced to another structure for dissipative force even if the properties of structures are identical. Computer simulation and control experiment are carried out and the effectiveness of presented mechanism is confirmed.
Two-Mode Resonator and Contact Model for Standing Wave Piezomotor
Authors: Andersen Brian , Blanke Mogens , Helbo Jan
Published: November 2020

The paper presents a model for a standing wave piezoelectric motor with a two bending mode resonator. The resonator is modelled using Hamilton’s principle and the Rayleigh-Ritz method. The contact is modelled using the Lagrange Multiplier method under the assumption of slip and it is shown how to solve the set of differential-algebraic equations. Detailed simulations show resonance frequencies as function of the piezoelement’s position, tip trajectories and contact forces. The paper demonstrates that contact stiffness and stick should be included in such a model to obtain physically realistic results and a method to include stick is suggested.
Sensor Electromechanics and Distributed Signal Analysis of Piezo(Electric)-Elastic Spherical Shells Based on the Bending Approximation
Authors: Tzou H. S. , Smithmaitrie P.
Published: November 2020

Spatially distributed modal voltages and sensing signal generations of a distributed piezoelectric sensor layer laminated on spherical shells of revolution are investigated in this study. The generic sensing signal equation is derived based on the direct piezoelectric effect, the Gauss theory, the open-circuit assumption, the Maxwell equation, and also the generic double-curvature thin shell theory. Due to difficulties in analytical solution procedures, assumed mode shape functions based on the bending approximation theory are used in the modal signal expressions and analyses. Spatially distributed electromechanical characteristics resulting from various meridional and circumferential membrane/bending strain components are evaluated and major signal sources are identified. Analytical results suggest that the spatially distributed modal voltages clearly illustrate the distinct modal behavior, similar to mode shapes. The major signal source of a free-edge hemispherical shell is the circumferential bending component. Accordingly, circumferential layout of distributed sensor strips would provide effective monitoring and diagnosis of free hemispheric shells.