bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Torus Flow Y′ = A + B cos Y + C cos X and its Relation to the Quasiperiodic Mathieu Equation
Authors: Mason Stephanie , Rand Richard
Published: February 2021

We obtain power series solutions to the “abc equation” dydx=a+bcosy+ccosx, valid for small c, and for small b. This equation is shown to determine the stability of the quasiperiodic Mathieu equation, z¨+(δ+ϵA1cost+ϵA2cosωt)z=0, in the small ϵ limit. Perturbation results of the abc equation are shown to compare favorably to numerical integration of the quasiperiodic Mathieu equation.
Multiple Time Scale Analysis for Bifurcation From a Double-Zero Eigenvalue
Authors: Luongo Angelo , Paolone Achille , Di Egidio Angelo
Published: February 2021

The multiple scale method is applied to analyze bifurcations from a double zero eigenvalue of general multiparameter dynamical systems. Due to the coalescence of the eigenvalues, the Jacobian matrix at the bifurcation is nilpotent. This entails using time scales with fractional powers of the perturbation parameter. The reconstitution method is employed lo obtain a second-order o.d.e. in the unique unknown amplitude. It coincides with Bogdanova-Arnold’s normal form for the bifurcation equation. Referring to an example, the present approach and the classical center manifold plus normal form method are compared. Finally, the mechanical behavior of a non-conservative two d.o.f. system is studied.
Effect of Coulomb Damping on Buckling of a Simply Supported Beam
Authors: Yabuno H. , Oowada R. , Aoshima N.
Published: February 2021

The present work describes a significant influence of a slight Coulomb damping on buckling of the simply supported beam subjected to an axial compressive force. Coulomb damping in the supporting points produces equilibrium regions around the well-known stable and unstable steady states under the pitchfork bifurcation which are analytically obtained in no consideration of the effect of Coulomb damping. After the transient response, the beam can stop any states in the equilibrium region, which becomes wider in the vicinity of the bifurcation point, depending on the initial condition. Also, the imperfection due to gravity is considered and it is theoretically shown that the equilibrium region is connected in the case when the imperfection due to gravity is relatively small comparing with the effect of the Coulomb damping, while the steady states under the pitchfork bifurcation in no consideration of the effect of Coulomb damping are necessarily disconnected by imperfection. Experimental results confirm the theoretically predicted effect of Coulomb damping in the supporting point on the buckling behavior of the beam.
Dynamics and Stability of Partial Immersion Milling Operations
Authors: Zhao M. X. , Balachandran B. , Davies M. A. , Pratt J. R.
Published: February 2021

In this paper, numerical and experimental investigations conducted into the dynamics and stability of partial immersion milling operations are presented. A mechanics based model is used for simulations of a wide range of milling operations and instabilities that arise due to regeneration and/or impact effects are studied. Poincaré sections are used to assess the stability of motions. The studies reveal that apart from Hopf bifurcation of a periodic motion, a period-doubling bifurcation of a periodic motion may also lead to chatter in partial immersion milling operations. Issues such as tooth contact time variation and structure of stability charts are also discussed.
Experimental and Analytical Investigation of the Subcritical Instability in Metal Cutting
Authors: Kalmár-Nagy Tamás , Pratt Jon R. , Davies Matthew A. , Kennedy Michael D.
Published: February 2021

A single-degree-of-freedom dynamic cutting fixture is used to map out a part of the lobed stability boundary in a simple high-speed machining experiment. The experiment reveals the hysteretic nature of the instability. A 1 DOF mechanical model is derived using parameters identified from the experiment. We then show the existence of a subcritical Hopf bifurcation in this delay-differential equation model which corresponds to the observed experimental instability. The calculation is based on center manifold reduction. Then time domain simulation is used to solve the full nonlinear equation of motion that allows for the tool to leave the workpiece giving excellent agreement with the experiment.
Suppression of Parametric Resonance of a Cantilever Beam by a Pendulum-Type Vibration Absorber
Authors: Yabuno Hiroshi , Kawazoe Jun , Aoshima Nobuharu
Published: February 2021

The dynamic response of a parametically excited cantilever beam with a pendulum-type vibration absorber is presented. The equation of motion and the associated boundary conditions are derived considering the static friction for the rotating motion at the pivot of the pendulum. It is thoretically shown that the static friction plays a dominant role in the suppression of the parametric resonance. The boundary conditions are different between the cases when the motion of the pendulum is locked by the static friction and when it’s not. According to this variation of the boundary conditions depending on the pendulum motion, the natural frequencies of the system are automatically changed and the unstable regions for the parametric resonance are also shifted, so that the parametric resonace does not occur. Furthermore experimental results verify the effectiveness of the pendulum as a vibration absorber for the parametric resonance.
Nonlinear Transient Localization and Low Dimensional Models of a Flexible System With a Clearance
Authors: Ma Xianghong , Vakakis Alexander F.
Published: February 2021

Transient nonlinear localization in a system of two rods coupled with a nonlinear backlash spring is studied in this work. The method of Karhunen-Loeve (K-L) decomposition is then used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. In addition, 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. Reconstructions of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction.
Comparison of Two Rate-Independent Hysteresis Models With Application to Piezoceramic Transducers
Authors: Royston Thomas J. , Lee Soon-Hong , Friedman Gary
Published: February 2021

The applicability of and relationship between two rate-independent hysteresis models that have been used to describe hysteresis in piezoceramic transducers are investigated. It is shown that the generalized Maxwell resistive capacitor hysteresis model is a particular case of the classical Preisach hysteresis model. The Preisach function that reduces the Preisach model to the Maxwell resistive capacitor model is derived. It is also shown that the inverse of the Maxwell model is this same particular case of the classical Preisach model. A Maxwell model identification procedure based on Preisach identification principles is formulated. The applicability of the classical Preisach and Maxwell hysteresis models for identifying and simulating piezoceramic dielectric behavior is investigated experimentally via studies on a 1-3 piezoceramic composite. Results indicate that both hysteresis models can accurately represent piezoceramic hysteresis. It is noted that the identified relationship between Preisach and Maxwell hysteresis models may prove useful in a wider range of hysteresis applications than just those involving piezoceramics.
Random Vibration Studies of a SDOF System With Shape Memory Restoring Force
Authors: Duval Luis , Noori Mohammad N. , Hou Zhikun , Davoodi Hamid , Seleecke Stefan
Published: February 2021

Intelligent and adaptive material systems and structures have become very important in engineering applications. The basic characteristic of these systems is the ability to adapt to the environmental conditions. One of the new class of materials with promising applications in structural and mechanical systems are Shape Memory Alloys (SMA). The mechanical behavior of shape memory alloys in particular shows a strong dependence on temperature. This property provides opportunities for the utilization of SMAs in actuators or energy dissipation devices. However, the behavior of systems containing shape memory components under random excitation has not yet been addressed in the literature. Such study is important to verify the feasibility of using SMAs in structural systems. In this work a non-deterministic study of the dynamic behavior of a single degree-of-freedom (SDOF) mechanical system, having a Nitinol spring as a restoring force element is presented. The SMA spring is characterized using a one-dimensional phenomenological constitutive model based on the classical Devonshire theory. Response statistics for zero mean random vibration of the SDOF under a wide range of temperature is obtained. Furthermore, nonzero mean analysis of these systems is carried out.
Ideal Elastic-Plastic Oscillators Subjected to Stochastic Input
Authors: Caddemi S. , Di Paola M.
Published: February 2021

The paper deals with the evaluation of the probabilistic response of an ideal elastic-plastic single degree of freedom oscillator subjected to a normal white noise. The analysis has been conducted on the hypothesis that accumulated plastic displacements are a compound homogeneous Poisson process independent of the external excitation. In this case plastic displacements can be treated as an additional external noise, to be identified, acting on a linear system.

In the paper a time domain approach to obtain the two variable non stationary correlation function is proposed. Hence the evolutionary power spectral density function is also obtained.

A numerical example is presented in order to show the accuracy of the presented procedure in comparison to Monte Carlo simulations.
Poincaré Map-Based Continuation of Periodic Orbits in Dynamic Discontinuous and Hysteretic Systems
Authors: Lacarbonara Walter , Vestroni Fabrizio , Capecchi Danilo
Published: February 2021

A numerical algorithm is proposed to compute variation of periodic solutions and their codimension-one bifurcations in discontinuous and hysteretic systems in the relevant control parameter space. For dynamic systems with discontinuities and hysteresis, some components of the associated vector fields are nondifferentiable. Therefore, one cannot resort on classical numerical tools based on the evaluation of the Jacobian of the vector field for path-following analyses. Using the pertinent state space, periodic orbits are sought as the fixed points of a Poincaré map based on an appropriate return time. The Jacobian of the map is computed numerically via either a forward or a central finite-difference scheme and a Newton-Raphson procedure is used to determine the fixed points. The continuation scheme is a pseudo-arclength algorithm based on arclength parameterization. The eigenvalues of the Jacobian of the map — Floquet multipliers — are computed to ascertain the stability of the periodic orbits and the associated bifurcations. The procedure is used to construct frequency-response curves of a bilinear, a Masing-type, and a Bouc-Wen oscillator in the primary and superharmonic frequency ranges for various excitation levels. The proposed numerical strategy proves to be very effective in capturing a rich class of solutions and bifurcations — including jump phenomena, pitchfork (symmetry-breaking), and period-doubling.
A0 Wave in a Submerged Stiffened Cylindrical Shell
Authors: Baillard André , Conoir Jean-Marc , Décultot Dominique , Maze Gérard , Klauson Aleksander , Metsaveer Jaan
Published: February 2021

The backscattering of a normal incident plane acoustic wave by a stiffened cylindrical shell is considered. The studied cylindrical shell is made of stainless steel and its internal to external radius ratio is b/a = 0.98. The shell submerged in water is strengthened by an internal plate of the same material and thickness, which is diametrically soldered.

As for the unstiffened shell, A wave (Scholte-Stoneley wave) and S0 wave (first symmetrical Lamb wave) are detected in the frequency range investigated (50–200 ka where k is the wave number in water). On the contrary, the presence of the plate into the tube allows the detection of A0 wave (flexural Lamb wave) whereas it is not observed for the unstiffened shell, owing to the attenuation of the wave during the propagation around the tube. In particularl, A0 wave could be reflected on the junction with enough energy to re-emit in water. Furthermore, wave type conversions are allowed by way of the junctions: S0–A0 wave conversions are observed.
Modal Parameters Estimation and Model Order Selection of a Structure Excited by a Random Force
Authors: Larbi N. , Lardies J.
Published: February 2021

A multivariate maximum likelihood procedure for the estimation of modal parameters is presented. The vibrating system is excited by a random force and sensors output only are used to estimate the natural frequencies and damping coefficients of the system. The method works in time domain and a vector autoregressive moving average (VARMA) process is used. The information about modal parameters is contained in the multivariate AR part, which is estimated using an iterative maximum likelihood algorithm. This algorithm uses a score technique and output data only. The order of the AR part is obtained via the Minimum Description Length associated with an instrumental variable procedure. Experimental results show the effectiveness of the method for model order selection and modal parameters estimation.
Stochastic Stability of a Universal-Joint Driven Torsional System
Authors: Asokanthan S. F. , Wang Xiao-Hui
Published: February 2021

Torsional instabilities in a two-degree-of-freedom system driven by a Hooke’s joint due to random input angular speed fluctuation are investigated. Linearised analytical models are used for calculating the largest Lyapunov exponent. Instability behaviour is then characterised by examining the sign of this exponent. Conditions for the onset of instability via sub-harmonic parametric resonances has been shown to coincide with those for the deterministic case. However, the onset of instability via sum as well as the difference type combination resonance is found to be different from that of the deterministic case. The instability conditions for the system under input angular speed fluctuation have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predictions for the deterministic and the stochastic cases are compared. The effect of fluctuation probability density as well as that of inertia loads on the stability behaviour of the system has been examined.
Analysis of Dynamic Couplings in Two-Stage Geared Systems
Authors: Raclot J. P. , Velex P.
Published: February 2021

A modular model for the simulation of the dynamic behavior of multi-stage spur and helical gears is presented. It is mostly based on shaft finite elements combined with some specific gear elements which account for torsional-flexural-axial couplings, parametric and external excitations. Each tooth contact on theoretical base planes is assimilated to a line contact and discretized in accordance with the contact line evolutions when pinions and gears are rotating. A local stiffness and a normal deviation which represent gear tooth elasticity and tooth shape modifications or/and errors are associated with each cell of the time-dependent grid.

Seeking particular stable solutions only, the equations of motion are linearized and solved by using a specific spectral method which has been adapted to parametrically excited systems submitted to broad band parametric and external excitations.

Numerical simulations (dynamic transmission errors and displacements) have been performed for two different two-stage geared trains, i. e., a dual speed reducer (two pinion-gear pairs) and a dual mesh reverse idler (3 gears). The role and the definition of profile modifications (short/long reliefs), the contributions of pitch errors and the influence of the mesh relative orientation on the system dynamic behavior are examined. Finally, the nature and the intensity of the inter-mesh couplings in a double stage geared unit are discussed.
Numerical Simulation of Nonlinear Spur Gear Dynamics
Authors: Arakere Nagaraj K. , Nataraj C.
Published: February 2021

An analytical investigation of the nonlinear dynamics of a high-speed spur-gear pair supported on journal bearings is presented. Dynamic tooth loads result from the interaction between periodic variation of gear mesh stiffness, involute tooth profile errors and gear rotor dynamics. Accurate estimation of dynamic tooth loads, as the gear teeth engage and disengage, is critical for fatigue life estimation. Load-deflection characteristics of a spur gear mesh and the periodically varying gear mesh stiffness is developed using a finite element model. Relative displacement between the gear teeth (transmission error) due to tooth deflection along the line of action is evaluated. The coupled torsional-lateral vibrations of a spur-gear pair supported on journal bearings is modeled as a six degree of freedom system. The time dependent radial and tangential forces acting on the gear shaft supported on journal bearings is evaluated. Short bearing theory is used for modeling the journal bearing dynamics. The resulting nonlinear equations of motion are numerically integrated to obtain gear and pinion whirl orbits due to unbalance excitation and dynamic tooth load variation. Dynamic tooth loads are compared with the mean load due to torque transmission.
New Higher Order Numeric Quadratures for Regular or Singular Functions on an Interval: Applications for the Helmholtz Integral Equation
Authors: Helluy Philippe , Maire Sylvain , Ravel Patrice
Published: February 2021

A high order integration method is presented for regular or singular integrands over an integral. This method appears to be very useful to compute the integrals of the green function in the numerical resolution of boundary integral equations.
Simulation Method of Torsional Vibration Waveform of Reciprocating Engine Crankshaft Systems by Transition Matrix Method
Authors: Wakabayashi Katsuhiko , Honda Yasuhiro , Kodama Tomoaki , Okamura Hiroshi
Published: February 2021

The torsional vibration of the crankshaft system of high speed diesel engines has become more excessive with the increase of engine power and with the decrease of engine rigidity. So it is necessary in the design stage to improve accuracy in the calculation of maximum torsional vibration amplitude at resonant engine speed. At first, this paper refers to a method for obtaining experimentally engine damping that is necessary for the calculation of torsional vibration. If the value of the damping cannot be accurately estimated, the accuracy of the calculated result is still not satisfactory. In this experiment, the decay constant is obtained from the record of the damped, free torsional vibration waveforms which can be got by stopping abruptly combustion in steady operating. It is also shown that the damping ratio, which is approximately 0.03 to 0.04 in high-speed, small diesel engines, can be got from the already-obtained decay constant. Secondly, authors try to calculate directly resultant amplitude by using a step by step transition matrix method. The simulated waveforms of torsional vibration of a high speed diesel engine are compared with the experimental results and it is shown that the calculated results by the transition matrix method are accurate. At the same time, this paper refers to a method for the estimation of engine damping coefficient that is necessary for the calculation of torsional vibration. In this method, the damping coefficient can be got from the previously obtained damping ratio.
Optimization of Plate and Shell Surfaces
Authors: Awrejcewicz Jan , Krysko Vadim A.
Published: February 2021

A problem of plate and shell surface optimisation has been formulated and solved. The corresponding theorem has been stated and proved. An algorithm for an optimal surface search has been proposed and its reliability has been discussed. Three examples have illustrated both the introduced theory and the numerical algorithm.
Modal Characteristic of Cantilevered Beams and Plates: A Study of Transition From Beam-Like to Plate-Like Behaviour
Authors: Tangchaichit K. , Oyadiji S. O.
Published: February 2021

The paper presents the finite element (FE) analysis of the free vibrations of cantilevered aluminium alloy beams and plates of 5mm thickness and of length-to-breadth ratios ranging from a ratio of 20 for a beam down to a ratio of 0.25 for a plate. The analysis was carried out using the ABAQUS FE programme. For each ratio, a total of 20 natural frequencies and mode shapes were predicted. The objective of the paper was to demonstrate that a transition zone for beam-like to plate-like behaviour of structural components can be approximately defined for various length-to-breadth ratios. It is shown that the frequency parameters of cantilevered plates asymptotically approach the frequency parameters of cantilevered beams at high length-to-breadth ratios. In addition, it is shown that at the transition point for beam-like to plate-like behaviour, which occurs at small length-to-breadth ratios, the difference between the frequency parameters of cantilevered beams is less than the frequency parameters of cantilevered plates about 3 %.
Intermodal Coupling in Flexible Spinning Disk-Spindle Systems
Authors: Deshpande Moreshwar , Mote C. D.
Published: February 2021

The coupling between the disk and spindle vibration modes of a rotating disk-spindle system is analyzed through the free vibrations of a rotating, flexible spindle with N attached flexible disks. The spindle is modeled as an extensible Kirchhoff-Love rod and the disks as Kirchhoff plates. Couplings between the longitudinal, torsional and flexural deformations of the spindle and the transverse and in-plane motions of the disk are studied analytically. A kinematically rich model captures couplings that have not been predicted previously. Discretization of these modes as a series of orthonormal functions allows for the construction of the characteristic matrix. The structure of this matrix is exploited to partition the eigenvalue problem into six natural classes and to provide simple, exact rules governing the coupling between the modes of the disk-spindle system. The longitudinal spindle vibration modes and the zero nodal diameter transverse disk modes are coupled inertially at all rotation speeds. The torsional spindle modes couple to the zero nodal diameter in-plane disk modes at all non-zero rotation speeds. This coupling is absent in a stationary disk-spindle system. For non-zero rotation speeds, the flexural modes of the spindle in the two orthogonal planes containing the undeformed spindle centerline and the one nodal diameter transverse and in-plane disk modes couple. The one nodal diameter transverse disk modes couple to the one nodal diameter in-plane disk modes through the flexural compliance of the spindle; this coupling cannot be observed through study of the disk alone.
Linear In-Plane Free Vibration of a Rotating Disk
Authors: Hamidzadeh H. R. , Dehghani M.
Published: February 2021

This paper discusses linear in-plane free vibration of a homogeneous, isotropic, linear visco-elastic rotating disk. Two-dimensional theory of elastico-dynamic is employed to develop the general governing equations of motion. In this analysis, a constant angular velocity is assumed. The wave equations and Bessel Functions of the first and second kind are utilized to obtain the natural frequencies. Natural frequencies are found for a number of modes with several clamping ratios. These natural frequencies were compared with the available established results. Also, the influence of rotational speed and clamping ratio on the natural frequencies and the mode shapes of vibration are determined. The analysis provides information about the elastic stability of the rotating disks for several modes of vibration.
An Analytical Solution for the Nonlinear Vibration of Rotating, Thin Disks
Authors: Luo Albert C. J. , Mote C. D.
Published: February 2021

The response, natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the Luo and Mote’s plate theory of 1998. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish, and they are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers becomes larger. The critical speeds of softening disks decrease with increasing deflection amplitudes.
Frequency Clusters in the Spectrum of Annular Cylinders
Authors: Tzou K. I. , Wickert J. A. , Akay A.
Published: February 2021

As the length of a traction-free annudar cylinder is increased, distinct members within any family of radial or longitudinal shear modes have natural frequencies that asymptotically approach a common non-zero value. Such modes, potentially having significantly different numbers of nodes along the cylinder’s generator, can have natural frequencies that are indistinguishable from one another within the resolution of test equipment or numerical simulation. The three-dimensional vibration model discussed here predicts the formation of narrow “frequency clusters” with the cylinder’s increasing length, the converged value of which bounds from below the frequencies of all modes within a particular family. In addition to these spectral characteristics, frequency clusters have implications for the forced response of annular cylinders. For the particular families of modes that are of interest here, the steady state harmonic response at frequencies near a cluster can be spatially confined with displacements that decay rapidly away from the point of maximum response. At other driving frequencies, the response is distributed more uniformly along the length of the cylinder. The derived analytical model is compared with results from laboratory measurements, and from the predictions of wave propagation theory in the limit of infinite cylinder length.
An Explicit Scheme for Structural Dynamics Analysis
Authors: Tchamwa Bertrand , Conway Ted , Wielgosz Christian
Published: February 2021

The purpose of this paper is to introduce a new simple explicit single step time integration method with controllable high-frequency dissipation. As opposed to the methods generally used in structural dynamics, with a consistency experimentally chosen of second order, the new method is only first-order-consistent but yields smaller numerical errors in low frequencies and is therefore very efficient for structural dynamic analysis.

The new method remains explicit for any structural dynamics problem, even when a non-diagonal damping matrix is used in linear structural dynamics problem or when the non-linear internal force vector is a function of velocities. Convergence and spectral properties of the new algorithm are discussed and compared to those of some well-known algorithms. Furthermore, the validity and efficiency of the new algorithm are shown in a non-linear dynamic example by comparison of phase portraits.
Vibration Control of a Rigid-Flexible Satellite During Attitude Maneuver
Authors: DeSouza Luiz Carlos Gadelha , DaSilva Silmara Alexandra
Published: February 2021

The paper presents the results of an active structural vibration control of a flexible satellite performed by a proof-mass actuator (PMA) during an attitude rotation maneuver. The satellite investigated is composed of a rigid rub plus a cantilevered flexible beam with the PMA located at the beam free end. As the satellite maneuvers from rest to a pre-defined position, the rigid body motion can excite the flexible part of the satellite. The PMA tasks is to damp-out any residual vibration caused by this maneuver efficiently. The rigid/flexible satellite is modeled, using a relatively simple structural dynamics approach. Having found the vibration modes of the structure, expressions for kinetic and potential energy are derived. Lagrange’s equation is then applied to obtain the satellite equations of motion. The PMA gain selection is based oil an analytical approach which shows that the pole and zero of the fundamental mode is dominant. The efficiency of the PMA using velocity feedback with a PI control law was examined by numerical simulations for different control maneuvers strategies. It was shown that one such controller has damped the residual flexible vibration successfully. However, it was also shown that the control system efficiency is function of the maneuver strategy.
Hybrid Approach to Tomographic Reconstruction of Bubbles in Two-Phase Flows Using Algebraic Reconstruction Technique (ART), Genetic Algorithms (GA) and Simplex Method
Authors: Rajesh A. , Kihm K. D. , Yang L. , Yen J.
Published: February 2021

Main hurdles in the application of genetic algorithms to complex problems are two fold. One is the high computational cost due to their slow convergence rate. The other is to reduce the number of input parameters of a conventional genetic algorithm as in the case of tomographic reconstruction of bubbles. In our present work great strides have been made to alleviate both the problems by using a Hybrid model of Algebraic Reconstruction Technique (ART), Simplex Method and Genetic Algorithm (GA). Our results showed that the hybrid approach is an effective and robust optimization image reconstruction technique.
Singular Perturbation Analysis of an Electrohydraulic Servo-Drive With Discontinuous Reduced Dynamics
Authors: Manhartsgruber Bernhard
Published: February 2021

This paper deals with the position control of a hydraulic servo-drive for translatory motion. The application of a nonlinear composite feedback control based on singular perturbation methods (Kokotovic, Khalil & O’Reilly 1986) is described. A comparison with linear output and state feedback shows the benefits of nonlinear control. The nonlinear design uses feedback linearization for the reduced system and simple proportional feedback for the control of the pressure difference (fast system). The feedback linearization results in a standard second order behavior of the reduced system with cutoff frequency and damping as decoupled design parameters. The proposed method is especially suitable for oscillation drives. Experimental results are given for step responses and sine tracking.
The Estimation of Viscous and Coulomb Damping in Harmonically Excited Oscillators
Authors: Liang J.-W. , Feeny B. F.
Published: February 2021

This paper proposes a simple identification algorithm for estimating both viscous and dry friction in harmonically forced single-degree-of-freedom mechanical vibration systems. The method is especially suitable for the identification of systems for which the traditional free-vibration scheme is difficult to implement. Numerical simulations are included to show the effectiveness of the proposed algorithm. A numerical perturbation study is also included for insight on the robustness of the algorithm.
A Finite Element Analysis of Friction Damping in a Slip Joint
Authors: Chen Weijiang , Deng Xiaomin
Published: February 2021

Micro-slip along frictional interfaces often provides the dominant damping mechanism in a built-up structure and plays an important role in the dynamic behavior of the structure. This paper presents the results of a finite element study of the effect of dry friction on the damping response of a slip joint. The emphasis of this paper is to understand the evolution of the slip and stick regions along the joint interface during loading and to quantify the amount of energy dissipation during cyclic loading and its dependence on structural and loading parameters. Finite element predictions have been compared to experimental measurements and early analytical predictions in the literature. This study seems to demonstrate the potential of the finite element method in providing adequate “numerical” test data for formulating lumped-parameter structural models that can simulate the nonlinear dynamic behavior of bolted joints.
A Design Optimization Process Based on an Energy Finite Element Formulation
Authors: Borlase George , Vlahopoulos Nickolas , Garza-Rios Luis Octavio
Published: February 2021

The Energy Finite Element Analysis (EFEA) offers an alternative solution to the established Statistical Energy Analysis (SEA) for simulating the vibration of large scale structures. A brief theoretical overview and comparison of the two methods is presented first. Numerical models for a fishing boat are utilized for a comparison between the two formulations. In order to demonstrate the powerful capabilities of EFEA in the area of simulation based design, an optimization routine is integrated with an EFEA solver. The optimized distribution of damping over the hull of a vessel is computed. The formulation of the optimization process is presented. The definition of the design variables, the objective function, and the constraints is discussed. The flow chart of the optimization process, and a comparison between the initial and the optimized design are presented.
Modeling of Track-Wheel-Terrain Interaction for Dynamic Simulation of Tracked Vehicle Systems
Authors: Ma Zheng-Dong , Perkins Noel C.
Published: February 2021

A mathematical model of track-wheel-terrain interaction is presented herein to support the dynamic simulation of tracked vehicles. This model combines approximate and known constitutive laws for terrain response with a new representation for the track element. The resulting track-wheel-terrain model allows the computation of the track tension and the normal and shear forces at the track-terrain interface as the track negotiates terrain of arbitrary profile. A key feature of this model is the uniform treatment of contact between the track and the roadwheels and the track and the terrain. Treating both contact problems in the same manner significantly simplifies the problem formulation and also reduces difficulties in computing points of track-wheel and track-terrain separation. The model takes the form of a two-point nonlinear boundary value problem that accounts for tension variations along the track (due to the non-uniformly distributed normal pressure and traction), track extensibility, and geometrically large (nonlinear) track deflections. Solutions are obtained using a finite element formulation. Both the model and the solution method are formulated with a view towards implementation within a multibody dynamics code for simulating a full vehicle. Several examples illustrate the capabilities of the proposed model.
Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams
Authors: Takahashi Yoshitaka , Shimizu Nobuyuki
Published: February 2021

There are three basic finite element formulations which are used in the dynamics of flexible beams. These are the floating frame of reference approach, the finite segment method and the large rotation vector approach. Recently, the absolute nodal coordinate formulation was proposed by A.A.Shabana et al. In this procedure, there is no need to transform the element matrices since the equations of motion are defined in terms of absolute nodal coordinates. The mass matrix becomes constant, whereas the stiffness matrix becomes nonlinear function of time, even in case of linear elastic problems. One possible method to avoid such cumbersome of the absolute nodal coordinate formulation in calculating clastic forces is to assume the infinitesimal deformation theory against beams undergoing large rotation.

In this paper, a new formulation to calculate the elastic forces and add the rotary inertia effects in the expression of the inertia forces. This formulation is based on the assumption that the deformations within each element remain very small. The expression of the resulting clastic force is simple, and the need for performing coordinate transformation is avoided. As the method assumes that the deformation of the beam from a selected beam axis is very small, a large number of finite elements is required for large deformation problems. However, the formulation has been found to be efficient for large rotation and medium deformation problems. Numerical examples are demonstrated for this formulation by using planar flexible pendulum problems.
A Numerical Approach to Solving Flexible Multibody Systems Using the Absolute Nodal Coordinate Formulation
Authors: Yakoub R. Y. , Shabana A. A.
Published: February 2021

By utilizing the fact that the absolute nodal coordinate formulation leads to a constant mass matrix, a Cholesky decomposition of the mass matrix can be used to obtain a constant velocity transformation matrix. This velocity transformation can be used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. In this case, the inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motions. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this paper. A flexible four-bar linkage is presented in this paper in order to demonstrate the use of Cholesky coordinates in the simulation of the small and large deformations in flexible multibody applications. The results obtained from the absolute nodal coordinate formulation are compared to those obtained from the floating frame of reference formulation.
Modular Modeling and Simulation of Multibody Systems
Authors: Kübler Ralf , Schiehlen Werner
Published: February 2021

Complex engineering systems such as automobiles are often relieved by a modular approach for modeling and simulation to make it treatable by a team of engineers. The functional decomposition is due to different engineering disciplines and engineering intuition.

The resulting subsystems are considered as dynamic blocks with inputs and outputs. The global system structure is given by interconnections of inputs and outputs of corresponding blocks. Since the global system structure is independent of the internal subsystem description this procedure allows for independent and parallel modeling of the internal dynamics of each block. Although this approach is widely used in control theory and also more and more in mechatronics, the mechanical parts are traditionally modeled as one multibody system.

In this paper a modular formulation of multibody systems is proposed which is based on the block representation of a multibody system with corresponding input and output quantities. Multibody system blocks can be connected by means of arbitrary joints and coupling elements resulting in a global system with high degree of modularity in the modeling procedure. The option to use different simulation tools for modular simulation of the global system behavior has the potential to even more exploit the modular system structure.
Optimal Motions for Underactuated Manipulators
Authors: Sohl Garett A. , Bobrow James E.
Published: February 2021

In this paper we develop an algorithm for solving optimal control problems for underactuated open chain manipulators. A local solution to the nonlinear optimal control problem is obtained using a constrained parameter optimization procedure. As part of the algorithm, a recursive dynamics formulation for underactuated serial chains is derived using matrix exponentials and the geometric framework provided by Lie groups and Lie algebras. The benefit of the matrix exponential formulation is the ability to derive explicit analytic gradients of the dynamics. These gradients are essential for our algorithm since the parameter optimization is ill-conditioned aid approximate numerical gradients do not produce meaningful solutions. Interesting example solutions are provided for a two dof acrobot, a simple branched chain and a 7 dof human diver.
Minimum Jerk Traction Control of a Wheeled Mobile Robot Moving Over a Hump
Authors: Ayalew A. , Lai E. , Oyadiji S. O.
Published: February 2021

A new technique is presented for the minimization of jerk for wheeled mobile robots (WMRs) traveling on uneven terrain. A robot may jerk as it traverses a road obstacle. Consequently, wheel-ground contact loss is one of the undesirable dynamic effects that can cause loss of control and robot instability. By considering the dynamics of the robot with respect to the longitudinal, pitching and vertical motions of the platform, the new technique calculates the dynamic compensation needed to ideally counter the onset of jerk by controlling the magnitude of the input drive torque to the wheels. Simulation results showed that the technique has the potential to substantially reduce the magnitude of jerk of a WMR during longitudinal maneuver over a road obstacle with a positive gradient.
Free and Forced Vibration of a Kinked Cantilever Beam
Authors: Reddy B. S. , Simha K. R. Y. , Ghosal A.
Published: February 2021

In this paper we use the assumed modes method to derive an analytical model of a kinked cantilever beam of unit mass carrying a kink mass (mk) and a tip mass (mt). The model is used to study the free and forced vibration of such a beam. For the free vibration, we obtain the mode shape of the complete beam by solving an eight order polynomial whose coefficients are functions of the kink mass, kink angle and tip mass. A relationship of the form f(mk,mt,δ)=mk+mt(4+103cosδ+23cos2δ)=constant appears to give the same fundamental frequency for a given kink angle, δ, and different combinations of kink mass and tip mass.

To derive the dynamic equations of motion, the complete kinked beam mode shape is used in a Lagrangian formulation. The equations of motion are numerically integrated with a torque applied at the base and the tip response for various kink angles are presented. The results match those obtained from a traditional finite element formulation.
Multirate Integration for Real-Time Simulation of Wheel Loader Hydraulics
Authors: Buzdugan Laurenţiu I. , Balling Ole , Lee Peter Chien-Te , Balling Claus , Freeman Jeffrey S. , Huck Frank
Published: February 2021

This paper details a real-time simulation of an articulating wheel loader, which is comprised of a multibody system modeling the chassis and the bucket assembly and a set of subsystems. The hydraulic subsystem is modeled by a set of ODE’s which represent the oil pressure fluctuations in the system. An Adams-Bashforth-Moulton integration algorithm has been implemented using the Nordsieck form to develop a constant step-size multirate integration scheme, modeling the interaction between the hydraulic subsystem and multibody dynamics models. An example illustrating the simulation of a wheel loader bucket operation is presented at the end of the paper.
Influence Coefficients Obtained by Hammer Beat Permit Significant Time Savings When Balancing Simple Flexible Rotors
Authors: Wiese D. , Breitwieser M.
Published: February 2021

The following paper presents a method for balancing simple flexible rotors with the help of influence coefficients obtained by hammer beat. The method permits time savings of approx. 50% compared to the conventional influence coefficient method. Initial positive results obtained on a flexible roll are also presented.
High Cycle Fatigue Cracks at Radial Fan Impellers Caused by Aeroelastic Self-Excited Impeller Vibrations: Part 2 — Mechanism and Mathematical Model
Authors: Ni Alexander
Published: February 2021

The radial impeller of the main fan of hydrogen cooled generator has been noted to sustain fatigue failure. Experimental data pointed out to the impeller selfexcitation as the cause of the failure. According to the mechanism and the mathematical model suggested in the paper the impeller selfexcitation is due to the feedback between the natural impeller vibrations and the acoustic field in the side room adjacent to the impeller. The impeller vibrations induce the pressure oscillations in the side room that in turn influence the impeller. Under special conditions of the fan dynamic behaviour and the acoustic properties of the fan side room this feedback leads to the selfexcitation. The suggested mechanism and the model fit all the experimental data. Their validity has been also later confirmed by the maintaince experience of other similar machines.
A Genetic Algorithm Based Balancing Framework for Flexible Rotors
Authors: Qiu Hai , Qu Liangsheng , Sun Ruixiang
Published: February 2021

Most of the methods in flexible rotor balancing currently used rely on the repeated running up and down processes of the balanced machine. The ordinary balancing methods without test runs are regularly based on too many hypotheses and depended on prior knowledge of bearings. The latter restricts their wide application in practice. This paper establishes a balancing process frame with both unbalance and bearing parameters as inputs and the vibration responses on bearings as outputs. The authors determine the rotor unbalance as an inverse engineering problem using genetic algorithms (GA). This method can simultaneously evaluate the bearing parameters and their working situations in the service environments of large rotating machinery.
Identification of Rotating Asymmetry in Rotating Machines by Using Reverse dFRF
Authors: Lee Chong-Won , Kwon Kye-Si
Published: February 2021

A quick and easy but comprehensive identification method for asymmetry in an asymmetric rotor is proposed based on complex modal testing method. In this work, it is shown that the reverse directional frequency response function (reverse dFRF), which indicates the degree of asymmetry, can be identified with a simple method requiring only one vibration sensor and one exciter. To clarify physical realization associated with estimation of the reverse dFRF, its relation to the conventional frequency response functions, which are defined by the real input (exciter) and output (vibration sensor), are extensively discussed.
A New Approach to Prediction of the Self-Excited Torsional Vibration of Rolling Mill Drives in Rolling Slippage
Authors: Wang Zhang-Hai , Zhang W. J. , Wang De-Jun
Published: February 2021

This paper addresses the self-excited vibration in rolling processes, particularly in the case of rolling mill drive system. A mathematical model is developed which accounts the non-linearity of the system due to the rolling slippage for friction present between the work piece and the roller. To predicate the self-excited vibration, the condition under which the self-excited vibration occurs is derived which is related to the rolling normal force and the rolling speed. As the self-excited vibration causes instantaneous breakage of a system, the study reported here will thus be very useful and of significance.