bluuebunny/crossref_metadata_2025_split huggingface dataset:
Frequencies of Elastic Oscillations of a Tether-Platform System
Authors: Misra A. K. , Modi V. J. , Torchinsky S. 
Published: April 2021

Abstract
The paper investigates the longitudinal and transverse oscillations of an orbiting tether connecting a flexible platform and a subsatellite. The variation of tension along the tether due to the tether mass, as well as the effect of the platform equilibrium tilt on the tether tension are taken into account. The effects of tether to subsatellite mass ratio r, nondimensionalized offset a and platform equilibrium tilt ψo on the frequencies of elastic oscillations are examined. It is observed that the frequencies of longitudinal oscillations depend mainly on r, while those for the transverse oscillations can be expressed in the form λn2 = anr−1 + bn + Cnαψo, where λn is the nondimensionalized nth natural frequency, an, bn are constants, and cn varies linearly with r−1.
Approximate Formulas for the Transient Resonance Response of Mechanical Systems With Slowly Varying Natural Frequency
Authors: Irretier H. , Leul F. 
Published: April 2021

Abstract
The transient vibration problem of SDOF-system with constant natural frequency during run-up and shut-down for a linearly changing speed has already been solved by a number of authors using exact methods. However, during the transition process the natural frequency in many practical cases changes with time. In the present paper, the influence of natural frequency changes with respect to time is investigated using numerical simulation. Further, considering the computation time required, the paper suggests approximate formulas to estimate the maximum resonance amplitude during this transition. To illustrate the accuracy of the formulas, numerical results are shown in graphical formats.
Transfer Function Formulation of Constrained Distributed Systems
Authors: Tan C. A. , Chung C. H. 
Published: April 2021

Abstract
The transfer function formulation of constrained distributed systems is presented. The methodology is illustrated for subsystems under pointwise constraints and distributed systems consisting of multiple subsystems. A general displacement method (GDM) is used to determine the eigensolution of the constrained systems. It is shown that GDM requires only the natural boundary conditions (force constraints) be imposed at the subsystem interface. The methodology is applied to two examples. Curve veering and mode localization phenomena are found in an elastic structure on an elastic foundation.
Dynamic Analysis of Flexible Multi-Body Systems With Time-Variant Mode Shapes
Authors: Amirouche F. M. L. , Xie M. 
Published: April 2021

Abstract
The paper extends the theory of flexible multi-body systems to include time-variant mode shapes to account for the changes of boundary conditions that a flexible body undergoes while in motion. The method presented herein makes use of finite element methods to discretize the elastic body, then the nodal coordinates are related to the modal coordinates through the mode shapes. The latter are computed separately and their rate of change is accounted for in the dynamical equations of motion. The resulting governing equations of motion are presented in a computer form and a possible application problem is proposed.
A Preprocessor for the Treatment of Elastic Bodies in Multibody Systems
Authors: Sorge Kai , Pfeiffer Friedrich 
Published: April 2021

Abstract
A preprocessor providing the inertia data of elastic bodies for multibody algorithms is considered. The desired capability of including stress stiffening terms leads to a high computational effort. The method presented allows a straight forward implementation of the basic formulas by starting with the development of a special purpose symbolic calculator. A rotating elastic ring serves as an example.
Free Vibration of Simply Connected Bodies of Revolution by Boundary Collocation
Authors: Houmat A. , Hutchinson J. R. 
Published: April 2021

Abstract
A boundary collocation method is presented for solving the problem of free vibrations of isotropic, linearly elastic simply connected bodies of revolution of arbitrary shape and arbitrary boundary conditions. The problem is formulated in terms of a series of exact solutions of the governing differential equations in spherical coordinates. Boundary conditions are satisfied at a discrete number of points on the boundary. Results are obtained for a number of simply connected bodies of revolution. For a solid sphere with stress free boundary, the results are compared with known solutions. For other shapes, the results are compared with finite element solutions obtained using ANSYS. All comparisons show that the boundary collocation method produces excellent results.
Random Mobility Variation of Disordered Periodic Structures
Authors: Cai G. Q. 
Published: April 2021

Abstract
Due to material, geometric and manufacturing irregularities, a structure designed to be spatially periodic cannot be exactly periodic. The departure from perfect periodicity is referred to as disorder, and it is known to cause spatial localization of normal modes and attenuation of wave propagation even if the structure is undamped. In this paper, another effect of disorder is investigated; namely, possible energy concentration near where a excitation is applied, thus, inducing higher level of structure response, A computational procedure is developed for calculating the mobility, or mechanical admittance, of deterministically disordered periodic structures based on wave propagation theory, and then extended to the case of randomly disordered periodic structures. It is shown that, given the probability distribution of the disordered parameters of a periodic structure, the mean and standard deviation of the mobility magnitude can be obtained. The results are exact if the number of the periodic cell units is not large, and approximate if the number is large. Depending on the excitation frequency, the mean mobility magnitude of a disordered system may be either greater or smaller than that of the perfectly periodic counterpart.
Shock Design Rules for the Multi-Foundation Problem
Authors: Abdelhamid Mohamed K. , Cunniff Patrick F. 
Published: April 2021

Abstract
Dynamic analysis of equipment attached to shock excited vehicles is greatly simplified by spectral analysis. Using the modal shock design values to provide estimates of the maximum values of critical stresses in a base driven structure is a standard procedure used by the Navy for heavy equipment. This paper presents new results for design analysis that uses shock design values for those cases where the points of attachment between the equipment and the vehicle move differently from each other. This problem is commonly labeled the multi-foundation problem. The paper adopts the modal analysis approach and links the design rules of shock design analysis to bounding solutions derived from modal analysis. The design rule proposed for the multiple foundation case in this study requires the availability of the design shock values at different points of attachment between equipment and foundation. The method is easily programmable and can accommodate various equipment foundation models. A series of numerical experiments were conducted to establish a bench mark evaluation for the newly developed design rule. Comparison between the current standard procedures and the new design rule showed that the new rule estimates critical stresses that are closer to their true maximum values thus presenting an improvement over the current standard procedures.
Linearized Dynamic Models for Robot Manipulators With Varying Link Parameters
Authors: Li Chang-Jin , Sankar T. S. , Hemami A. 
Published: April 2021

Abstract
In this paper, two fast computational algorithms are developed for effective formulation for the linearized dynamic robot models with varying (kinematic and dynamic) link parameters. The proposed algorithms can generate complete linearized (inverse) dynamic models for robot manipulators, taking variations (e.g., inexactness, inconstancy, or uncertainty) of the kinematic and dynamic link parameters into account. They can be applied to any robot manipulator with rotational and/or translational joints, and can be utilized, also, for sensivitity analysis of similar mechanical systems. The computational complexity of these algorithms is only of order O(n), where n is the number of degrees-of-freedom of the robot manipulator.
On the Inherent Characteristics of the Dynamics of Robot Manipulators
Authors: Tu Q. , Rastegar J. 
Published: April 2021

Abstract
The inherent characteristics of the (nonlinear) dynamics of robot manipulators are studied. The study is based on a new method, referred to as the trajectory pattern method. The inverse dynamics models of the manipulator are divided into classes of inverse dynamics models, each corresponding to a different trajectory pattern. For each trajectory pattern, the structure of the resulting inverse dynamics model is fixed and is used to study the characteristics of the dynamics of the manipulator by examining the harmonic content of the required actuation torques (forces) and the relative significance of each harmonic. The harmonic content of the actuating torques is shown to be a function of the path length in the joint coordinate space and the harmonic content of the selected trajectory pattern, but is independent of the number of degrees-of-freedom of the manipulator. The relative contribution of each harmonic is a function of the path length, direction of motion, the position of the path of motion within the workspace of the manipulator, and the magnitude of the fundamental frequency. The study provides a systematic approach to path and trajectory planning from the vibration control point of view. As an example, the characteristics of the dynamics of a spatial 3R manipulator is studied for motions with two different path lengths, starting from a specified point and extending in different directions.
Robot Task Oriented Dexterity and Dynamic Performance: A Statistical Approach
Authors: Beretta A. , Marchis V. , Sinatra R. 
Published: April 2021

Abstract
Robot task oriented dexterity has recently reached a well-known acknowledgment for its capability of definig robot arm manipulability figures, over the working space. Because it seemed to the authors that not yet robot dynamic performances have been taken into account in defining its local properties, it has been studied a simple 2R robot arm, in order to identify the most siutable parameters for this scope.
By simulating a mathematical model forced with random input signals (forces), its dynamic behaviour has been investigated with a Monte Carlo approach. Without willing to obtain a complete modal analysis, some numerical parameters have been found as capable to identify system dynamics, e.g. the principal direction of system free oscillations, and its eigenfrequency value. Discussion of the results over the workspace and as a function of system mechanical stiffness properties is also performed.
A Cartesian Workspace Generator for Robot Arm Workcell Obstacle Collision Avoidance
Authors: Luk Tak-Lai Daryl , Sneckenberger John E. 
Published: April 2021

Abstract
Most of the methods for planning collision-free robot manipulator arm morions to accomplish collision-free end-effector paths are based on explicit representation of the sub-space of the robot work space that is free of arm motion with obstacles collision. This sub-space is called the robot arm free space and most path planners represent this free space in joint space. If the robot arm free space is represented in joint space, then each point in the free space corresponds to a robot arm configuration for which no arm-obstacle collision occurs. This paper presents a new approach for generating the robot arm free space for an articulated type robot manipulator. This approach uses an oscillating slider crank mechanism for defining the free-space boundary when certain arm-obstacle collisions occurs. The robot arm free space, importantly, is generated in Cartesian space instead of joint space.
Response of a Rotating Beam Subject to an Accelerating Force
Authors: Argento A. , Scott R. A. 
Published: April 2021

Abstract
A method is given by which the response of a rotating Timoshenko beam subjected to an accelerating fixed direction force can be determined. The beam model includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up in general form using multi-integral transforms and the inversion is expressed in terms of convolution integrals. These are numerically integrated for a uniformly distributed load having an exponentially varying velocity function. Results are presented for the displacement under the load’s center as a function of position. Comparisons are made between the responses to a constant velocity load and a load which accelerates up to the same velocity.
Spontaneous Sidebanding in High Speed Rotordynamics
Authors: Ehrich Fredric 
Published: April 2021

Abstract
Several observations have been made in the Fourier spectra of high speed rotordynamic response of uniformly spaced frequency spikes on either side of key synchronous or subharmonic or superharmonic response frequencies. In instances where this so-called “sidebanding” could not readily be explained as the nonlinear interaction or combination tones of two distinct responses at slightly different frequencies, we have referred to this class of phenomena as spontaneous sidebanding.
It is invariably noted that the sideband spacing frequency appears to be a whole number fraction (1/J) of the operating speed which suggests that the wave form is periodic and completes a full cycle every J rotations of the rotor. Using a numerical model of a rotor which simulates local contact with a stator in close proximity as a bilinear spring, several studies have been carried out to explore the circumstances for this spontaneous sidebanding. Two general classes of this type of response have been found.
A) For highly nonlinear systems, the chaotic-like response in transition zones between successive orders of subharmonic and superharmonic operation is actually periodic and results in spontaneous sidebands clustered around the key subharmonic or superharmonic frequencies.
B) In trans-critical operation of highly nonlinear and lightly damped systems, a major sideband frequency spike is noted at a frequency which is approximately the system’s natural frequency. Recognition of this fact permits a simple estimate of the repetition index (J).
All these observations from operation of the numerical model have been compared with experimental data derived from incidents of spontaneous sidebanding on aircraft gas turbine rotors. Excellent qualitative agreement has been found in most instances.
Weight-Excited Vibrations of Rotating Curved Beams
Authors: Wauer Jörg 
Published: April 2021

Abstract
Flexural vibrations of a slender rotating beam whose centre line is assumed to be naturally curved are considered. The beam, simply supported and axially restrained rotates at a constant speed about a horizontal axis in a gravity field. In one case, the rotational axis is parallel to the line connecting the centroids of the end cross-sections, and, in the other case, it is perpendicular to that line. A modal truncation of the governing nonlinear boundary value problem yields a set of ordinary gyroscopic differential equations of the Duffing type. For the cases of a cross-section with extremely different bending stiffnesses and a circular cross-section, the vibrational behaviour is analyzed in detail. The steady-state response (neglecting the influence of gravity) and its stability are considered first. A numerical investigation of weight-excited oscillations follows, where both periodic and even chaotic motions may occur. The effect of different damping mechanisms is addressed. A comparison with the dynamic snap-through of a non-rotating arch and the nonlinear vibrations of a rotating straight bar concludes the contribution.
Nonlinear Steady-State Rotordynamic Analysis Using Transfer Coefficient Method
Authors: Kobayashi M. , Saito S. , Yamauchi S. 
Published: April 2021

Abstract
This paper proposes a new method for steady-state, large-order nonlinear rotordynamic calculations: it uses a method called the transfer coefficient method (TCM), which is more convenient than the transfer matrix method. Since TCM calls for only the displacement as the independent variable, whereas both the displacement and the force are needed as the state variables in the conventional transfer matrix method, TCM promises a substantial saving of computation time without incurring loss in the accuracy of calculation. First, the outline of TCM is explained, then the nonlinear calculations for a rotor of many degrees of freedom are presented. This steady-state nonlinear calculation method is based on the discreet Fourier transform (DPT, FFT) and substructure synthesis. As an example, the nonlinear response due to unbalance mass is calculated and discussed in the case of the rotor which is supported by three bearings with two nonlinear squeeze film dampers.
A Slewing Motor-Beam System: Performance, Behavior and Dimensional Analysis
Authors: Sah Jy-Jen F. , Mayne Roger W. 
Published: April 2021

Abstract
This paper considers the behavior of a slewing beam driven by a DC motor. State equations are presented based on a finite element representation of the beam and a dynamic motor model. The equations are nondimensionalized to view the system parameters in dimensionless groups. Attention is particularly focused on a “damping group” which allows beam vibration to be damped by interaction with the motor. Results are presented in both the frequency domain and time domain which show the effects of motor-beam interaction. These include a change in the beam vibration modes from clamped-free to pinned-free and the development of significant first and second mode damping in a frictionless beam representation.
Virtual Balancing of Rotors Supported by Magnetic Bearings
Authors: Chen H. Ming , Ku C. P. Roger 
Published: April 2021

Abstract
A rotor supported by magnetic bearings can be made to spin about its inertia axis, thus greatly attenuating the imbalance forces that are transmitted through the bearings. Conventional control schemes using tracking notch filters to achieve this purpose are sometimes unstable. This paper presents a rotordynamic analysis, in the form of a computer code, to explain and predict stability in systems using these filters. An alternative balancing scheme, called Virtual Balancing, which is used to implement stable balancing with magnetic bearings, is also described. This scheme treats the bearings as balancing planes and applies an influence coefficient method to relate machine casing vibrations to feed-forward control signals injected to the bearings.
A Comparison of Experimental Results and Theoretical Predictions for the Rotordynamic Coefficients of Short (L/D = 1/6) Labyrinth Seals
Authors: Pelletti Joseph M. , Childs Dara W. 
Published: April 2021

Abstract
Experimental results for the rotordynamic coefficients of short (L/D = 1/6) teeth-on-stator and teeth-on-rotor labyrinth seals are presented. The effects that pressure ratio (fluid density), rotor speed, fluid pre-swirl and seal clearance have on these coefficients are studied. Tests were run out to speeds of 16000 rpm with a supply pressure of 17.3 bar and seal clearances ranging from 0.229–0.419 mm. The experimental results are compared with theoretical predictions of a two control volume compressible flow model.
The experimental results show that decreases in pressure ratio and increases in rotor speed are stabilizing while increases in fluid pre-swirl and seal clearance are destabilizing for both seal configurations. The theoretical model correctly predicts the effects of pressure ratio, rotor speed and fluid pre-swirl on the cross-coupled stiffness. It also predicts reasonable values for direct damping for all test conditions. However, the theory incorrectly predicts the effect of seal clearance on these coefficients. Consequently the theoretical predictions are much better for the large clearance seals.
Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads
Authors: Choi S. H. , Pierre C. , Ulsoy A. G. 
Published: April 2021

Abstract
The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.
Rotor System Modeling With Foundation Matrices From Experimental Modal Data
Authors: Stephenson Robert W. , Rouch Keith E. 
Published: April 2021

Abstract
In a rotor system, the bearing housing and foundation structure can have a significant effect on the dynamics of the rotor. A general procedure is presented to include the foundation effects in a rotor system analysis. The procedure uses modal analysis techniques and measured frequency response functions of the actual foundation structure. From this test data, mass, damping, and stiffness matrices are constructed. These matrices can then be assembled with a finite element model of the shaft and bearings to form the overall rotor system model.
Unbalance response and system natural frequencies obtained from a laboratory rotor mounted on a flexible foundation are presented, and compared to results computed from a system model which includes foundation matrices constructed from a dynamic test on the actual foundation.
Rotor Whirl Measurements on a Long Rotating Cylinder Partially Filled With Liquid
Authors: Colding-Jorgensen Jorgen 
Published: April 2021

Abstract
A theoretical analysis of a long flexibly suspended, rotating cylinder partially filled with liquid has been presented earlier (Colding-Jørgensen, 1990). Special emphasis has been placed on dynamic stability, application in centrifuges, and the influence of external damping.
The present paper presents, experimental results for comparison with the theoretical analysis, especially in regard to unstable speed ranges, whirl speed relative to rotational speed, and limit cycle amplitudes with external damping.
The theory agrees quantitatively with regard to speed ranges and whirl frequency ratios but only qualitatively with regard to whirl amplitudes, indicating the need for further development of the non-linear analysis of the fluid motion with external damping.