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Duffing systems excited by harmonic excitations and subjected to noise additions are considered, and it is examined whether the noise addition can be used to steer the response from one stable mode to another. To help with this examination, the authors propose a methodology for estimating the probability that a short duration Gaussian white noise can be used to generate or destroy stable modes of a single nonlinear oscillator as well as a set of coupled nonlinear oscillators. This estimation is done by using the path integral method to find the transient joint probability density function at discrete points in time and then integrating the probability density function over the basins of attraction of the responses of the deterministic system. Results are provided and discussed for the single Duffing oscillator and two coupled Duffing oscillators forced by a near resonance harmonic excitation and noise addition. This work can form a basis for carrying out noise influenced energy movement or localization in the arrays of nonlinear oscillators and have relevance for applications in sensors, energy harvesting devices, and more. [ABSTRACT FROM AUTHOR]

The authors consider a stochastic model based on the interaction and phase coupling amongst wave components that are modified envelope soliton solutions to the nonlinear Schrödinger equation. A probabilistic study is carried out and the resulting findings are compared with ocean wave field observations and laboratory experimental results. The wave height probability distribution obtained from the model is found to match well with prior data in the large wave height region. From the eigenvalue spectrum obtained through the Inverse Scattering Transform, it is revealed that the deep-water wave groups move at a speed different from the linear group speed, which justifies the inclusion of phase correction to the envelope solitary wave components. It is determined that phase synchronization amongst elementary solitary wave components can be critical for the formation of extreme waves in unidirectional sea states. [ABSTRACT FROM AUTHOR]

Noise is present in a wide variety of engineering systems, and it can play a significant role in influencing system dynamics. Under the influence of noise, it has been shown that the response of many discrete-time dynamical systems can be moved away from a particular region. In the present study, the partial control scheme constructed for a chaotic system is applied for confining the trajectories inside a particular region despite the presence of white noise. The proposed algorithm is independent of the dimension of the system. As an illustration, the partial control method has been applied to restrict the response of a Duffing oscillator to a certain state-space region. Different noise forms are considered and numerical results are presented to illustrate the effectiveness of this control method. [ABSTRACT FROM AUTHOR]

Reliable ocean wave forecasts are critical for reducing the risk posed by extreme waves for ships and offshore infrastructure. Despite insights gained from theoretical investigations and constantly improving operational wave forecasting systems, the emergence of extreme waves remain unpredictable. In this article, the authors propose a data-driven modelling approach to generate high resolution wave forecasts for capturing individual waves, including rogue waves. To this end, a decomposition of the sea surface into a set of rapid oscillations and slowly varying amplitudes is utilized. The slow amplitude variations are subsequently forecasted by using universal, data-driven methods. In this approach, the extrapolation range of the data-driven techniques is extended by the slowness of the amplitude variations. The method's capabilities are demonstrated by using available measurements from an experimental wave tank and field data from ocean buoys. • Novel data-driven methodology for ocean wave forecasting. • Combination of physical modelling with data-driven techniques. • Extensive validation of the proposed methodology with experimental data and field measurements. • Accurate forecasts in real-time. • Prediction of rogue waves up to one minute in advance. [ABSTRACT FROM AUTHOR]

In the present article, torsional vibrations and whirling motions of an extended Jeffcott rotor–stator system confined within a fixed stator are numerically explored for both forward and backward whirling motions. The governing equations are constructed in a generalized polar coordinate system for describing non-constant whirling speeds and impact motions. Torsional vibrations and whirling motions are examined by using the derived reduced-order equations. It is found that both forward and backward whirling motions with contact have different, but constant steady state whirling speeds. Furthermore, numerical studies have been undertaken to understand the influence of noise on the system dynamics. The trigonometric representation of non-Gaussian excitation as a harmonic excitation with a random phase modulation is modified by introducing a new state variable. The Euler–Maruyama simulation scheme is used for numerical integration. It is observed that for a low value of friction coefficient, with a sufficient level of noise introduction in the drive speed, the system dynamics for the cases of forward and backward whirling with contact can be significantly influenced. The present studies point to potential beneficial uses of noise modulated rotor drive speeds for controlling rotor–stator contact interactions. • Torsional vibrations and whirling motions of an extended Jeffcott rotor–stator. • Non-constant whirling speeds and impact motions. • Stochastic dynamics of torsional vibrations and whirling motions for a Jeffcott rotor. • Numerical studies to understand the influence of noise on the system dynamics. [ABSTRACT FROM AUTHOR]

To utilize noise for systems, which are transmitting or receiving information, the information rate is a necessary metric to consider. The phase lag, which is the difference between the sender (applied forcing) and receiver (the oscillator) phases, has a significant effect on the information rate. However, this phase lag is a nonlinear function of the noise level. Here, the effects of phase lag on the information rate for a Duffing oscillator are examined and comparative discussions are made with phase lag from linear response theory. The phase lag is shown to be an important variable in calculating the information rate. [ABSTRACT FROM AUTHOR]

The dynamics of mechanical systems, such as turbomachinery with multiple blades, are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and transitions between them may occur under the influence of random factors. A methodology for finding most probable escape paths and estimating the transition rates in the small noise limit is developed and applied to a collection of arrays of coupled monostable oscillators with cubic nonlinearity, small damping, and harmonic external forcing. The methodology is built upon the action plot method [Beri et al., Phys. Rev. E 72, 036131 (2005)] and relies on the large deviation theory, the optimal control theory, and the Floquet theory. The action plot method is promoted to non-autonomous high-dimensional systems, and a method for solving the arising optimization problem with a discontinuous objective function restricted to a certain manifold is proposed. The most probable escape paths between stable vibrational modes in arrays of up to five oscillators and the corresponding quasipotential barriers are computed and visualized. The dependence of the quasipotential barrier on the parameters of the system is discussed. [ABSTRACT FROM AUTHOR]

An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery blade. Due to the nature of the nonlinear restoring forces acting on the cantilever structure, the structure's response includes regions of multi-stability and hysteresis. Here, a large number of trials are used to show that random perturbations can be used to create a transition between a high amplitude response and a low amplitude response of the cantilever. The observed transition behavior occurs from a high amplitude response to a low amplitude response, but not vice versa. Stochastic modeling of the system, Monte Carlo simulations, and calculations of the stochastic system's quasipotential are used to explain the nearly one-directional transition behavior. These noise-influenced transitions can also occur in other physical systems. • Construction of an experimental setup to study stochastic dynamics of a rotating beam. • Measurements of noise-induced transitions from high- to low-amplitude responses. • Quasipotential analysis and Monte Carlo simulations of noise-induced transitions. [ABSTRACT FROM AUTHOR]

• Wheel interaction generated longitudinal and transverse force chains in the soil. • Force networks in the soil are concentrated in the forward path of the wheel. • Traction performance of the wheel increases with lug length and traction load. • Non-monotonic behavior observed for wheel performance with respect to lug width. • Performance is similar for angular velocity and slip controls as slip increases. Terramechanics plays an important role in determining the design and control of autonomous robots and other vehicles that move on granular surfaces. Traction capabilities, slippage, and sinkage of a robot are governed by the interaction of a robot's appendage with the operating terrain. It is important to understand how the terrain flows under this appendage during such an interaction. In this work, dynamics of soil performance and locomotion performance of a lugged wheel travelling on soft soil are numerically investigated. Studies are conducted with a two-dimensional model by using the discrete element method to analyze the interactions between a lugged wheel and the soil. The soil performance is studied by examining the force distribution and evolution of force networks during the course of the wheel travel. For two different control modes, namely, slip-based wheel control and angular velocity-based wheel control, the performance parameters such as, sinkage, traction, traction efficiency, and power consumption of the wheel are compared for various wheel configurations. The findings of this work are expected to be useful for optimal design and control of the lugged wheel travelling on deformable surfaces. [ABSTRACT FROM AUTHOR]

Legged locomotion has advantages when one is navigating a flowable ground or a terrain with obstacles that are common in nature. With traditional terra-mechanics, one can capture large wheel-terrain interactions. However, legged motion on a granular substrate is difficult to investigate by using classical terra-mechanics due to sharp edge contact. Recent studies have shown that a continuum simulation can serve as an accurate tool for simulating dynamic interactions with granular material at laboratory and field scales. Spurred by this, a computational framework based on the smoothed particle hydrodynamics (SPH) method has been developed for the investigation of single robot appendage interaction with a granular system. This framework has been validated by using experimental results and extended to study robot appendages with different shapes and stride frequencies. The mechanics' results are expected to help robot navigation and exploration in unknown and complex terrains. [ABSTRACT FROM AUTHOR]

In the present effort, a data-driven modeling approach is undertaken to forecast aperiodic responses of non-autonomous systems. As a representative non-autonomous system, a harmonically forced Duffing oscillator is considered. Along with it, an experimental prototype of a Duffing oscillator is studied. Data corresponding to chaotic motions are obtained through simulations of forced oscillators with hardening and softening characteristics and experiments with a bistable oscillator. Portions of these datasets are used to train a neural machine and make response predictions and forecasts for motions on the corresponding attractors. The neural machine is constructed by using a deep recurrent neural network architecture. The experiments conducted with the different numerical and experimental chaotic time-series data confirm the effectiveness of the constructed neural network for the forecasting of non-autonomous system responses. [ABSTRACT FROM AUTHOR]

With the aim of enhancing the understanding of the complex dynamics of deep drilling, an integrated model with complex time delays and Stribeck friction is presented for studies on the axial-torsional dynamics of a drill string. Various aspects of the drill string are considered, including spatial distribution, structural and external damping, dry friction-induced damping, boundary conditions, and complex bit-rock interactions. The drill-string structure is spatially discretized by using the finite element method. With the resulting discretized complex delay system, stability analysis is conducted following the semi-discretization procedure. Through parametric studies, the effects of drilling parameters, dry friction, boundary conditions, and rock-strength properties on the drilling stability are obtained. Subsequently, an optimally tuned boundary condition with compliance is deployed at the top drive to expand the stable region and mitigate self-excited vibrations in the operational parameter space of drilling. To find the distribution of stress along the drill string, numerical simulations are conducted. The dynamical stress caused by self-excited vibrations is illustrated in the spatial–temporal plane. Strain and stress analysis reveal wave propagation along the drill string, including traveling and standing waves. The dynamic effective stress along the drill string is studied, and the von Mises effective stress is determined by combining the axial stress and torsional stress. On the basis of this information, the locations of the vulnerable points along the drill string are found in terms of structural strength. Finally, the tuned boundary condition at the top is deployed in the numerical simulations to show vibration control effectiveness. The results point to two possible vibration-cancellation approaches that can benefit from a tuned top boundary. The findings of this work can serve as a basis for identifying the locations of vulnerable points and alleviating the levels of axial-torsional vibrations in drilling applications. • The dynamic model integrates dry friction, boundaries, complex time delay, and loss of contact. • Stability analysis considers the effects of RPM, WOB, dry friction, boundary, and rock strength. • Traveling and standing waves are identified, and the vulnerable points along the drill string are determined. • Vibrations can be eliminated or partially mitigated by a tuned compliant boundary at the top. [ABSTRACT FROM AUTHOR]

Dry granular materials have been the subject of many investigations, while wet granular materials, which widely exist in many real-world applications, have only received limited attention. The aim of this paper is to address the missing gap in continuum modeling of wet granular materials. To study the wet granular flows, a grain-scale capillary interaction is introduced, as additional cohesive stress in the continuum-scale framework. We coupled the viscoplastic constitutive law for dry granular material and cohesion model for wet isotropic granular material to capture the behavior of wet granular materials. This combined model is implemented in a smooth particle hydrodynamics framework because the meshfree nature of this method captures the large deformation of granular flows without local grid distortion. The Wendland kernel is used as the interpolation kernel to improve numerical stability. This framework is validated by comparing numerical results with recent experimental findings for both dry and wet cases. The comparisons are illustrative of the potential of the framework to capture the behavior of granular materials across different phases. For different levels of friction and water content, the run-out dynamics and shear strength properties of granular materials in the final quasi-static regime are investigated. For granular flows on flat surfaces, compared with dry granular materials, with the introduction of surface tension in wet granular materials, it is found that there are increases in shear stresses locally and globally, enabling stronger internal forces to support structures with larger angles of repose. The surface energy-induced cohesion is found to play an important role in low friction cases compared to high friction cases. To benchmark the numerical framework presented here, granular column collapses on curved surfaces are also investigated. For flows on curved surfaces, although there are also increases in internal shear stresses, the differences in final profiles between wet granular materials and dry granular materials are not as pronounced as that on flat surfaces due to geometric constraints. The findings of this work are demonstrative of the capabilities of the smooth particle hydrodynamics method for the study of wet granular materials. This effort can serve as a step forward in the quest for a unified continuum theory and computational framework of granular material dynamics. [ABSTRACT FROM AUTHOR]

Abstract In the present study, the influence of noise on the responses of continuous-time dynamical systems are considered. In particular, the influence of white Gaussian noise on the frequency responses of monostable and bistable, softening Duffing oscillators are studied. A combination of experimental, analytical, and numerical studies are undertaken to understand the shifting of jump-up and jump-down frequencies and an eventual collapse of upper and lower responses branches of into one response curve with no jump instabilities for the considered Duffing oscillator. It is noted that with noise, the hysteresis observed in the response of the nonlinear oscillator without noise can be destroyed. Highlights • Noise influenced frequency responses of softening Duffing oscillators investigated through experimental–numerical studies. • Shifting of jump-up and jump-down locations in the response curves by using noise illustrated for Duffing oscillators. • Use of noise to destroy the hysteresis characteristic observed in the response of a nonlinear oscillator without noise. [ABSTRACT FROM AUTHOR]

In many mechanical systems, rotating structures experience continuous rotor-stator contact and torsion motions are dominant in the response. Drill strings used in the oil and gas industry represent one example of rotating structures. Torsion vibrations can be deleterious to the components and operations of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal input to the rotation speed of a drill string are studied. The drill string is modeled as an extended Jeffcott rotor with sinusoidal drive speed modulation. After constructing a three degree-of-freedom model to capture lateral and torsion motions, the equations of motion are reduced to a single differential equation governing torsion vibrations during continuous stator contact. An approximate solution has been obtained by applying the Method of Direct Partition of Motions to obtain an analytical approximation for the solution of this governing equation of motion. The results show that for a rotor undergoing either forward whirling or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce regions of negative slope in the variation of friction coefficient with respect to the contact surface relative speed. Experiments with a laboratory scale drill-string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the reduced-order models. These findings suggest that the developed reduced-order models can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the considered drive-speed modulation scheme can be useful for attenuating drill-string vibrations. [ABSTRACT FROM AUTHOR]

The dynamics of a modified Jeffcott rotor is studied, including rotor torsional deformation and rotor-stator contact. Conditions are studied under which the rotor undergoes either forward synchronous whirling or self-excited backward whirling motions with continuous stator contact. For forward whirling, the effect on the response is investigated for two commonly used rotor-stator friction models, namely, the simple Coulomb friction and a generalized Coulomb law with cubic dependence on the relative slip velocity. For cases with and without the rotor torsional degree of freedom, analytical estimates and numerical bifurcation analyses are used to map out regions in the space of drive speed and a friction parameter, where rotor-stator contact exists. The nature of the bifurcations in which stability is lost are highlighted. For forward synchronous whirling fold, Hopf, lift-off, and period-doubling bifurcations are encountered. Additionally, for backward whirling, regions of transitions from pure sticking to stick-slip oscillations are numerically delineated. [ABSTRACT FROM AUTHOR]

A co-simulation strategy for modeling the unsteady dynamics of flying insects and small birds as well as biologically inspired flapping-wing micro-air-vehicles is developed in this work. In particular, the dynamic system under study is partitioned in two subsystems (the structural model and the aerodynamic model) that exchange information in a strong way. The vehicle or insect system is modeled as a collection of rigid bodies and lifting surfaces that can undergo deformations such as spanwise twisting, in-plane bending, out-of-plane bending, and an arbitrary combination of these deformation mechanisms. To account for the loads associated with the airflow, an aerodynamic model based on an extended version of the unsteady vortex-lattice method is used. The motion equations are integrated by using a fourth-order predictor-corrector method along with a procedure to stabilize the solution of the resulting differential-algebraic equations. The numerical results obtained for the unsteady lift and dynamics of a fruit fly in free hover flight are found to be in close agreement with prior experimental results reported in the literature. Furthermore, the inclusion of an adequate wing deformation pattern results in an increase of the lift force compared with that of a rigid wing surface, pointing to the importance of wing flexibility on aerodynamic performance. From the findings reported in this paper, it is believed that the numerical simulation framework presented here could serve as a computational tool for further studies of flying insects and micro-air-vehicles. [ABSTRACT FROM AUTHOR]

Wave fields for near homoclinic, single mode rogue-wave solutions of the periodic nonlinear Schrödinger equation are presented. Parameters of candidate solutions are estimated and refined through an eigenvalue solution procedure. An overview of the estimation and refining procedure used by the authors is provided. Solutions are scaled to facilitate experimental implementation. The continuous wavelet transform is used to carry out time–frequency analyses and the results obtained are demonstrative of the dispersion relation as well as the time varying side band energy transfer associated with the Benjamin–Feir instability. The analysis framework and approach used are validated with the Peregrine solution. Other extreme wave solutions are analyzed as well. The framework presented here could serve as a basis for experimental investigations into single mode rogue waves as well as other localizations in wave fields. [ABSTRACT FROM AUTHOR]

The article features a study conducted by the Department of Electrical and Computer Engineering and the Institute for Systems Research of the University of Maryland regarding dynamics and control of dive-plane dynamics of supercavitating vehicles in College Park, Maryland. Researchers made an analytical and numerical investigations and considered dominant nonlinearities of planning forces. It revealed that two controllers are proposed to realize stable inner-loop dynamics, a linear state feedback control scheme and a switching control scheme. They found that when they compare the linear feedback control scheme, the switching control scheme increases the region of attraction with reduced control effort which is advantageous in avoiding saturation in magnitude.

In this work, the authors explore the influence of noise on the dynamics of coupled nonlinear oscillators. Numerical studies based on the Euler–Maruyama scheme and experimental studies with finite duration noise are undertaken to examine how the response can be moved from one response state to another by using noise addition to a harmonically forced system. In particular, jumps from a high amplitude state of each oscillator to a low amplitude state of each oscillator and the converse are demonstrated along with noise-influenced localizations. These events are found to occur in a region of multi-stability for the system, and the corresponding noise levels are reported. A method for recognizing how much noise is required to induce a change the system dynamics is developed by using the response basins of attraction. The findings of this work have implications for weakly coupled, nonlinear oscillator arrays and the manner in which noise can be used to influence energy localization and system dynamics in these systems. • Experiments on the influence of finite duration noise on coupled, nonlinear oscillators. • First experiments of its kind with a combination of hardening and softening oscillators. • Empirical and numerical observations related to the influence of noise on localization. • Numerical studies with low and high number of coupled, nonlinear oscillators. • Noise-influenced dynamics in the context of response localization elucidated. [ABSTRACT FROM AUTHOR]

A method to determine parameters governing periodic Riemann theta function rogue-wave solutions to the nonlinear Schrödinger equation is presented. A map of parameter values leading to candidate solutions is developed. In addition to candidate solutions, an overview of qualitative aspects of the solution space can be gained from this map. Based on these findings, several new extreme wave solutions are presented. Although the computations required to determine the map are quite demanding, it is shown that these computations can be efficiently accelerated with a parallel computing architecture. A general purpose computing on a graphics processor unit (GPGPU) implementation yielded a 400x acceleration over a single threaded high level implementation. This acceleration enabled exploration and examination of the solution space, which otherwise would not have been possible. In addition, the solution methodology presented here can be extended to explore other classes of solutions. [ABSTRACT FROM AUTHOR]

Abstract: Modeling, numerical, and experimental efforts undertaken to develop a fundamental understanding of latching in a MEMS shock sensor are presented. A two degree-of-freedom model is developed and numerical studies are conducted with this model. These studies, which help shed light on difficult to observe experimental aspects, are used to examine the interaction forces between the shock sensor mass and latch, bounce effects, and loss of contact between the mass and the latch. High-speed video images of the shock sensor motions collected during a latching event are shown, and these results are used to verify the model predictions. Parametric studies conducted to examine the sensitivity of the design to friction and the effects of the latch mass and stiffness properties on the latch bounce are presented and discussed. [Copyright &y& Elsevier]

• Pendulum impact on a granular surface creates force chains along its wake. • The force chains due to pressing pendulum are in diagonal and horizontal directions. • The momentum transferred to the media can cause buckling of top rows of granules. • Larger pendulum speeds result in larger particle speeds in horizontal direction. • The pendulum speed does not affect vertical speeds of particles significantly. Interactions between a speed-driven pendulum and an array of photoelastic particles are studied to further the current understanding of granular media response during legged locomotion. A two-dimensional experiment is set up and used to study the motions of granular particles and force chains inside the media. A pendulum with a drive at the pivot is used to swing the pendulum through the granular media. For four different pendulum actuation speeds, high speed videos are recorded in order to capture granular media response during the interactions with the pendulum. Image processing algorithms are employed to track positions and calculate velocities of the granular particles. For all studied drive speeds, the maximum particle speed in the vertical direction is found to be the same, whereas in the horizontal direction, the maximum particle speeds are found to be higher with higher rotor speeds. In addition, the photoelastic property of the particles allows the authors to observe force distribution inside the media, and the evolutions of force chains in two dimensions. For a selected drive speed, snapshots of the force chains inside the granular media during the interactions with the pendulum are presented. Through this study, the authors have introduced dynamical use of photoelastic particles to unravel soil dynamics during legged locomotion. This approach can be used to obtain insights into particle dynamics and force chains inside the media and form a picture of the collective soil behavior during interactions with locomotion mechanisms. [ABSTRACT FROM AUTHOR]

Drillstring vibrations can be undesirable for drilling operations. Here, attention is focused on vibrations of the upper portion of a drillstring as these vibrations can cause drillpipe wear and casing wear. A reduced-order model is developed to study the motions of a drillstring by taking fluid loading and stabilizer effects into account. In this model development, the distributed nature of the fluid loading is taken into account, and the drillstring is treated as a beam structure. Perturbation analyses are carried out with the reduced-order system, and the system responses are examined for primary and secondary (subharmonic and superharmonic) resonance excitations. The analytical-numerical results reveal the rich nature of the system behavior and help understand the drillstring motions during various resonance conditions. [ABSTRACT FROM AUTHOR]

The article focuses on Professor Fabrizio Vestroni, who teaches Structural Mechanics at the University of Rome La Sapienza. It states that Vestroni's academic career has spanned almost 30 years and that he has had a significant impact in the fields of structural dynamics and nonlinear vibrations, engineering education, and by mentoring graduate students. It mentions that he has promoted and chaired a significant number of workshops at La Sapienza and was instrumental in organizing conferences and mini-symposia in the fields of structural identification and linear and nonlinear dynamics.

Studies of fluid-structure interactions associated with flexible structures such as flapping wings require the capture and quantification of large motions of bodies that may be opaque. As a case study, motion capture of a free flying Manduca sexta, also known as hawkmoth, is considered by using three synchronized high-speed cameras. A solid finite element (FE) representation is used as a reference body and successive snapshots in time of the displacement fields are reconstructed via an optimization procedure. One of the original aspects of this work is the formulation of an objective function and the use of shadow matching and strain-energy regularization. With this objective function, the authors penalize the projection differences between silhouettes of the captured images and the FE representation of the deformed body. The process and procedures undertaken to go from high-speed videography to motion estimation are discussed, and snapshots of representative results are presented. Finally, the captured free-flight motion is also characterized and quantified. [ABSTRACT FROM AUTHOR]

Within this paper, an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre-stress and large variable curvature. The static configuration, mode shapes, and natural frequencies of the pre-stressed beam are obtained by using geometrically exact, Euler-Bernoulli beam theory. The beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform, closed cross-section, as well as the boundary conditions under consideration. The static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite-element analysis software. In addition to the modal analysis about general static configurations, special consideration is given to an initially straight beam that is deformed into semi-circular and circular static configurations. For these special circular cases, the partial differential equation of motion is reduced to a sixth-order differential equation with constant coefficients, and solutions of this system are examined. This work can serve as a basis for studying slender structures with large curvatures. [ABSTRACT FROM AUTHOR]

Abstract: In this work, torsional vibrations of a Jeffcott rotor subjected to continuous stator contact are analytically and numerically studied for both forward and backward whirling motions. Torsional oscillations of this system are complex due to nonlinear coupling with lateral vibrations, and nonlinearities originating from frictional forces between the rotor and stator. The phenomena observed in numerical simulations of the three degree-of-freedom Jeffcott rotor are explained through analysis of a derived reduced-order equation. It is found that during forward whirling, torsional oscillations are unlikely to exist in both the full and reduced-order models. Special consideration is provided to the torsional response during high-speed backward whirling. Although the rotor is subject to discontinuous friction, during high-speed backward whirling, it is found that the predictions from the full system and reduced-order models for the torsional oscillations are smooth in nature. Further analysis of the reduced-order system reveals that high-frequency forcing acts to smoothen out the discontinuity on the slow scale. Additionally, a centrifugal stiffening effect is experienced by the torsional motions during both forward and backward whirling. [Copyright &y& Elsevier]

Abstract: Experimental and numerical investigations are conducted into drill-string motions. The numerical efforts are carried out by using a reduced-order model with attention to stick–slip interactions between a drill string and an outer shell. These efforts are complemented by experimental studies conducted with a unique, laboratory scale model. Qualitative and quantitative changes in the system behavior are studied with respect to the rotation speed and mass imbalance. Comparisons are made between the numerical findings and the corresponding experimental results. In addition, the influence of contact conditions between the drill string and the outer shell on the drill-string dynamics is also examined. The findings of the work suggest that small changes in the system rotation speed can have a significant influence on the nature of drill-string motions and they also provide guidelines for steering the system out of regions of undesirable dynamics and maintaining drill-string motions close to the center of a borehole. [Copyright &y& Elsevier]

In the present study, a computational investigation was carried out to understand the influence of flexibility on the aerodynamic performance of a hovering wing. A flexible, two-dimensional, two-link model moving within a viscous fluid was considered. The Navier-Stokes equations governing the fluid dynamics were solved together with the equations governing the structural dynamics by using a strongly coupled fluid-structure interaction scheme. Harmonic kinematics was used to prescribe the motions of one of the links, thus effectively reducing the wing to a single degree-of-freedom oscillator. The wing's flexibility was characterized by the ratio of the flapping frequency to the natural frequency of the structure. Apart from the rigid case, different values of this frequency ratio (only in the range of 1/2 to 1/6) were considered at the Reynolds numbers of 75, 250 and 1000. It was found that flexibility can enhance aerodynamic performance and that the best performance is realized when the wing is excited by a non-linear resonance at 1/3 of the natural frequency. Specifically, at Reynolds numbers of 75, 250 and 1000, the aerodynamic performance that is characterized by the ratio of lift coefficient to drag coefficient is respectively increased by 28%, 23% and 21% when compared with the corresponding ratios of a rigid wing driven with the same kinematics. For all Reynolds numbers, the lift generated per unit driving power is also enhanced in a similar manner. The wake capture mechanism is enhanced, due to a stronger flow around the wing at stroke reversal, resulting from a stronger end of stroke vortex at the trailing edge. The present study provides some clues about how flexibility affects the aerodynamic performance in low Reynolds number flapping flight. In addition, it points to the importance of considering non-linear resonances for enhancing aerodynamic performance. [ABSTRACT FROM AUTHOR]

Abstract: A microelectromechanical shock sensor, which uses a latching mechanism to record a shock event above a specified threshold level, is discussed in this article. The fabrication process for the shock sensor, which includes wafer-level vacuum packaging, is detailed along with the design features. These features include a reset actuator for reuse of the sensor, a no-power operation scheme when the reset actuator is not activated, and a control circuit to minimize power used to unlatch the sensor. In order to describe the shock-sensor dynamics and interaction with the latch mechanism, a preliminary non-linear model has been developed. Experimental results are presented and compared with model predictions. [Copyright &y& Elsevier]

In this paper, a reduced-order drill-string model with coupled axial and torsion dynamics is studied. Nonlinear effects associated with dry friction, loss of contact, and the state-dependent delay, which all arise from cutting mechanics, are considered. The linearized system equations are derived, and the local stability analysis is carried out analytically by using the D-subdivision method. The obtained results are presented in terms of stability crossing curves, which are parameterized by using the rotation speed and the cutting depth. A numerical continuation method is developed and used to follow periodic orbits of systems with friction, loss of contact, and state-dependent delay. Bifurcation diagrams are constructed to capture the possible routes from either a nominal stable operational state or a stable limit-cycle motion without stick slip to a limit-cycle motion with stick slip. It is shown that the system can experience subcritical Hopf bifurcations of equilibrium solutions and cyclic fold bifurcations. Based on this work, an observer based control scheme is proposed by using a continuous pole placement method for time-delay systems. The effectiveness of the controller in suppressing stick-slip behavior is shown through simulations. [ABSTRACT FROM AUTHOR]

• Novel type of delay called complex delay proposed to better capture drill bit's cutting action. • Integrated model with enhanced bit-rock interface for drill-string dynamics constructed. • Algorithms developed for determining complex delay variation and drilling stability • Parametric studies conducted to understand the influence of different parameters. • Complex delay helps accurate capture of dynamics, cutting volume, and power consumption. In this article, an integrated model with spatially distributed inertia and general boundary conditions for the axial-torsional dynamics of a drill string is developed and studied. Based on the cutting geometry of the bit-rock interface, a notion called a "complex delay" is introduced. In the proposed complex-delay model, both the state-dependent delay from the torsional vibration and the multiple regenerative effects due to the loss of contact of drill bit are taken into account. Focusing on the system dynamics with the time delay, an efficient algorithm is developed to discretize and calculate the complex time delay by using a recursion method. The drill-string structure is spatially discretized by using the finite-element method. Numerical studies are conducted and several types of self-excited vibrations are illustrated, including stick-slip motions and bit bounce. The consideration of the complex delay in the drilling process suggests that the maximum number of regeneration periods can exceed ten and that multiple regenerative effects dominate the time-delay effects when the drill bit bounces away from the rock surface and experiences loss of contact. Finally, comparisons are made between the results obtained with the traditional state-dependent-delay model and the proposed complex-delay model. The results reveal that the complex-delay model is volume conservative in terms of the total cut material during the drilling process, while the state-dependent-delay model is not volume conservative. With just the state-dependent-delay model, due to the violation of cutting volume conservation, the result is an unrealistic torque on bit and a higher energy consumption of the drill bit, which all lead to an inaccurate picture of the system dynamics. By contrast, with the proposed complex-delay model, one is able to better capture the cutting dynamics and energy consumption of the drill bit. The findings also reveal that the time-delay effects are weakened, when loss of contact is experienced by the system. [ABSTRACT FROM AUTHOR]