bluuebunny/crossref_metadata_2025 huggingface dataset:
Acoustic Control Modeling of Conical Bores With Actuating Boundary Conditions
Authors: Farinholt Kevin M. , Leo Donald J.
Published: November 2020

An investigation of the natural frequencies and mode shapes associated with sealed conical bores having actuating boundary conditions is presented. Beginning with the one dimensional wave equation for spherically expanding waves, modal characteristics are developed as functions of cone geometry and actuator parameters. This paper presents both analytical and experimental comparisons for the purpose of validating model and development techniques. An investigation of the orthogonality and adjointness of the solution is presented. A discussion of incorporating driving forces in the system model for the purpose of coupling control actuators with internal acoustics is also included. Including these driving forces, a state space model of the system is developed for the purpose of applying modern feedback control. This paper concludes with a study on applying Linear Quadratic Regulator techniques to this system, relating tradeoffs between spatially averaged pressure and control voltages. The results of our simulations indicate that pressure reductions of 30% are attainable with average control voltages of 14.4 volts, given an example geometry.
Adaptive Feedforward Active Noise Control in an Acoustic Duct
Authors: Ohadi A. R. , Esmailzadeh E. , Alasty A.
Published: November 2020

The single-reference/multi-output active noise control (ANC) of an accurate physical model of an acoustic duct system has been investigated. Computer model of a multi-channel ANC system with tonal and sweep sine input signals, and an adaptive feedforward algorithm that minimizes the generic cost function are developed. Results obtained for various single-input/single-output (SISO) configurations of ANC systems were compared. The dynamic response of a single-reference/multi-output ANC system, using Minimax and MEFXLMS algorithms, is studied and the effect of acoustical feedback neutralization in a multichannel ANC system is studied. Simulation results demonstrate that the multi-channel adaptive feedforward ANC system, using the Minimax algorithm, has a superior performance in comparison to the same system with MEFXLMS.
Optimization of a Resonant Bimorph Actuator Drive
Authors: Mockensturm Eric M. , Koopmann Gary H. , Frank Jeremy , Lesieutre George A.
Published: November 2020

A rotary actuator driven by piezoelectric bimorphs has been developed for various smart structure applications. A rotary (roller) clutch rectifies bimorph oscillation into rotational motion to convert electrical to mechanical power. While prototype actuators perform well, they were designed with just engineering intuition. Here, a mathematical model of the actuator is developed. Using empirical data collected from a prototype actuator and a roller clutch, the mathematical model was tuned so that it predicted accurately the performance of the prototype. The model was then used to optimize the design of the actuator. The model predicts that performance can be significantly increased by making slight modifications to the prototype. Work to verify these predictions of the mathematical model is underway.
High Dynamic Range Colocated Sensoriactuator for Control of High-Speed Optical Systems
Authors: Knowles Gareth , Bower Bruce
Published: November 2020

Vibratory load transmission reduction for precision space A major challenge to the aerospace industry is to develop precision beam steering optics with clear aperture as large as 8 inches that operate at bandwidths of 1KHz, have throws of 3–10 mrad, and position accuracy of 100 nrad. The proposed technology promises to meet these requirements by introducing a new piezoelectronically driven colocated sensoriactuation system. The novel sensor promises to enable ultra-linear, 1nm resolution and 4 KHz small signal bandwidth in a small package. The sensor is integrated into the actuation mechanism in order to provide advantageous colocated functioning. The actuation mechanism is of unique high stiffness and shear strength capable of driving at high-bandwidth with no low coupling modes present. The proposed technology offers a lower cost, lighter weight, lower volume solution that can markedly increase performance capability. The approach is applied to the problem of controlling fast optics for precision optical compensation or hyperspectral imaging. The paper presents aspects of design experiment and system measurement.
Model-Based Estimation of Impact Forces Affecting Elastic Structures: Simulation and Experiment
Authors: Abicht Claus , Bormann Jens , Müller Peter C. , Söffker Dirk , Ulbrich Heinz
Published: November 2020

The paper introduces into the concept of model-based impact estimation of elastic structures. Based on the model of the affected linear structure a robust linear observer technique is applied to estimate the unknown impacts. The complete procedure of impact estimation is shown by simulations. Results of the observer-based estimation of unknown impacts are presented. As a new result, it is observed that the proposed observer technique can generally (but with limitations) be applied to elastic structures.
A Simple Dynamic Modeling of Head Slap in Hard Disk Drive
Authors: Lee Seong-Hun , Lee Jeong-Hak , Kim Kwang-Joon
Published: November 2020

In order to understand mechanism of the impact between head and disk of a HDD subject to a shock and to improve the shock resistance effectively, it is essential to develop a dynamic model which can represent well the head slap. Although motion of the head and disk subject to a shock requires modeling by a continuous system to be rigorous, in this study, a simplified lumped parameter model is developed to understand basic dynamics of the head slap and to determine crucial parameters for the improvement of the structural design. In addition, drop test results of the HDD are presented to back to up the derived model.
A Mobile Mechanism With Slant Leg on a Vibratory Floor
Authors: Yamaguchi Hideya , Yashima Masahito
Published: November 2020

This paper investigates the characteristics of a mobile mechanism that consists of a main mass and a slant leg with a rotational spring at the joint. The device travels on an oscillating floor due to the difference in the friction force between forward and backward directions during the stick-slip motion. Numerical simulation and experimentation show that the direction and velocity of movement are controlled by the exciting frequency. Furthermore, the effects of the angle of the slant leg and the sliding coefficient of friction on those characteristics are investigated.
Distributed Friction and Microslip in Mechanical Joints With Varying Degrees-of-Freedom
Authors: Quinn D. Dane
Published: November 2020

This work considers the effect of distributed friction on the dynamics arising from a simple model for a jointed structure. A hierarchy of models is developed, parameterized by the degree-of-freedom n, which physically corresponds to the number of possible slip zones. When the resulting system is subjected to harmonic forcing, numerical simulations indicate that the instantaneous power dissipated by the frictional forces is sensitive to n. However, the frictional work per unit forcing cycle is, surprisingly, relatively insensitive to the degree-of-freedom, provided n is greater that some minimum number which depends on the amplitude of the external forcing as well as the maximum frictional force. Finally, representative simulations are shown as both the amplitude and frequency of the external forcing are varied. This model provides a starting point for the development of reduced-order models of structural interfaces.
Vibration Control of a Beam Using a Sliding Support
Authors: Nguyen Phillip H. , Ginsberg Jerry H.
Published: November 2020

This paper discusses a concept for controlling flexural vibration of a beam in which a pin support oscillates harmonically parallel to the beam’s axis. This induces a periodic fluctuation of the effective inertia and stiffness, which represents a source of parametric excitation. A model of the response is developed by using a Ritz series modified to allow the basis functions to be time, as well as position, dependent. Solutions are obtained by numerically integrating the equations of motion. Vibration control requires identification of the support frequency, amplitude, and phase angle that reduce the overall motion relative to what would be obtained if the support were stationary. It is shown that resonances can be controlled in this manner. However, the concept is shown to be ineffective for broadband vibration reduction because the parametric excitation merely shifts the resonant frequencies, while it also induces new resonances.
Input-Shaped Control of Gantry Cranes: Simulation and Curriculum Development
Authors: Forest Craig , Frakes David , Singhose William
Published: November 2020

Knowledge of vibrations and controls has increased significantly by utilizing emerging computer capabilities. Engineering education should embrace this technology through computer simulations that predict and display the dynamic response of interesting systems. For example, manipulating payloads with an overhead gantry crane can be challenging due to the oscillations induced by the crane motion. The problem gets increasingly difficult when the work environment is cluttered with obstacles. This paper describes a simple input shaping solution to the vibration problem and shows how this problem and concept were integrated into the curriculum of an undergraduate system dynamics and controls course at the Georgia Institute of Technology. Furthermore, an educational tool is used to gather data on how crane operators attempt to navigate around obstacles. The results show that input shaping reduces the likelihood of collisions between the payload and obstacles, while at the same time allowing operators to be more aggressive in selecting navigation paths.
Obstacle Avoidance for 2D Hyper-Redundant Manipulators Using Harmonic Potential Functions and the Mode Shape Technique
Authors: Fahimi F. , Ashrafiuon H. , Nataraj C.
Published: November 2020

Obstacle avoidance for discrete-link two-dimensional (2D) hyper-redundant manipulators in known environments is considered. The manipulator is divided into two sections, a proximal section that has not entered the space among obstacles and a distal section among the obstacles. Harmonic potential functions were used, in order to avoid local minima in cluttered environments. A modified panel method is used to generate the potential of any arbitrary shaped obstacle in two-dimensional space. An alternative backbone curve concept and an efficient fitting method are introduced to control the trajectory of proximal links. The fitting method is recursive and avoids the complications involved with solving large systems of nonlinear algebraic equations. Combination of the safe path derived from the harmonic potential field and the backbone curve concept leads to an elegant kinematic control strategy that guarantees obstacle avoidance for planar hyper-redundant robotic manipulators.
The Robust Adaptive Control of Free-Floating Space Manipulator Systems
Authors: Li Chen , Yanzhu Liu
Published: November 2020

In this paper, the kinematics and dynamics of free-floating space manipulator systems are analyzed, and it is shown that the Jacobian matrix and the dynamic equations of the system are nonlinearly dependent on inertial parameters. In order to overcome the above problems, the system is modeled as under-actuated robot system, and the idea of augmentation approach is adopted. It is demonstrate that the augmented generalized Jacobian matrix and the dynamic equations of the system can be linearly dependent on a group of inertial parameters. Based on the results, the robust adaptive control scheme for free-floating space manipulator with uncertain inertial parameters to track the desired trajectory in workspace is proposed, and a two-link planar space manipulator system is simulated to verify the proposed control scheme. The proposed control scheme is computationally simple, because we choose to make the controller robust to the uncertain inertial parameters rather than explicitly estimating them online. In particular, it require neither measuring the position, velocity and acceleration of the floating base with respect to the orbit nor controlling the position and attitude angle of the floating base.
Finite Element Analysis of Thermal Buckling and Postbuckling of Composite Plates With Embedded SMA
Authors: Weifang Zhong , Jing Zou , Yongdong Wu
Published: November 2020

Based on Von Karman strain-displacement relations and variational principles, the FEM formulations, which are used to analyze the thermal buckling, and thermal postbuckling of composite plates with embedded SMA are presented in this study. The recovery stress and young modulus are calculated by one-dimensional constitutive model. Some numerical examples are also presented. The results indicate that activated SMA can suppress the thermal buckling of the plates and reduce thermal postbuckling deflections.
An Experimental Approach to the Design of PVDF Modal Sensors
Authors: Cuhat Daniel , Davies Patricia
Published: November 2020

The principle of modal sensing is based on the use of a shaped PVDF piezoelectric film measuring strains on the surface of a bending beam and acting as a modal filter. So far, the use of this type of sensors has remained confined to studies involving uniform structures with classical boundary conditions. The goal of this paper is to present an experimental methodology for the design of a shaped modal sensor applicable to an non-uniform Euler-Bernoulli beam with arbitrary boundary conditions. This approach is illustrated with test data collected on a cantilever beam structure with a laser Doppler velocimeter.
Scattering and Transmission of Mixed-Mode Waves in Delaminated Thick Composite Beams
Authors: Mahapatra D. Roy , Gopalakrishnan S. , Sankar T. S.
Published: November 2020

A spectral finite element model is developed to study scattering and transmission of axial-flexural-torsional coupled waves in multi-sitedelaminated thick composite beams. The analysis may find its suitability and superiority to capture the high frequency dynamics of laminated composite structure in vibrating environment and for health monitoring in combination with non-destructive test data. Spectral finite element considering first order shear deformation is used to model the delaminated segments along the span of the beam, as well as the delaminated ply-groups in thickness direction. This spectral element is derived from exact solution to the 3D governing wave equations in Fourier domain. As aresult, the thin sublaminates and beam segments do not lock. Spatial discretization is carried out in a similar way as in conventional finite element method. The major differences from conventional finite element method are (1) the transformation of all the fields from temporal to frequency domain is carried out using Fast Fourier Transform (FFT) algorithm, (2) the global system is solved at each frequency step (3) fine meshing at the delamination tip to capture the crack-tip singularity (as in conventional finite element discretization) is not required (4) the overall system size becomes many order smaller than that in conventional finite element methods. The study essentially includes unsymmetry induced due to ply orientations and due to multiple delamination across beam thickness. A case study is presented to show the effect of wave transmission and scattering by a single through delamination in unidirectional composite beam.
An Experimental Study of the Nonlinear Dynamics of a Portal Frame Foundation for a Non Ideal Motor
Authors: Brasil Reyolando M. , Garzeri Flávio J. , Balthazar José M.
Published: November 2020

An experimental approach to the study of forced nonlinear vibrations of portal frames excited by nonideal motors is presented. The interaction of the structure with the excitation source may lead to the occurrence of interesting phenomena during the forward and reverse passage through the several resonance states of the systems. As an application, a rotating unbalanced motor with limited power is considered mounted on the horizontal beam of a simple portal frame. As a starting point the problem is reduced to a three-degree-of-freedom model, and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. Next, experimental work on a prototype is described. The results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, modal saturation and energy transference due to internal coupling and external resonance are observed at certain levels of excitation.
Experimental Non-Linear Model Updating Applied in Cylindrical Journal Bearings
Authors: Cavalca Katia Lucchesi , Idehara Sérgio Junichi , Dedini Franco Giuseppe , Pederiva Robson
Published: November 2020

The present paper proposes the use of non linear model updating applying unrestricted optimization method, in order to obtain a methodology, which allows the calibration of mathematical models in rotating systems. An experimental set up for this purpose consists of a symmetric rotor, on a rigid foundation supported by two hidrodynamic cylindrical bearings and with a central disk of considerable mass, working as na unbalancing excitation force. Once the numeric and experimental values are obtained, error vectors are defined, which are the minimization parameters, through the variation of the numeric model parameters. The method presented satisfactory results, as it was able to calibrate the mathematical model, and then to obtain reliable responses for the physical system studied. The research also presents a contribution for the rotating machine desing area as it presents a relatively simple methodology on the updating and revalidation of computacional models for machines and structures.
Experimental Investigation of Dry Friction Damping and Cubic Stiffness Non-Linearity
Authors: Stanbridge Anthony B. , Ewins David J. , Sanliturk Kenan Y. , Ferreira Janito V.
Published: November 2020

Experimental vibration techniques used in the characterisation of the two most common types of non-linear structure are described here. The first is used to determine friction contact hysteresis loops to provide data which can be incorporated into large, otherwise linear, structural models, to predict non-linear vibration responses. The second is a method of measuring frequency response functions (FRFs) of structures with non-linear, amplitude-dependent stiffness and damping, including the ‘unstable’, overhanging part of the FRF curve, by using a controlled-amplitude, stepped-frequency sinusoidal input. These apparently rather different test techniques are in fact connected by the fact that, in order to be effective, they both require an additional mass to be installed, on the input side of the force transducer.
Nonlinear Resonance and Parametric Instability of a Power Transmission Belt: Numerical Analysis With Experiments
Authors: Vestroni Fabrizio , Pellicano Francesco , Catellani Giulia , Fregolent Annalisa
Published: November 2020

In this paper a numerical approach is developed to forecast the dynamic behavior of a power transmission belt running on eccentric pulleys. Basic partial differential equations are developed, considering the elastic effect of the lower branch of the belt. Nonlinear resonances and dynamic instabilities are analyzed in detail using a high dimensional discrete model, obtained through the Galerkin procedure. The numerical analysis is performed by means of direct simulations and a continuation software. Numerical results are compared with available experimental data. It is shown that the numerical method is able to predict correctly the amplitudes of oscillation in several operating conditions: direct and parametric resonances. Frequency response curves are obtained when the belt is harmonically excited close to the first and second linear natural frequency. The damping ratio and the linear frequencies are identified at zero axial speed.
Eigenstructure Calculation for Mixed Vibratory Systems Composed of a Continuous Beam and Concentrated Actuators
Authors: Panza Michael J.
Published: November 2020

A calculation of the eigenstructure for mixed vibratory systems composed of a continuous beam and concentrated actuators is presented. The combined distributed and lumped element systems include actuators for active vibration control. The focus of this paper is on open loop models where with zero voltage input to the actuators. The continuous beam is isolated and discretized via modal analysis and combined with the actuator dynamics to form an asymmetric system. The resulting system is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system parameters. The solution is expressed as a series using the isolated beam mode eigenfunctions as a basis. The coefficients in the series are obtained from the complex eigensolution of the asymmetric system. Two examples are used to show a comparison of the complex mixed system and real isolated beam natural frequencies and mode shapes. The effect of beam and actuator parameter values are investigated via a key dimensionless parameter.
Bifurcations and Chaos in the Response of a Rigid Rotor Supported by Eccentric Squeeze-Film Dampers
Authors: Inayat-Hussain Jawaid Iqbal , Kanki Hiroshi , Mureithi Njuki W.
Published: November 2020

In the unbalance response analysis of rotors supported by squeeze-film dampers with centering springs, the fluid-film forces are usually computed based on the assumption that the rotor exhibits a circular centered whirl orbit motion. The validity of this assumption is, however, limited to the ideal case of squeeze-film dampers with centering springs that are perfectly adjusted to offset the gravitational force. In most practical applications, eccentric operation of these dampers is almost unavoidable since precise setting of the centering springs in a real environment is usually not possible. In this paper the bifurcations in the response of a rigid rotor in eccentric squeeze-film dampers are investigated. The values of the bearing parameter (B), gravity parameter (W) and spring parameter (S) are respectively fixed at 0.015, 0.05 and 0.3, while the unbalance parameter (U) is varied from 0.05 to 0.8. The results indicated that the rotor might lose its stability due to period-doubling and saddle node bifurcations. Chaotic response of the rotor was also observed for 0.365 < U < 0.367 and 0.381 < U < 0.392. The transitions to chaos in these two regimes were respectively via the period-doubling and type 3 intermittency routes. The levels of rotor unbalance where non-synchronous and chaotic motions were observed in this study are only an order of magnitude higher than the specified levels for rigid rotors. Such levels of unbalance may easily occur in practice due to in-service erosion or in the event of a partial or an entire blade loss.
Dynamics and Stability of a Nonlinear Brake Model
Authors: Wauer Jörg , Heilig Jürgen
Published: November 2020

The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.
Mechanics of Regenerative Vibration in Drilling: Analytical and Experimental Study of the Formation of Lobed Holes
Authors: Bayly Philip V. , Lamar Michael T. , Calvert Sean G.
Published: November 2020

Large-amplitude vibrations in drilling often occur near multiples of the rotation frequency, even when these frequencies are much lower than the system’s first natural frequency. These vibrations are responsible for out-of-round, “lobed” holes. A simplified model of the mechanics of this phenomenon is presented in this paper. The model includes cutting and “rubbing” forces on the drill, but inertia and damping of the tool are neglected at low speeds. This quasi-static model remains dynamic because of the regenerative nature of cutting; the force on each cutting element depends on both the tool’s current position and its position at the time of the previous tooth passage. Characteristic solutions, including unstable retrograde “whirling” modes, are found in terms of eigenvalues and eigenvectors of a discrete state-transition matrix. These unstable modes correspond closely to behavior observed in drilling tests.
Coupled Slow and Fast Dynamics of Flow Excited Elastic Cable Systems
Authors: Kim WanJun , Perkins N. C.
Published: November 2020

Analytical studies of vortex-induced vibration (VTV) of cables during lock-in have considered small amplitude and relatively fast dynamic responses about an equilibrium configuration. However, this equilibrium may change as a result of the significantly increased mean drag created during lock-in. In response to increased drag, the cable may slowly drift downstream causing appreciable changes in cable geometry and tension. The resonance conditions for lock-in may be preserved during this slow drift or they may be disrupted. A nonlinear cable/fluid model is discussed mat captures both fast (small amplitude) motions due to VIV and slow (large amplitude) motions due to drift. These two different time scales of motion are clearly observed in numerical simulations. The significant interplay of the slow drifting motion and the fast VTV is highlighted.
Nonlinear Modeling and Identification of the Dynamic Behavior of Polyurethane Foam
Authors: Singh R. , Davies P. , Bajaj A. K.
Published: November 2020

The analysis of the steady-state response of a polyurethane foam and mass system to harmonic excitation is given. The foam’s uni-directional dynamic behavior motion is modeled by using nonlinear stiffness, linear viscoelastic and velocity proportional damping components. The relaxation kernel for the viscoelastic model is assumed to be a sum of exponentials. Harmonic balance is used to develop one- and two-term solution approximations that are utilized for system identification. The identification process is based on least-squares minimization of a sub-optimal cost function that uses response data at various excitation frequencies and amplitudes. The effect of number, spacing and amplitudes of the harmonic input on the results of the model parameter estimation is discussed. Model-order choice and the feasibility of describing the system behavior at several input amplitudes with a single set of parameters are also addressed.
The Asymptotic Stability of Weakly Perturbed Two Dimensional Hamiltonian Systems
Authors: Arnold Ludwig , Imkeller Peter , Namachchivaya N. Sri
Published: November 2020

The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers Oscillator driven by either a multiplicative or an additive white noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ε and dissipation ε the exponent grows proportional to ε1/3.
Stabilisation of Period-1 Orbits of the Hénon Map: Parametric Variation and Additive Noise
Authors: Davies Huw G.
Published: November 2020

Slow sinusoidal modulation of a control parameter can maintain a low period orbit of a nonlinear dynamic system into parameter regions where the low period orbit is unstable, and a higher period orbit would normally occur. We examine this case for a period-doubling bifurcation of the Hénon map. Whether or not effective stabilisation of the period-1 orbit takes place depends on both the frequency of the variation and on the noise. Increasing the frequency tends to stabilise the orbit; increasing the noise level is destabilising. We use matched asymptotic expansions to describe the response, and find explicit expressions for the response which can estimate whether and where an apparent period doubling occurs.
P-Bifurcation Aspects of a Modified Duffing Oscillator Near Equilibrium
Authors: Fofana M. S. , Szwarc Dariusz
Published: November 2020

A unified framework for the study of stability of solutions to delay differential equations perturbed deterministically and stochastically has been presented. We review the concepts of Hopf bifurcation, centre manifold, integral averaging method and pth–moment Lyapunov exponent, and then demonstrate their role in the stability study of a modified Duffing oscillator with time delay. Sufficient conditions ensuring Đ- and Þ–bifurcations and the changes in character of the probability density function are established for fixed and positive time delay.
Dynamics of Semi-Actively Controlled Vehicles Involving Wheel Hop
Authors: Verros G. , Natsiavas S.
Published: November 2020

The present study investigates dynamic response of vehicle models, subjected to road excitation. In these models, a semi-active control strategy is applied on the suspension dampers, which is based on a switch of their damping coefficient between different values, so that the resulting system approximates the performance of a vehicle involving sky-hook damping. An alternative control strategy is also applied, which is passive and is based on selecting a different damping ratio when the wheel velocity relative to the car body is positive or negative. Both of these control strategies lead to oscillator models with parameter discontinuities. Similar terms are also introduced into the equations of motion by considering wheel hop phenomena, where a vehicle wheel leaves the ground temporarily. First, simple quarter-car models are examined but the analysis is also applied to more complicated models. For these models, their dimensions are reduced substantially by applying a component mode synthesis approach. Subsequently, this allows the efficient application of appropriate methodologies for predicting response spectra of the nonlinear models to periodic road excitation. Finally, results obtained by direct integration of the equations of motion are also presented for transient road excitation. In all cases, the results are compared to those obtained for vehicles with suspensions including passive shock absorbers. Moreover, special consideration is given to cases where wheel hop is possible to occur.
A Simple Adaptive Feedback Controller for Tower Cranes
Authors: Omar Hanafy M. , Nayfeh Ali H.
Published: November 2020

The objective of crane control is to build an algorithm to move a load from point to point in the shortest time without inducing large swings. We assume that this objective cannot be accomplished in less than a single oscillation cycle of the load. Therefore, the controller is built to move the load such that it completes only one oscillation cycle at the end of the motion. Consequently, the settling time of the system should be equal to the period of oscillation of the load. This criterion enables the calculation of the controller feedback gains for varying load weight and cable length. The controller is built first for overhead cranes and then modified for tower cranes. Two controllers are used, one for the rotational motion of the tower and the other for the translational motion of the trolley. Numerical simulations show that the controller is effective in reducing the load oscillations and transferring the load in a reasonable time compared with that of optimal control.
The Attitude Stability for Longitudinal Motion of Underwater Vehicle
Authors: Wang Deshi , Xiao Renbin , Yang Ming
Published: November 2020

Although the equations describing the longitudinal motions of underwater vehicles are typically nonlinear, the linearized equations are still employed to design the depth controller by the traditional analysis methods in engineering for the sake of simplicity. The reduction of the nonlinearity loses the dynamics near the singular points, which may be responsible for the sudden climb or dive. The nonlinear systems limited in the longitudinal plane of the underwater vehicles are analyzed on center manifold through the bifurcation theory. It focuses on the case that single zero root in Jacobi matrix occurs at equilibrium points corresponding to nominal trajectory with varied angles of the elevator or the direction change of the flows. The center manifolds are calculated and one-dimensional bifurcation equations on the center manifolds are obtained and analyzed. Based on the transcritical bifurcation diagram, we have found the mechanism of the attitude stability loss as well as the abnormal trajectory of autonomous underwater vehicles. It gives good explainations to the practical climbing jump and diving fall and delivers the theoretical tools to design the controller and to design dynamics. Numerical simulation verifies the results.
Stochastic Nonlinear Dynamics of a Beam System With Impact
Authors: van de Wouw N. , de Kraker A. , Nijmeijer H.
Published: November 2020

In this paper, a strongly nonlinear beam-impact system under both broad-banded and small-banded, Gaussian noise excitations is investigated. The response of this system is investigated both numerically, through a multi-degree-of-freedom (MDOF) model, and experimentally focusing on frequency-domain characteristics such as stochastic equivalents of harmonic and subharmonic solutions. Improved understanding of these stochastic response characteristics is obtained by comparing them to nonlinear periodic response features of the system. It will be shown that in modeling such a continuous linear system with a local nonlinearity, the linear part can be effectively reduced to a description based on several modes. Combining this reduced linear part with the local nonlinearity in a reduced nonlinear model is shown to result in an analysis model, which can be used to accurately predict the stochastic response characteristics of the original, continuous, nonlinear system. It is shown that the inclusion of more modes in the model will result in a response, which differs significantly from that of a SDOF (single-degree-of-freedom) model, giving a better correspondence with experimental results, also in the frequency range of the first mode.
Stick-Slip Dynamics of a Two-Degree-of-Freedom System
Authors: Awrejcewicz Jan , Olejnik Pawel
Published: November 2020

Two-degree-of-freedom autonomous system with friction is analyzed numerically. The friction coefficient has been smoothened using are tan function. The standard, but slightly modified chaos identification tools have been applied for the analyzed discontinuous system. Some interesting examples of stick-slip regular and chaotic dynamics have been illustrated and discussed.
Application of Mechanized Mathematics in Rotor Dynamics
Authors: Wang Liguo , Huang Wenhu , Hu Chao
Published: November 2020

The mechanized mathematics-Wu elimination method is a vigorous method in solving nonlinear algebraic equations in China, but it is still not so popular in the West. In this paper the mechanized mathematics-Wu elimination method is introduced in brief and is used to solve the problem of dynamic behavior of a rotor-bearing system with nonlinear supports. The whirl equations of a short bearing-rotor system with two disks considering gyro-moment are studied. The idea of the characteristic set of Wu method is combined with Maple’s symbolic calculation. The whirl parameter of a rotor mounted on two supports are analyzed. The analytical results showing the relations of the bearing parameters and instability speed are presented.
Mechanical Fault Diagnosis for Abnormal Vibration Excited by Steam in High Pressure Turbine of Turbo-Generator Set
Authors: He Xiaoyin , He Zhengjia
Published: November 2020

Violent vibration occurred at high-pressure turbine of a turbo-generator. When steam input or load capacity was changed, the vibrations were also varied. Wavelet packets, FFT spectrum and cepstrum were adopted synthetically to obtain diagnosis information. According to signal analyses and factual evidences, it was clear that there existed violent vibration (be nonlinear) excited by steam in high-pressure turbine. We investigated the maintenance conditions, and found that the four main pipes of steam input had different lengths after their thermal expansion, which lead to skew at the body of high-pressure turbine. The intervals between rotor and stator were non-uniform. So, besides a moment of couple was generated onto the rotor, a force was also generated. This force excited the rotor of the high-pressure turbine to vibrate with its natural frequency. After repairing the four main pipes, its vibration became normal as the turbo-generator was running. It is important to combine signal processing with practical investigation. Only in this way can we obtain correct diagnosis results and achieve successful maintenance.
Prediction for the Rub-Impact Phenomena in Rotor Systems
Authors: Wu Zhiqiang , Chen Yushu
Published: November 2020

By the method (Wu, 2001) developed by authors for singularity analyzing of the bifurcation of the periodic solutions in nonlinear dynamical systems with clearance, the bifurcation patterns of non-impact-rub response and a method for predicting rub-impact are given. It is shown that there are much more types of bifurcation patterns when the clearance constraint is take into account. Given their physical meanings of the parameters in practical rotor systems, the resonant periodic solutions of rotor systems consist of 11 different types of bifurcation patterns among of which the following four types are more likely to appear, (1) patterns without impact and jump, (2) jump patterns without impact, (3) impact pattern without jump and (4) patterns with impact and jump. Based on these results, parameter conditions for rub-impact phenomena are derived. These conditions can give more direct guidance to the design of rotor systems. The method proposed here can be used to predict rub-impact phenomena in more complicated rotor systems.
Nonlinear Dynamic Analysis of Partial Rotor Rub With Experimental Observations
Authors: Choi Yeon-Sun , Bae Chul-Yong
Published: November 2020

Partial rotor rub occurs when an obstacle on the Stator of a rotating machinery disturbs the free whirling motion of a rotor, which is more common than full annular rub for the cases of rubbing in rotating machinery. The nonlinearity due to the intermittent contacts and friction during partial rotor rub makes the phenomenon complex. The several nonlinear phenomena of superharmonics, subharmonics, and jump phenomenon are demonstrated for the partial rub using an experimental apparatus in this study. The forward or backward components in its orbit patterns are calculated using the directional spectrum for the experimental results and are demonstrated by numerical simulations. A piecewise-linear model and a rebound model using the coefficient of restitution are investigated on the basis of experimental observations in order to adopt an analytical model of the contact between the rotor and stator during whirling motion. The contact stiffness, coefficient of restitution, and friction coefficient for the contact during partial rub are calculated from the comparison between the numerical simulation and the experimental results. Also, the numerical simulations for the model of partial rub are done for the various system parameters of clearance, contact stiffness, and friction coefficient in order to find the nonlinear behavior of partial rotor rub.
Computer Aided Analysis of Non-Linear Vibrating Systems
Authors: Rao J. S. , Puri Tarun
Published: November 2020

This paper presents an overview of a computer package to analyze nonlinear vibrations in single degree of freedom systems. This software is designed to aid a new designer and learner of nonlinear vibration principles. It is developed so that it is user friendly and needs very little assistance. It also gives the output in the form of plots so that the user has a quick explanation of the physical phenomenon. In addition the program also gives an animation of the mass to find the way in which it vibrates during the motion.

The software developed considers free and forced vibration of nonlinear systems governed by Duffing, Van der Pol and any general nonlinear system governed by second order differential equation. The solutions are presented graphically in time domain and frequency domain. The graphical representation includes phase plane plots. Chaotic dynamics of Duffing’s oscillator is also included in the software.
Axial Nonlinear Mechanical Vibrations of Large Power Transformer Windings During Short Circuit
Authors: Xu Jian-Xue , Chen Zhen-Mao
Published: November 2020

In this paper, the axial nonlinear vibrations of the transformer winding under steady state operation case and short circuit case are studied in single degree and multi-degree models.

In the case of having ampere-turn balance, the steady state response of the former model is obtained by using multi-scale method and periodic shooting method, analytically and numerically. At the same time, the computing method of Jacobi matrix in the periodic shooting method has been modified, so that the computing CPU time is saved. For multi-degree mechanical model of a single phase transformer windings, the time domain response and relation between the response and various parameters are obtained by Runge-Kutta method.

For ampere-turn unbalance case, an electric-mechanical coupled problem, that the electric force depends the displacement of the winding are foomed, and the nonlinear forced Mathieu equation is established for this problem; and then the nonlinear dynamical response and global dynamical behaviors are analyzed.

Finally, for a 20 MVA single phase three windings transformer, a series of short circuit experiments have been performed and the axial dynamical response force, magnetic field, strain etc. have been measured. The theoretical results well agree with the experimental results.
Research Into the Use of Fractal Geometry for Condition Monitoring of Machinery
Authors: Liu Tianxiong , Hua Hongxing , Chen Zhaoneng , Zhu Jimei
Published: November 2020

A new method of condition monitoring is proposed. Wavelet transform and fractal geometry are the means. A variety of condition monitoring techniques are currently in use for diagnosis of machinery faults. However, little research into the detection of fractal characteristics in processing signals has been done. This paper establishes wavelet transformation based on the noise signal for analysis of the correlation dimension of the typical working condition. Correlation dimension of the decomposing coefficient of wavelet transformation is calculated to identify the working condition. A field experiment shows the correlation dimension of similar working conditions has similar values while different working conditions show distinct characteristics. The correlation dimensions of the typical working condition of a pump plotted here have a different domain. The experimental results and correlation graph confirmed the proposed method’s feasibility and validity.
Visco-Elastic Systems Under Narrow-Band Excitation
Authors: Xu Wei , Rong Haiwu , Fang Tong
Published: November 2020

The study of the response of nonlinear systems to narrow-band random excitation is importance. For example, the excitation of secondary system would be a narrow-band random process if the primary system could be modeled as a single -degree-of-freedom system with light damping subject to borad-band excitation. In the theory of nonlinear random vibration, most results obtained so far are attributed to the response of nonlinear oscillators to borad-band random excitation. In comparison, results on the effect of narrow-band excitation on non-linear oscillators are quite limited. Furthermore, some results in this area are disputable.

For linear viscoelastic systems under both additive and multiplicative borad-band excitation excitations, Ariaratnam studied the stochastic stability of the system by using the method of stochastic averaging. Cai, Lin and Xu determined the condition for asymptotic sample stability of the system by using an improved stochastic averging procedure. In this paper, the response of visco-elastic systems to combined deterministic harmonic and random excitation is investigated. The method of harmonic balance and the method of stochastic averaging are used to determine the response of the system. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increase, the steady state solution may change form a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions and jumps may exist.
The Analysis of Nonlinear Random Vibration of Vehicles
Authors: Miao Jingliang , Liu Haixiang
Published: November 2020

In Engineering, Vehicles in motion which undergo some random excitation given by the surroundings, may result in violent vibrations. The calculated results indicate that:

1) the softening nonlinear spring isolator usually is effective.

2) In the vibration system, sometimes, added more damping meterial can not effectively isolate the vibration of vehicles. But choosing the reasonable forms of nonlinear structures just is a effective isolating method.
The Nonlinear Vibration of a Vehicle and Passenger System
Authors: Yu Ke , Luo Albert C. J. , He Yuancheng
Published: November 2020

The vibration of passengers in a vehicle traveling on a rough pavement surface is investigated. The nonlinear equations of motion for a vehicle and passenger system with impacts are derived, and the corresponding equilibrium and stability are investigated. The dynamic responses for the vehicle and passenger system with and without impacts are simulated numerically. This investigation shows that the strong torsional spring is required in order to reduce the vibration amplitudes of passengers and to avoid impacts between the vehicle and passenger.
The Effect of Nonlinear Stiffness on the Maximum Response of the Shock-Isolating System Under Shock Action
Authors: Weng Xue-Tao , Zhu Shi-Jian , Qian Wei-Jian , He Lin
Published: November 2020

This paper discusses the affection of elastic element’s nonlinear dynamic stiffness, shock stiffness and damping on the maximum response of the shock-isolating system through calculating and comparing the maximum displacement and acceleration of the shock-isolating system under distinct prerequisites. The result shows that under the same shock action, a shock-isolating system with desired nonlinear dynamic stiffness, shock stiffness and damping has better shock-isolating performance than the system with linear ones.
Prospect of Applying Controlling Chaotic Vibration in the Waterborne-Noise Confrontation
Authors: Jiang Rong-Jun , Zhu Shi-Jian , He Lin , Qian Wei-Jian
Published: November 2020

This paper taking the Duffing system with nonlinear soft stiffness as an example, discusses the possibility of applying the chaotic phenomenon to get a broadband frequency output for a single frequency input. Thereby proves the application value of controlling chaos in the waterborne-noise confrontation.