bluuebunny/crossref_metadata_2025_split huggingface dataset:
Analysis of Piecewise Linear Systems With Displacement and Time Regions by Vector Fields
Authors: Nakai Mikio , Murata Shinji , Hagio Seiji 
Published: February 2021

Abstract
A generalized solution methodology based on piecewise linear vector fields is proposed for piecewise linear systems with singular regions or asymmetric restoring forces which vary spatially and temporally. In matrix representation for these systems, state variables in each region can be explicitly expressed as a function of the time the orbit spends between two boundaries or the time the orbit takes to pass through the boundary. The time can be determined by the Brent method, and periodic solutions can then be obtained. Analytical solutions are validated on a system with 3-regions of displacement and 2-regions of time, a circumferential vibration of gear meshing system, by using the newly developed numerical method.
Stability Analysis of Finite Difference Model of Orthogonal Metal Cutting in Presence of Random Noises
Authors: Rodkina Alexandra , Wiercigroch Marian 
Published: February 2021

Abstract
The dynamics of a nonlinear cutting process in the presence of random noise is defined and investigated. This approach is adequate for a wide range of models describing the orthogonal metal cutting processes by a single-degree-of-freedom oscillator, where the nonlinearity comes from the cutting force in form of a variable resistance force. The method of Lyapunov–Krasovskii functional was adopted to analyze the necessary conditions for a stable operation. The conditions ensuring an asymptotic stability in the presence of random noises are established.
Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics
Authors: Zhang Jiazhong , de Kraker Bram , van Campen Dick H. 
Published: February 2021

Abstract
An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.
Nonlinear Vibrations of an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Cylindrical Tank: Resonance With an Axisymmetric Mode
Authors: Ikeda Takashi , Murakami Shin 
Published: February 2021

Abstract
The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a cylindrical tank are investigated. When the structure is vertically subjected to a sinusoidal excitation, and when the natural frequency of the structure is equal to twice the natural frequency of the first axisymmetric mode of sloshing, modal equations governing the coupled motions are derived. Then, the theoretical resonance curves are presented by using the method of harmonic balance and an FFT analysis. As a result, it is demonstrated that the resonance curve for the structure changes from a shape with a peak to a flat shape as the liquid level decreases. It is also clarified that amplitude-modulated motions appear when the tuning condition is deviated. In experiments, theoretical resonance curves were qualitatively in good agreement with the experimental results.
Dynamics of a Cubic Nonlinear Vibration Absorber
Authors: Oueini Shafic S. , Chin Char-Ming , Nayfeh Ali H. 
Published: February 2021

Abstract
We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.
Stability Limitations for Multiple Centrifugal Pendulum Vibration Absorbers
Authors: Al-suwaiyan Abdallah S. , Shaw Steven W. 
Published: February 2021

Abstract
Centrifugal pendulum vibration absorbers are a type of tuned dynamic absorber used for the attenuation of torsional vibrations in rotating and reciprocating machines. They consist of masses that are constrained to move along a specific path relative to the rotating shaft of the machine. Previous analytical studies have considered the performance of multi-absorber systems with a very specific path and of single absorber systems with general paths. In this paper we investigate the performance and dynamic stability of systems comprised of multiple, identical centrifugal pendulum vibration absorbers that have general paths. The study is carried out by considering a scaling of the system parameters based on physically realistic ranges of dimensionless parameters, which allows for application of the method of averaging. It is found that performance is limited by two distinct types of instabilities. In one of these, the systems of absorbers lose their synchronous character, while the other is a classical nonlinear jump behavior that affects all absorbers identically and leads to disastourous results. These results are used to evaluate the performance of systems with common types of absorber paths, namely circles and cycloids. The analytical results are compared against numerical simulations and good agreement is found.
The Impact of High Speed Machining Technology on the Design and Fabrication of Aerospace Components
Authors: Halley J. E. , Helvey A. M. , Smith K. S. , Winfough W. R. 
Published: February 2021

Abstract
Recently, several new machining techniques have been developed which have driven dramatic changes in the manufacture of aerospace components with thin ribs and webs. There are many such components in commercial and military aircraft, and until recently these components we fabricated as sheet metal assemblies. Through an improved understanding of the dynamic interaction between the tool and workpiece, it has now become economically competitive to create components with thin ribs and webs as monolithic units machined from a solid block by milling.
Ribs are those thin structures created at the periphery of the end mill, as opposed to webs, which are the thin structures created at the face of the end mill. It is easy to see that as the ribs and webs become thinner, the stiffnesses will decrease, and chatter will become more problematic. Chatter during the machining of such parts can result in damage to the part (even cutting through the thin structure) or at least poor surfaces which require hand finishing. This paper outlines the basic technology required to produce these kinds of components efficiently, and cites several examples.
Tool Oscillation and the Formation of Lobed Holes in a Quasi-Static Model of Reaming
Authors: Bayly Philip V. , Young Keith A. , Halley Jeremiah E. 
Published: February 2021

Abstract
A quasi-static model of reaming is used to explain oscillation of the tool during cutting and the resulting roundness errors in reamed holes. Tools with N evenly-spaced teeth often produce holes with N+1 or N-1 “lobes”. These profiles correspond, respectively, to forward or backward whirl of the tool at N cycles/rev. Other whirl harmonics (2N cycles/rev, e.g.) are occasionally seen as well. The quasi-static model is motivated by the observations that relatively large oscillations occur at frequencies well below the natural frequency of the tool, and that in this regime the wavelength of the hole profile is largely independent of both cutting speed and tool natural frequency. In the quasi-static approach, inertial and viscous damping forces are neglected, but the system remains dynamic because regenerative (time-delayed) cutting and rubbing forces are included. The model leads to an eigenvalue problem with forward and backward whirl solutions that closely resemble the tool behavior seen in practice.
Some Nonlinear Effects of Magnetic Bearings
Authors: Steinschaden Norbert , Springer Helmut 
Published: February 2021

Abstract
In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used.
The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.
Nonlinear Modeling and Control of Hysteresis in Active Material Systems
Authors: Webb Glenn V. , Lagoudas Dimitris C. , Kurdila Andrew J. 
Published: February 2021

Abstract
Active material actuators present a significant challenge to researchers interested in applying them to aerospace structures. Materials such as shape memory alloys, piezo-ceramcs and electrorheological fluids exhibit hysteresis to varying degrees. Not only do they exhibit hysteresis, but in some cases the hysteresis is non-stationary. We present a methodology that allows for design of controllers for the structural system from linear system theory. This is accomplished by compensating, or linearizing, the hysteresis nonlinearity using an adaptive model of hysteresis. Experimental results for adaptive control of shape memory alloy actuators with non-stationary hysteresis are provided.
Reduced Order Nonlinear Navier Stokes Models for Synthetic Jets
Authors: Rediniotis Othon K. , Kurdila Andrew J. 
Published: February 2021

Abstract
While the potential for the use of synthetic jet actuators to achieve flow control has been noted fro some tme, most studies of these devices have been empirical or experimental in nature. Several technical issues must be resolved to achieve rigorous, model-based, closed loop control methodologies for this class of actuator. The goal of this paper is consequently two-fold. First, we seek to derive and evaluate model order reduction methods based on proper orthogonal decomposition that are suitable for synthetic jet actuators. Secondly, we seek to derive rigorously stable feedback control laws for the derived reduced order models. The readability of the control strategies is discussed, and a numerical study of the effectiveness of the reduced order models are summarized.
Chatter in Turning Process Incorporating the Effect of Ploughing Force
Authors: Wang Z. C. , Cleghorn W. L. , Yu S. D. 
Published: February 2021

Abstract
In this paper, the stability analysis of turning process is performed based on a new cutting force model which includes the effect of ploughing force. This approach utilized the Laplace transform to identify the characteristic roots of the examined machining system. The stability of the machining system can then be determined by examining the locations of the characteristic roots. The stability curve for a specific turning process can then be plotted. The effect of different cutting force models on the stability is also investigated. The results clearly demonstrate some chatter phenomena observed by other researchers.
Model Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes
Authors: Pesheck E. , Pierre C. , Shaw S. W. 
Published: February 2021

Abstract
Equations of motion are developed for a rotating beam which is constrained to deform in the transverse (flapping) and axial directions. This process results in two coupled nonlinear partial differential equations which govern the attendant dynamics. These equations may be discretized through utilization of the classical normal modes of the nonrotating system in both the transverse and extensional directions. The resultant system may then be diagonalized to linear order and truncated to N nonlinear ordinary differential equations. Several methods are used to determine the model size necessary to ensure accuracy. Once the model size (N degrees of freedom) has been determined, nonlinear normal mode (NNM) theory is applied to reduce the system to a single equation, or a small set of equations, which accurately represent the dynamics of a mode, or set of modes, of interest. Results are presented which detail the convergence of the discretized model and compare its dynamics with those of the NNM-reduced model, as well as other reduced models. The results indicate a considerable improvement over other common reduction techniques, enabling the capture of many salient response features with the simulation of very few degrees of freedom.
Forced Oscillations of Rotating Shaft With Nonlinear Spring Characteristics and Internal Damping: Subharmonic Oscillation of Order 1/3 and Entrainment
Authors: Ishida Yukio , Murakami Shin 
Published: February 2021

Abstract
An elastic rotating shaft supported by ball bearings may have nonlinear spring characteristics due to clearance and internal damping due to friction between the shaft and the bearings. In such a system, self-excited oscillations appear in the post critical region and nonlinear forced oscillations appear at various resonance points. In this paper, a phenomenon in the neighborhood of the critical speed of the subharmonic oscillation of order 1/3 of a forward whirling mode is discussed. It is clarified that, similar to the case of the subharmonic oscillation of order 1/2 of a forward whirling mode, an entrainment phenomenon appears due to the interplay between self-excited oscillations and forced oscillations.
Surface Waves on Solid Objects and Shells: Application of Alternate Theoretical Approaches
Authors: Gérard A. , Bao X. L. , Raju P. K. , Überall H. 
Published: February 2021

Abstract
Surface waves on elastic objects can be generated by a variety of forced excitation mechanisms. We choose to study them theoretically as excited by an incident acoustic wave, and to obtain their resonances which are caused by their phase match over closed path. The resonance frequencies then serve to obtain the surface wave phase velocity dispersion curves, and the “Regge trajectory” of their resonances.
Exact Stationary Response Solutions of Nine Classes of Nonlinear Stochastic Systems Under Stochastic Parametric and External Excitations
Authors: Wang Rubin , Yasuda Kimihiko 
Published: February 2021

Abstract
In this paper, a systematic procedure is developed to obtain the stationary probability density function for the response of a general nonlinear system under parametric and external Gaussian white noise excitations. In reference [15], nonlinear function of system was expressed to the polynomial formula. The nonlinear system described here has the following form: x¨+g(x,x˙)=k1ξ1(t)+k2xξ2(t), where g(x,x˙)=∑i=0∞gi(x)x˙i and ξ1,ξ2 are Gaussian white noises. Thus, this paper is a generalization for the results studied in reference [15]. The reduced Fokker-Planck (FP) equation is employed to get the governing equation of the probability density function. Based on this procedure, the exact stationary probability densities of many nonlinear stochastic systems are obtained, and it is shown that some of the exact stationary solutions described in the literature are only particular cases of the presented generalized results.
Dynamics of Spinning Disc Parametrically Excited by Noise
Authors: Ramakrishnan Narayanan , Namachchivaya N. Sri 
Published: February 2021

Abstract
The nonlinear dynamics of a circular spinning disc parametrically excited by noise of small intensity is investigated. The governing PDEs are reduced using a Galerkin reduction procedure to a two-DOF system of ODEs which, govern the transverse motion of the disc. The dynamics is simplified by exploiting the S1 invariance of the equations of motion of the reduced system and further, reduced by performing stochastic averaging. The resulting one-dimensional Markov diffusive process is studied in detail. The stationary probability density distribution is obtained by solving the Fokker-Planck equation along with the appropriate boundary conditions. The boundary behaviour is studied using an asymptotic approach. Some aspects of dynamical and phenomenological bifurcations of the stationary solution are also investigated. The scheme of things presented here can be applied in principle to a four-dimensional Hamiltonian system possessing one integral of motion in addition to the hamiltonian and having one fixed point.
The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair
Authors: Kuang J. H. , Lin A. D. 
Published: February 2021

Abstract
In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The surface wear on the tooth is derived by Archard’s wear equation. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.
A Study on the Instability of Disk-Shaped Gear
Authors: Ren Guangming , Yan Litang 
Published: February 2021

Abstract
In this paper the theory and experiment concerning vibration instability of disk-shaped gear are presented. At first the self-exciting force of gear is searched and the works done by the exciting force and damping force are analyzed. Then the vibration instability of the disk-shaped plain gear is studied with multiple scale’s method of the nonlinear perturbation method. The vibration characteristics of a coupled pair of bevel gears are investigated experimentally. Both theoretical and experimental investigations show that there are actually self-exciting vibrations on the gear. Under certain conditions the forward traveling wave vibration of the driving gear and the backward traveling wave vibration of the driven gear can be instable.
Transmission Modelling for Gear Rattle Analysis
Authors: Wang Yu Michael , Radhakrishnan Manoj , Zhao Weijie 
Published: February 2021

Abstract
This paper describes a model for torsional vibration of automotive manual transmissions. The model is developed for the purpose of analysis and prediction of gear rattles. Elements of the model include engine, clutch, gear mesh, gear backlash, and shaft flexibility. A numerical method — finite element method in the time domain (FET) — is employed for the dynamic analysis. Results are presented which show the effectiveness of the modelling and analysis scheme.
Eigensensitivity of Planetary Gear Free Vibration Properties
Authors: Lin Jian , Parker Robert G. 
Published: February 2021

Abstract
The natural frequency and vibration mode sensitivities to system parameters are rigorously investigated for both tuned and mistimed planetary gears. Parameters under consideration include support and mesh stiffnesses, component masses, and moments of inertia. Using the well-defined vibration mode properties of tuned (cyclically symmetric) planetary gears [1], the eigensensitivities are calculated and expressed in simple, exact formulae. These formulae connect natural frequency sensitivity with the modal strain or kinetic energy and provide efficient means to determine the sensitivity to all stiffness and inertia parameters by inspection of the modal energy distribution.
While the terminology of planetary gears is used throughout, the results apply for general epicyclic gears.
Modeling Axial Vibrations in Herringbone Gears
Authors: Jáuregui Juan Carlos , González Oscar M. 
Published: February 2021

Abstract
This paper addresses the axial vibrations of herringbone gears. Theoretically, herringbone gears balance their axial loads due to their symmetry; however, in practice, they present high vibrations. The reasons are manufacturing deviations such as lead angle errors, pitch error differences between each side of the gear, misalignment between pinion and gear axes, etc. These errors can be represented as an error function of sinusoidal form acting as forced vibrations over the teeth.
Although axial and lateral motions of a gear pair are generally coupled, the symmetric geometry of herringbone gears makes possible to analyze the axial and lateral stiffness as uncoupled functions. It is viable then to represent the axial motion as a single degree of freedom model.
The effect of each parameter of the error function is analyze individually in order to determine which has the greater effect in the system. Results are compared to field data showing good agreement.
Dynamic Response and Stability of a Spur Gear Pair
Authors: Nataraj C. , Arakere N. K. 
Published: February 2021

Abstract
This paper deals with the linearized dynamics of a high-speed spur-gear pair supported on linear orthotropic bearings. The mating teeth are modeled accurately and the effect of the dynamic stiffness variation on the dynamic response is taken into account and, in fact, forms the essence of this work. The resulting six degree of freedom system is nondimensionalized in order to reduce the model to a minimum number of independent parameters and to make the results valid for a wide range of practical situations. The equations are solved using a recently developed approximation technique using Chebyshev polynomials. It is shown that not accounting for the periodic variation of the stiffness can lead to drastic differences in dynamic response and stability.
Active Segmented Trim Panels for Aircraft Interior Noise Control: Theory and Experiments
Authors: Hirsch S. M. , Sun J. Q. 
Published: February 2021

Abstract
An active segmented trim panel for use as a secondary source for noise control in aircraft is designed, analyzed and tested. It consists of a rectangular segment of aircraft trim panel which is suspended by a flexible support. This support converts the stiff composite trim panel into flexibly-mounted pistons which can be driven by light-weight and low-profile force actuators. The active segmented trim panel offers an acoustic source of lower profile and lower mass, and requires only a simple modification of materials already installed on aircraft. This paper presents a summary of recent results of modeling and testing of an active trim panel configuration. Real-time noise control experiments are conducted using the active trim panels as secondary sources indicating that the present active segmented trim is a promising technology.