bluuebunny/crossref_metadata_2025 huggingface dataset:
A Method for Constraints Stabilization on Solving Multibody Dynamics
Authors: Koganezawa Koichi , Kaneko Kazuomi
Published: November 2020

This paper deals with methods for solving the multibody dynamics with constraints. The problem is considered in the framework of solving the Lagrange multipliers in addition to the system coordinates in the differential and algebraic equation (DAE) governing the dynamics with holonomic or non-holonomic constraints. The proposed methods are originally based on Baumgarte’s work for the holonomic constraints but its extensions to the non-holonomic constraints. Conventionally the Lagrange multipliers are solved algebraically and substituted into the dynamic equations (DAE). This paper, on the other hand, proposes a method to derive the ordinary differential equations with respect to the Lagrange multipliers. One can resort the ordinary numerical integration method to solve the Lagrange multipliers as same as to solve the ODE with respect to the system coordinates. Some examples of numerical solution for the mechanical models having holonomic and non-holonomic constraints shows the excellent stability of the constraints, which is superior to the Baumgarte’s stabilizing method and the penalty method.
The Composite Adaptive Control of Free-Floating Space Robot System With Prismatic Joint
Authors: Chen Li , Liu Yanzhu
Published: November 2020

In this paper, the kinematics and dynamics of a free-floating space robot system with prismatic joint are analyzed, and it is shown that the Jacobian matrix and the dynamic equations of the system cannot be linearly parameterized. With the augmentation approach, we demonstrate that the augmented generalized Jacobi matrix and the dynamic equation of the system can be linearly dependent on inertial parameters. Based on the results, the composite adaptive control scheme for a free-floating space robot with unknown inertial parameters to track the desired trajectory in workspace is proposed, and a two-link planar space robot system with prismatic joint is simulated to verify the proposed control scheme.
Modeling of Joints With Clearance in Flexible Multibody Systems
Authors: Bauchau Olivier A. , Rodriguez Jesus
Published: November 2020

This paper is concerned with the modeling of joints with clearance within the framework of finite element based dynamic analysis of nonlinear, flexible multi-body systems. For actual joints, clearance, lubrication and friction phenomena can significantly affect the dynamic response of the system. In this work, the effects of clearance and lubrication are studied for revolute and spherical joints. The formulation is developed within the framework of energy preserving and decaying time integration schemes that provide unconditional stability for nonlinear, flexible multibody systems. Numerical examples are presented that demonstrate the efficiency and accuracy of the proposed approach. The importance of modeling structural damping and limited driving power are discussed.
A Unified Formulation of Multibody Kinematic Equations in Terms of Absolute, Joint, and Indirect Coordinates
Authors: McPhee John J.
Published: November 2020

This paper reviews some of the coordinate sets employed in multibody dynamic formulations, including absolute, joint, absolute angular, and indirect coordinates. Linear graph theory is then combined with the concept of a “virtual joint” to develop a unified modelling methodology that is capable of representing any of these coordinate sets. An algorithm is proposed and demonstrated for generating the kinematic constraint equations for dependent coordinates, plus kinematic transformations between coordinates (e.g. velocity transformations). The effects of different coordinates on the dynamic equations for a simple manipulator are shown.
Dynamic Finite Element Modeling of Belt-Drives
Authors: Leamy Michael J. , Wasfy Tamer M.
Published: November 2020

In this study, a dynamic finite element model is developed for pulley belt-drive systems. The belt is modeled using truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for arbitrarily large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt span tensions. Excellent agreement is found.
Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part I — Theory
Authors: Mordfin Theodore G. , Tadikonda Sivakumar S. K.
Published: November 2020

Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact closed-form and numerical solutions are developed for the small elastic motions of a planar, flexible, single link system, in which the link is represented as an Euler-Bernoulli bar in transverse vibration. The link is connected to ground by a pin joint, and the articulation is controlled by proportional and proprotional/derivative (PD) feedback control laws. The characteristics of the closed-form solution are shown to consist of combinations of the characteristic expressions associated with classical end conditions. A large-articulation flexible body model of a controlled-articulation flexible link is then developed and linearized about an arbitrary reference angle. This model uses the method of assumed modes to represent the flexible behavior of the link. It is shown the model is analytically equivalent to a purely structural model which uses a hybrid set of assumed modes, and that numerical convergence can be investigated in terms of admissible functions and quasi-comparison functions. Numerical evaluation of the use of various types of assumed modes is presented in a companion paper.
Realization of Salto Backward Using a Horizontal Bar Exercise Robot
Authors: Takita Yoshihiro , Arai Shigenobu
Published: November 2020

This paper shows a realization of a horizontal bar exercise robot which flies through the air and lands on its feet. This robot has three links that are connected with two rotational joints driven by two DC motors. Each actuator is modeled by a damper and a torsional spring for which the setting angle is able to change during the motion. In order to find the target values of the control, an animation program is developed using the integration of these equations and a trial and error method is used to find them. As a result, an iron bar exercise was simulated by two types of action during the motion. In this paper a self-standing robot is made to realize the rotation around the iron bar and salto backward after the dismount. An experimental result demonstrates a motion that is comparable with the simulated one.
Investigation of the Dynamic Behavior of a Nonlinear Semi-Definite Mechanical System
Authors: Alsaif K.
Published: November 2020

The study reported in this paper investigates the dynamic behavior of a semi-definite nonlinear mechanical structure. It consists of a cantilever beam with uniform thickness subjected to a harmonic excitation at the base; two hinged rigid plates are attached at its free end. The plates can execute oscillations in the horizontal plane without restoring moments. The friction at the hinges is modeled as a Coulomb type with a nonlinear friction coefficient. The excitation parameters at which chaotic motion of the hinged plates is initiated are investigated experimentally as well as numerically. It is shown that the prediction of the dynamic response of this semi-definite system is not accurate in the resonance region. The prediction fails due to the existence of chaotic behavior in that region. The measurement of the dynamic response of the system is conducted using a He-Ne laser system. The numerical results are found to be in a good agreement with the experimental findings.
Nonlinear Effects in Dynamic Analysis of Flexible Multibody Systems
Authors: Samba Y. C. Mbono , Pascal M.
Published: November 2020

The work is concerned with the dynamics of multibody systems with flexible parts undergoing large rigid body motions and small elastic deformations. The standard method used in most cases leads to keep only linear terms with respect to the deformations. However, for large rates or large accelerations, this linearisation is sometimes too premature. In this work, a non dimensional analysis of the system is performed, with some estimate about the order of magnitude of the different parameters occuring in the dynamical model obtained by Kane’s method [1]. A flexible slider crank mechanism is used as a test example, together with AUTOLEV [2] software for numerical results.
Experimental and Analytical Investigation on Spaghetti Problem
Authors: Komaki Yoshimasa , Kobayashi Nobuyuki , Watanabe Masahiro
Published: November 2020

The dynamic behavior of the flexible beam, which is pulled into the slit of the elastic wall with a constant velocity, is discussed with multibody dynamics formulation and experiments. The vibration of the free tip of a flexible beam increases rapidly as pulling into the slit, and this behavior is called “Spaghetti Problem”. The effect of gap size of the slit on the behavior of Spaghetti Problem is especially focused. Dynamic behavior of the beam is simulated numerically and examined the accuracy of the presented formulation by changing the gap size and the pulling velocity of the beam as parameters. It is clarified that the presented modeling method simulates the experimental results quite well, and the gap size and the pulling velocity influence the increase of the lateral vibration near the inlet of the slit.
An Adding Mass Method for Stiffly Mechanical System Simulation and Applications to Construction Machinery
Authors: Imanishi Etsujiro , Yonezawa Satoshi , Sugano Naoki , Hirooka Eiko , Kobayashi Takahiro
Published: November 2020

A characteristic improvement method for dynamic simulation of a stiff mechanical system by adding mass is presented. Hydraulic systems with check valves and control valves on construction machinery exhibit piecewise-linear characteristics for hydraulic flow rate and spool stroke. The proposed improvement method involves no time delay in determining the mass by considering both eigenvalue distortion of the system and time response. This paper shows a practical application to the boom derricking system of a rough terrain crane, and demonstrates that this method is useful for dynamic simulation of hydraulic system including stiff piecewise-linear elements.
An Efficient Finite-Element Modelling Tool for Surgical Simulation: The ε-Mesh Radius
Authors: Azouz Naoufel , Payandeh Shahram
Published: November 2020

This paper presents an algorithm for determining the boundary volume of local mesh for haptic rendering. Here haptic rendering is defined as generation of reaction forces and contact shape information for graphical display. Haptic rendering consists of a number of components: a) scene representation b) scene modelling for global collision detection c) collision detection; d) contact profile and e) scene display. As oppose to classical Finite Element Method or Multi-Body Systems dynamics, haptic rendering deals with the modelling of object where the user can interact with them in the virtual environment. This paper concerns with some aspects related to the interaction between the surgeon tool (probe or micro-robot) and a model of human tissue and organ. Specifically the paper addresses analogies between traditional notion of mesh generation used in finite-element analysis and notion of haptic rendering. In fact, when the user interacts with the object, it is not clear which level of accuracy is needed for the creating the sense of reaction forces at the point of interaction. That is the motivation for proposing the notion of ε-mesh in analogy with the similar notion used in the theory of adaptive meshing. The ε-mesh radius is a scalar quantity defined as a function of the material properties of the contacting bodies, the expected local geometry of the bodies, the direction and relative approach velocities of the bodies. Relationships are presented which show how relative coarseness of the ε-mesh radius with respect to the mesh sizes outside of the radius affect the relative reaction forces.
Lund’s Pad Assembly Method for Tilting Pad Journal Bearings
Authors: Nicholas John C.
Published: November 2020

This paper summarizes the development during the last 50 years of tilting pad journal bearing analysis and design. The major impetus of this development was a landmark paper published by Jorgen Lund in 1964, “Spring and Damping Coefficients for the Tilting-Pad Journal Bearing.” His paper contained the first widely published dynamic coefficients for tilting pad bearings along with his pad assembly method equations.

In the 37 years since Lund’s publication, many other authors have written tilting pad journal bearing codes, the first of which were based on Lund’s assembly method. These assembly method codes were utilized for many years to analyze and design tilting pad bearings for improved rotordynamic performance. During this time, some key design tools were developed utilizing Lund’s method. Other authors have written newer codes which solve the energy and elasticity equations iteratively with the pressure equation, including pad degrees of freedom.

With the simple addition of a turbulence correction and heat balance, many designers continue to utilize Lund’s method, shunning the more modern codes.
Lund’s Elliptic Orbit Forced Response Analysis: The Keystone of Modern Rotating Machinery Analysis
Authors: Kirk R. Gordon
Published: November 2020

A total understanding of rotating machinery vibration analysis requires evaluation of critical speed placement, forced response sensitivity to imbalance, linear onset of instability prediction and full non-linear response analysis. Of these four areas of analysis, only the first three are applied as a basic design tool in modern turbo-machinery analysis. The prediction of multi-mass flexible rotor steady-state elliptic orbit response, including bearing damping and support flexibility, has been and remains in this author’s opinion, to be the basic workhorse and keystone of machinery design. This has now been true for over 35 years. The person responsible for developing this basic method of analysis has been a longtime friend of many engineers worldwide. This paper is written to acknowledge this contribution, one of many in fact, made by Jorgen W. Lund and is presented in memory of his life’s work at this occasion of honoring his contributions to our profession. The utility of the analysis will be discussed and the powerful insight it gives to complex machinery dynamic behavior will be illustrated.
Inertia Effects in Squeeze-Film Damper Bearings Generated by Circumferential Oil Supply Groove
Authors: Lund Jørgen W. , Myllerup Claus M. , Hartmann Henning
Published: November 2020

The dynamic properties of an industrial Squeeze-Film Damper (SFD) bearing design are described using the well-known perturbation approach, where the reaction forces induced by small movements away from the position of equilibrium are expanded into a Taylor series in terms of displacement, velocity, and acceleration. Although generally negligible, the acceleration term can become significant in SFD bearings when inertia effects in the damper lands are enhanced by the flow in a central circumferential oil supply groove. By using a bulk flow approximation in the oil supply groove an explicit expression is derived for the acceleration term. Experimental results confirm the significance of the oil supply groove geometry and appear to validate the bulk flow approximation.
Seven Major Steps to Improve Today’s High-Speed Balancing
Authors: Schneider Hatto , Buschbeck Andreas , Hoffmann Karl-Josef , Bornheimer Albert , Schmidt Joachim
Published: November 2020

There are some statements that today’s high-speed balancing of flexible rotors in a balancing machine may not be very effective. As a consequence often in-situ balancing may have to follow the high speed balancing process in order to achieve smooth running machines in operation.

There are other perceptions that individual rotors cannot be balanced sufficiently at all when coupled with other rotors later on.

If this is true, it may provoke problems with cost and delivery time as well as with the acceptance by the user.

When looking into the development in this field during the last decades it seems that despite (or because of) the use of computers some former experience got lost, and that available software does not fully utilize the latest findings and information on balancing of flexible rotors.

The paper describes possible reasons for this development and outlines seven steps for improving today’s high-speed balancing.
Flexible Rotor Balancing Taking Bearing Non-Linearity Into Account
Authors: Chen Peter Y. P. , Feng Ningsheng , Hahn Eric J.
Published: November 2020

This paper outlines a balancing method for non-linear rotor bearing systems with hydrodynamic bearings which utilises the unbalance response measured at a discrete number of measurement planes at a select number of speeds, as during a single rundown. Numerical experiments confirm that provided the system has been modelled correctly, the unbalance distribution is identified more accurately than by using the influence coefficient approach which assumes system linearity and increasingly so as the response orbits at the bearing increase. The identification accuracy is sensitive to measurement error, and if measurements are limited to field measurement accuracy of two digits, it is necessary to apply constraints, determined with the help of the linear approach, or otherwise reduce the number of unknown unbalances relative to the number of measurements, to extract the true solution.
Twice-Running-Speed Response due to Elliptical Bearing Clearances
Authors: Childs Dara W.
Published: November 2020

Yamamoto [1] examined a vertical Jeffcott rotor model with bearing clearances and showed that a small bearing “dead-band” clearance could have a dramatic influence on synchronous rotor response. Recent test results for a turbopump in a liquid-rocket-engine development program showed a twice-running-speed response (2E) on the order of 8 gs over a wide speed range, while synchronous response levels were only at an 0.5 g level. Childs [2] predicted a sharp 2E response for the Advanced Technology Development, High-Pressure Fuel Turbopump of the Space Shuttle Main Engine due to bearing clearances, when the running speed was nearly one half of a housing-mode natural frequency, i.e., when the 2E frequency was close to the housing mode natural frequency. However, his model did not predict significant 2E response over a broad running-speed range.

Ellipticity of the bearing dead-band clearances was suggested as a possible cause for the observed 2E phenomenon. An extension of Yamamoto’s analysis [1] is presented including bearing ellipticity to examine that proposed explanation. The analysis results show that clearance ellipticity will produce 2E response over a considerable running-speed range during which the bearing clearance is engaged; however, the predicted 2E-response amplitude corresponding to an ellipticity of 0.1 were about 10% of the synchronous levels, and the projected 2E acceleration levels were about 40% of synchronous. The predicted 2E response includes a resonance peak (that can be sharp) at speeds slightly above 25% of the rotor critical speed. The perturbation-analysis results provide an explanation for persistent, lower 2E-response levels observed in many turbopumps, but do not explain the high levels observed with this turbopump.
Theoretical Study on Instability Boundary of Rotor-Hydrodynamic Bearing Systems: Part I — Jeffcott Rotor With External Damping
Authors: Guo Zenglin , Kirk R. Gordon
Published: November 2020

The instability of rotor-hydrodynamic bearing systems has been a major concern in higher-speed rotating machine design. The threshold speed seems to be a barrier that cannot be driven through. However, if some kind of external damping is introduced, the situation may be different. At first, the study is conducted on the Jeffcott rotor with external damping for both vertical and horizontal configurations. For the vertical system, it has been shown by both analytical and numerical study that there is a threshold speed at which the rotor will get into an upper stable region from the previous unstable region. As for the horizontal system, an extended Lund Stability Method is presented, which, and with numerical analysis, has proven that the system may have two threshold speeds, which evolve a stability pattern as one region of instability sandwiched between two regions of stability. Then, the study is expanded to the extended Jeffcott rotor. With the introduction of equivalent journal mass, another threshold speed appears which forms a top and final boundary to the stable operation of the rotor. The results of a numerical study show that with the external damping increased, the first several unstable regions can be reduced or eradicated. The external damping has little effect on the last top threshold which is mainly dependent on the value of journal mass. It has also been shown that a certain value of external damping and small portion of journal mass would be very beneficial to improve the stability characteristics of the system over the entire speed range.
Experimental Investigation of a Platform Damper With Curved Contact Areas
Authors: Jareland Martin H.
Published: November 2020

This paper presents a set of experiments which have been performed with a new friction damper for a high pressure turbine. The main objective of these experiments was to tune a simulation model for the current damper. The simulation model used is valid for both microslip and macroslip. A number of other topics were also investigated, such as influence of glued platforms, repeatability of an experiment, comparison of new and used dampers, and the change in surface structure of the contact areas.

A similar set of experiments has been performed earlier with the current damper. On that occasion, it was found that the experiments and simulations did not agree as desired and therefore a new set of experiments was suggested. This paper presents the new experiments and the new simulations with a more precisely tuned model. The simulation model is tuned by selecting a suitable coefficient of friction and tangential stiffness for the contact interface model. It is found that the simulations agree well with the experimental results when the normal force is held constant and the excitation force is varied. The properties of the contact, contact area and pressure, are unchanged when the normal force is constant.

If a new damper is compared with a damper that has been used in a series of experiments, it is found that the resonance shifts to a lower frequency and that the amplitude increases. This is probably caused by a decrease in coefficient of friction due to wear of the contact surfaces.

The repeatability of an experiment has been investigated by running the same experiment five times in succession. It was found that the repeatability was very good if the position of the damper was not changed. The differences that were found were mainly due to wear on the contact surfaces. A comparison of sweeping forward or backward in frequency was also performed. It showed that the difference was small both for experiments with small motions in the contacts and for experiments with a high amount of macroslip.
Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals
Authors: Moore J. Jeffrey
Published: November 2020

Labyrinth seals are utilized inside turbomachinery to provide non-contacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure (Childs, 1993).

In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.
A Novel Frequency-Domain Method of Structural Damage Identification
Authors: Lee Usik , Shin Jinho
Published: November 2020

This paper introduces a frequency-domain approach of structural damage identification method (SDIM). The present SDIM is formulated from the exact dynamic stiffness matrix (DSM) equation of motion and then applied to beam structures. The appealing features of the present SDIM are: (1) it needs the DSM only for intact structure, (2) the excitation forces and the measured frequency response functions (FRFs) of damaged structure are only the required input data, and (3) it can locate and quantify many local damages at a time. The feasibility of the present SDIM is verified through some numerically simulated damage identification tests.
Application of Nonlinear Receptance Coupling to Dynamic Stiffness Evaluation for Reconfigurable Machine Tools
Authors: Yigit Ahmet S. , Ulsoy A. Galip
Published: November 2020

A systematic procedure is proposed to evaluate dynamic characteristics of design alternatives, for a Reconfigurable Machine Tool (RMT). The procedure is intended to be used in an automated design environment where various design alternatives are generated by kinematic synthesis based on a given task and specification. The evaluation procedure makes use of a substructuring method called nonlinear receptance coupling. The coupling method includes the effects of weakly nonlinear compliant joints through the use of describing functions for the nonlinearities involved. To demonstrate the utility of the proposed evaluation procedure design alternatives are generated based on a reduced order lumped parameter model of the RMT and examined with respect to the proposed criteria. It is shown that joint nonlinearities may affect dynamic stiffness considerably. It is also shown that the suggested criteria can distinguish various design alternatives with respect to their expected dynamic behavior.
Reduction of Arbitrary Dynamical Systems by Wavelet Bases
Authors: Ghanem Roger , Romeo Francesco
Published: November 2020

A procedure is developed for the identification and classification of nonlinear and time-varying dynamical systems based on measurements of their input and output. The procedure consists of reducing the governing equations with respect to a basis of scaling functions. Given the localizing properties of wavelets, the reduced system is well adapted to predicting local changes in time as well as changes that are localized to particular components of the system. The reduction process relies on traditional Galerkin techniques and recent analytical expressions for evaluating the inner product between scaling functions and their derivatives. Examples from a variety of dynamical systems are used to demonstrate the scope and limitations of the proposed method.
Karhunen-Loeve Decomposition for Reducing the Order and Monitoring the Dynamics of Coupled Oscillators
Authors: Ma Xianghong , Vakakis Alexander F. , Bergman Lawrence A.
Published: November 2020

Karhunen-Loeve - KL modes are used to discretize the dynamics of a four-bay linear truss. This is achieved by defining global KL modal amplitudes and employing the orthogonality relations between KL modes that are inherent in the KL decomposition. It is found that the KL-based low-order models can capture satisfactory the transient dynamics of the truss, even when only a limited number of them is used for the order reduction. A comparison between the exact and low-order dynamics in the frequency domain reveals that the low-order models capture the leading resonances of the truss. A series of experiments with a practical three-bay truss is then performed to validate the theoretical KL decomposition. A comparison between theory and experiment indicates agreement between the predicted and realized dominant KL mode shapes, but less so in the higher order modes. The reasons for this discrepancy between theory and experiment are discussed, and possible applications of the KL-based order reduction to passive and active control of practical large-scale flexible systems are outlined.
Dynamic Instability and Nonlinear Vibration of Doubly-Curved Cross-Ply Shallow Shells
Authors: Nayfeh Ali H. , Alhazza Khaled
Published: November 2020

We consider the dynamic instability and nonlinear vibration of doubly-curved cross-ply laminated shallow shells with simply supported boundary conditions. We investigate their responses and stability to a primary resonance (i.e., Ω ≠ ω11). The governing nonlinear partial-differential equations of motion are based on the von Karman-type geometric nonlinear theory and the first-order shear-deformation theory. We use the Galerkin procedure to reduce the governing nonlinear partial-differential equations to an infinite system of nonlinear coupled ordinary-differential equations. We use a combination of a shooting technique and Floquet theory to calculate the periodic responses of the shell and investigate their bifurcations. We show that for some shell parameters, a single-mode approximation misses some important dynamics, such as period-doubling, bifurcations.
Bayesian Estimation of Cumulative Damage From Seismic Response Records of Buildings
Authors: Heredia-Zavoni Ernesto , Zeballos Antonio , Montes-Iturrizaga Roberto , Esteva Luis
Published: November 2020

This paper discusses the estimation of probability distributions of damage using response records from instrumented buildings subjected to seismic excitations. The objective of the paper is to show how the information on the evolution of the mechanical properties of a system can be used to assess the state of cumulative damage. This implies expressing damage on the structural members in terms of its influence on the residual mechanical properties of the system. The information on the inelastic behavior from response records is used in a bayesian formulation along with a damage function to update prior probability distributions of damage. The damage function models the hysteretic cycles of inelastic response in terms of an initial damage and of the displacement amplitudes of the response cycles. It describes the evolution of the secant stiffness through the cycles of inelastic response as a function of cumulative damage and displacement amplitudes. The updating of probability distributions of damage for single degree of freedom systems is presented first. Extensions to the case of non-linear multi-degree of freedom systems are discussed next. Examples of reinforced concrete frames are given for illustrative purposes.
Analysis of a Class of Coupled Nonlinear Oscillators With an Application to Flow Induced Vibrations
Authors: Haaker T. I.
Published: November 2020

We consider in this paper the following system of coupled nonlinear oscillatorsx..+x-k(y-x)=εf(x,x.),y..+(1+δ)y-k(x-y)=εf(y,y.). In this system we assume ε to be a small parameter, i.e. 0 < ε ≪ 1. A coupling between the two oscillators is established through the terms involving the positive parameter k. The coupling may be interpreted as a mutual force depending on the relative positions of the two oscillators. For both ε and k equal to zero the two oscillators are decoupled and behave as harmonic oscillators with frequencies 1 and 1+δ, respectively. The parameter δ may therefore be viewed as a detuning parameter. Finally, the term ε f represents a small force acting upon each oscillator. Note that this force depends only on the position and velocity of the oscillator upon which the force is acting.

To analyse the system’s dynamic behaviour we use the method of averaging. When k and δ are choosen such that no internal resonance occurs, one typically observes the following behaviour. If the trivial solution is unstable, solutions asymptotically tend to one of the two normal modes or to a mixed mode solution.

For the special case with δ = 0 a system of two identical oscillators is found. If in addition k is O(ε) we obtain a 1 : 1 internal resonant system. The averaged equations may then be reduced to a system of three coupled equations — two for the amplitudes and one for the phase difference. Due to the fact that we consider identical oscillators there is a symmetry in the averaged equations. The normal mode solutions, as found for the non-resonant case, are still present. New mixed mode solutions appear. Moreover, Hopf bifurcations in the averaged system lead to limit cycles that correspond to oscillations in the original system with periodically modulated amplitudes and phases.

We also consider the case with δ = O(ε), i.e. the case with nearly identical oscillators. If k = O(ε) again a 1 : 1 internal resonant system is found. Contrary to the previous cases the normal mode solutions no longer exist. Moreover, different bifurcations are observed due to the disappearance of the symmetry present in the system for s = 0.

We apply some of the results obtained to a model describing aeroelastic oscillations of a structure with two-degrees-of-freedom.
Aeroelastic Oscillations of a Double Seesaw Oscillator
Authors: Lumbantobing H. , Haaker T. I.
Published: November 2020

In this paper we consider the resonan taeroelastic oscillations of a two-degree-of-freedom structure of a double seesaw type. The primary seesaw structure consists of a rigid frame hinged around a main axis. A secondary seesaw structure is hinged around a second axis located at one end of the primary frame. This secondary frame holds at one end a cylinder that interacts with a flow field. As a result, aeroelastic oscillations may occur. Assuming the wind and the damping forces to be small, we can apply the averaging method to analze the asymptotic dynamic behavior.

Here, we consider the case of non-resonance and in particular the cases of 1 : 2 and 1 : 3 resonance. In addition to the stable normal mode solutions as found in the non-resonance case, now we also find stable mixed-mode solutions. In the case of 1 : 3 resonance, we find for certain parameter values a Hopf bifurcation in the averaged equations, resulting in an unstable limit cycle. This limit cycle in the averaged equations corresponds with an oscillation of the original system with periodically modulated amplitudes and phases.
On Asymptotic Approximations of First Integrals for Weakly Nonlinear Oscillators
Authors: Waluya S. B. , van Horssen W. T.
Published: November 2020

In this paper a nonlinear oscillator problem will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate first in tegrals and periodic solutions. The existence, uniqueness, and stability of time-periodic solutions are obtained by using the approximations for the first integrals.
Rain-Wind Induced Vibrations of a Simple Oscillator
Authors: van der Burgh A. H. P.
Published: November 2020

In this paper a relatively simple mechanical oscillator is considered which may be used to study rain-wind induced vibrations of stay cables of cable-stayed bridges. In recent publications mention is made of vibrations of (inclined) stay cables which are excited by a wind-field containing rain drops. The rain drops that hit the cables generate a rivulet on the surface of the cable. The presence of flowing water on the cable changes the cross section of the cable experienced by the wind-field. A symmetric flow pattern around the cable with circular cross section may became asymmetric due to the presence of the rivulet and may consequently induce a lift-force as a mechanism for vibration. During the motion of the cable the position of rivulet (s) may vary as the motion of the cable induces an additional varying aerodynamic force perpendicular to the direction of the wind-field. It seems not to easy to model this phenomenon: several author state that there is no model available y ct.

The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom i.e. vertical vibrations are possible. We consider a ridge on the surface of the cylinder parallel to the axis of the cylinder. Let additionally the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillationare excited by an external force.

It may be clear that the small amplitude oscillations of the cylinder and hence of the ridge induce a varying lift and drag force. In this approach it is assumed that the motion of the ridge models the dynamics of the rivulet(s) on the cable. By using a quasi-steady approach to model the aerodynamic forces one arrives at a nonlinear second order equation displaying three different kinds of excitation mechanisms: self-excitation, parametric excitation and ordinary forcing. The firstresults of the analysis of the equation of motion show that even in a linear approximation for certain values of the parameters involved stable periodic motions are possible. In the relevant cases where in linear approximation unstable periodic motions are found, results of an analysis of the nonlinear equation are presented.
Parametric Vibration of Viscoelastic Moving Belts Using Standard Linear Solid Model
Authors: Hou Zhichao , Zu Jean W.
Published: November 2020

By using a standard linear solid model to describe the viscoelasticity of the belt material, a vibration analysis of a parametrically excited moving belt is performed. Closed-form solutions at principal resonance and summation resonance are derived at the first order approximation. The existence conditions and stability are discussed for the nontrivial solutions, yielding explicit expressions of the existence and the stability conditions in terms of the detuning parameter. Numerical examples clearly show the effects of tension fluctuations and translating speeds on the amplitudes of dynamic responses, the corresponding existence domains and the stability of the solutions. It is also demonstrated that the stability domains of the nontrivial solutions are different from those corresponding to elastic models.
Modeling and Chatter Suppression With Ultra-Precision in Dynamic Turning Metal Cutting Process
Authors: Pan Jingchuan , Su Chun-Yi
Published: November 2020

In turning metal cutting, the occurrence of self-excited vibration, so called chatter, is undesirable as it gives rise to production problems, causing detrimental effects on the machined surface finish and decreasing the machining efficiency. In this paper, in order for chatter suppression, a piezoactuator is introduced for the regulation of the machine tool displacement and the metal cutting system is modeled as a class of uncertain linear system with hysteresis and time delay. In order to overcome the chatter due to the hysteresis and time delay during the cutting process, an robust adaptive controller for the metal cutting system of ultra-precision is proposed and the simulation results shows that the proposed adaptive controller significantly eliminates the chatter phenomena.
Structure-Borne Vibro-Impact Resonances and Periodic Green Functions
Authors: Babitsky V. I. , Veprik A. M.
Published: November 2020

Impact interactions can excite complex nonlinear resonant responses in structures subjected to simple periodic excitation. The specific features of these resonances are concentration of high harmonics in corresponding waveforms, dependence of their behaviour on parameters and initial conditions, synergistic spatial effects, and generation of essential forces and stresses. An effective approach to analysis of these resonances was developed using special functions, called periodic Green functions. An introduction of these functions allows the regular study of resonant phenomena in vibro-impact systems based on structural presentations and without reference to differential equations of motion. The paper reviews some results on the application of periodic Green functions for analysis of resonant phenomena in vibro-impact structures with lumped and distributed parameters. The physical experiments support the results of analysis.
Nonlinear Transient Localization and Beat Phenomena due to Backlash in a Coupled Flexible System
Authors: Ma Xianghong , Vakakis Alexander F.
Published: November 2020

Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhunen-Loeve (K-L) decomposition is used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. The computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction. Poincare’ maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connecting the coupled rods.
The Dynamics of a Flexible Levitated Droplet
Authors: Dupac Mihai , Marghitu Dan B. , Beale David G.
Published: November 2020

In this paper, a nonlinear dynamics analysis of the simulated data was considered to study the time evolution of an electro-magnetically levitated flexible droplet. The main goals of this work are to study the behavior of the levitated droplet and to investigate its stability. Quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent were computed.
Topological Solitons in Non-Degenerate One-Component Chains: Part II — Numerical Study
Authors: Manevitch Leonid I. , Savin Alexander V. , Sigalov Grigori M.
Published: November 2020

In this paper, which is a direct continuation of part I, a numerical study of existence and stability of topological solitons revealed in part I is performed using smoothened potentials.
Symbolic Stability Boundaries and Root Locus Plots in Time-Periodic Systems
Authors: Butcher Eric A.
Published: November 2020

The recent development of a symbolic computational algorithm for approximating the parameter-dependent fundamental solution matrix of linear time-periodic systems is used to symbolically compute stability boundaries as an explicit function of the system parameters and to construct root locus plots. By evaluating this matrix at the end of the principal period, the parameter-dependent Floquet Transition Matrix (FTM), or the linear part of the Poincaré map, is obtained. The sub sequent use of well-known criteria enables one to obtain the equations for the stability boundaries in the parameter space as polynomials of the system parameters. The symbolic nature of the method also allows one to obtain root locus plots in the complex plane as a function of the system parameters. The roots of the FTM (Floquet multipliers) must lie within the unit circle for stability. Further, the technique can successfully be applied to periodic systems whose internal excitation is strong. The symbolic software Mathematica is used here to perform all symbolic calculations. Two illustrative example problems, viz., a parametrically excited simple pendulum and a double inverted pendulum subjected to a periodic follower force, are included.
Discontinuous Bifurcations in Stick-Slip Mechanical Systems
Authors: Galvanetto Ugo
Published: November 2020

Non-smooth dynamical systems exhibit continuous and discontinuous bifurcations. Continuous bifurcations are well understood and described in many textbooks, whereas discontinuous bifurcations are still the object of active research. Grazing bifurcations, C-bifurcations and other types of bifurcations characterised by jumps of the relevant Floquet multipliers have been described in the scientific literature. This paper deals with two discontinuous bifurcations found in mechanical systems affected by dry friction.
Computational Methods for Nonsmooth Acoustic Systems Arising in an Electromagnetic Hysteresis Identification Problem
Authors: Banks H. T. , Raye J. K.
Published: November 2020

Electromagnetic interrogation techniques have numerous useful applications, including locating mines or bunkers beneath the ground, and detecting abnormal tissue noninvasively within the body. Several recent successful such techniques involve using some type of interface, such as a superconductive metal backing or a standing acoustic wave grating, to reflect an oncoming electromagnetic wave. These electromagnetic wave reflections are then used to identify dielectric properties (conductivity and polarization) of the target materials. Many useful polarization models (for example, Debye, Lorentz, and higher order models) result in a hysteretic term in Maxwell’s equations. Thus, a wide class of electromagnetic interrogation problems involve identification of hysteresis mechanisms. We wish to examine a technique in which an acoustic wave traveling toward the oncoming electromagnetic wave acts as a virtual interface. As a first step in assessing this interrogation technique, we consider the equations describing an acoustic pressure wave produced by a windowed sine wave pulse traveling through a layered medium and develop computational methods for solving these equations. After considering several other approaches, we suggest that an adequate way to solve this system with the finite element method is to use a fully Galerkin scheme in a nonstandard weak formulation. Our approximation methods, resulting in large algebraic systems, are explained and computational findings are presented which support the efficacy of the approach.
Narrowband Control Design for Smart Structural Systems
Authors: Kolepp Daniel J. , Smith Ralph C.
Published: November 2020

This investigation focuses on the development of narrowband control strategies which are effective for structural systems subjected to both harmonic exogenous forces and stochastic uncertainties in the model or measurements. A cantilever beam with surface-mounted piezoceramic actuators is used as a prototypical structure since it exhibits physical attributes of a variety of vibrating structures but is sufficiently simple to facilitate initial control design. A PDE model for the structure is discretized using a spline-based Galerkin technique to obtain a semi-discrete system that is appropriate for finite-dimensional control design. A narrowband control method, which can be tuned to attenuate either natural frequencies or specific frequencies in the exogenous input, is developed and compared with standard LQR techniques through numerical examples.