Accepted Manuscripts

Hongjuan Liu, Hai Yu and Zhiliang Zhu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036519
A novel synchronization scheme called special hybrid projective synchronization (SHPS), in which the different state variables can synchronize up to positive or negative scaling factors, is proposed in this paper. For all the symmetric chaotic systems, research results demonstrate that the SHPS can be realized with a single-term linear controller. Take unified chaotic system with unknown parameter as an example, based on Lyapunov stability theory, some sufficient conditions and a parameter update law are derived for the implementation of SPHS, which are verified by some corresponding numerical simulations.
TOPICS: Synchronization, Stability, Control equipment, Computer simulation
Samuel Jackson and Stefanie Gutschmidt
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036520
To increase measurement throughput of atomic force microscopy, multiple cantilevers can be placed in close proximity to form an array for parallel throughput. In this paper, we have measured the relationship between amplitude and tip-sample separation distance for an array of AFM cantilevers on a shared base actuated at a constant frequency and amplitude. The data shows that discontinuous jumps in output amplitude occur within the response of individual beams. This is a phenomenon that does not occur for a standard, single beam system. To gain a better understanding of the coupled array response, a macro scale experiment and mathematical model are used to determine how parameter space alters the measured amplitude. The results demonstrate that a cusp catastrophe bifurcation occurs due to changes in individual beam resonant frequency, as well as significant zero-frequency coupling at the point of jump-to-contact. Both of these phenomena are shown to account for the amplitude jumps observed in the AFM array.
TOPICS: Atomic force microscopy, Cantilevers, Bifurcation, Resonance, Separation (Technology)
Jianzhe Huang and Albert C.J. Luo
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036518
In this paper, from the local theory of flow at the corner in discontinuous dynamical systems, obtained are analytical conditions for switching impact-alike chatter at corners. The objective of this investigation is to find the dynamics mechanism of border-collision bifurcation in discontinuous dynamical systems. Multi-valued linear vector fields are employed in the discontinuous dynamical system, and generic mappings are defined among the boundaries and corners. From mapping structures, periodic motions switching on the boundaries and corners are determined, and the corresponding stability and bifurcations of periodic motions are investigated by eigenvalue analysis. However, the grazing and sliding bifurcations are determined by the local singularity theory in discontinuous dynamical systems. From such analytical conditions, the corresponding parameter map are developed for periodic motions in such multi-valued dynamical systems in the single domain with corners. Numerical simulations of periodic motions are presented for illustrations of motions complexity and catastrophe in the discontinuous dynamical system.
TOPICS: Dynamics (Mechanics), Corners (Structural elements), Dynamic systems, Bifurcation, Chatter, Eigenvalues, Stability, Flow (Dynamics), Computer simulation, Collisions (Physics)
Filipe Marques, Fernando Isaac, Nuno Dourado, Antonio Pedro Souto, Paulo Flores and Hamid Lankarani
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036480
An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket which compose a spherical joint are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudo-penetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb's law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems' dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.
TOPICS: Dynamics (Mechanics), Clearances (Engineering), Friction, Coulomb's law, System dynamics, Energy dissipation, Equations of motion, Multibody systems, Dynamic modeling
J. H. Yang, Miguel A. F. Sanjuán and H. G. Liu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036479
When the traditional vibrational resonance (VR) occurs in a nonlinear system, a weak character signal is enhanced by an appropriate high-frequency auxiliary signal. Here, for the harmonic character signal case, the frequency of the character signal is usually smaller than one rad/s. The frequency of the auxiliary signal is dozens of times of the frequency of the character signal. Moreover, in the real world, the characteristic information is usually indicated by a weak signal with a frequency in the range from several to thousands rad/s. For this case, the weak high-frequency signal cannot be enhanced by the traditional mechanism of VR, and as such, the application of VR in the engineering field could be restricted. In the present work, by introducing a scale transformation, we transform high-frequency excitations in the original system to low-frequency excitations in a rescaled system. Then, we make VR to occur at the low-frequency in the rescaled system, as usual. Meanwhile, the VR also occurs at the frequency of the character signal in the original system. As a result, the weak character signal with arbitrary high-frequency can be enhanced. To make the rescaled system in a general form, the VR is investigated in fractional-order Duffing oscillators. The form of the potential function, the fractional-order and the reduction scale are important factors for the strength of VR.
TOPICS: Resonance, Signals, Excitation, Nonlinear systems
Takashi Ikeda, Yuji Harata and Shota Ninomiya
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036481
This paper investigates the vibration control of a tower-like structure with two degrees of freedom utilizing a square or nearly square tuned liquid damper (TLD) when the structure is subjected to horizontal, harmonic excitation. In the theoretical analysis, when the two natural frequencies of the two-degree-of-freedom (2DOF) structure nearly equal those of the two predominant sloshing modes, the tuning condition, 1:1:1:1, is nearly satisfied. Galerkin's method is used to derive the modal equations of motion for sloshing. The nonlinearity of the hydrodynamic force due to sloshing is considered in the equations of motion for the 2DOF structure. Linear viscous damping terms are incorporated into the modal equations to consider the damping effect of sloshing. Van der Pol's method is employed to determine the expressions for the frequency response curves. The influences of the excitation frequency, the tank installation angle, and the aspect ratio of the tank cross-section on the response curves are examined. The theoretical results show that whirling motions and amplitude modulated motions (AMMs), including chaotic motions, may occur in the structure because swirl motions and Hopf bifurcations, followed by AMMs, appear in the tank. It is also found that a square TLD works more effectively than a conventional rectangular TLD, and its performance is further improved when the tank width is slightly increased and the installation angle is equal to zero. Experiments were conducted in order to confirm the validity of the theoretical results.
TOPICS: Vibration control, Sloshing, Damping, Equations of motion, Excitation, Fluid-dynamic forces, Degrees of freedom, Dampers, Bifurcation, Frequency response, Theoretical analysis, Whirls
Balazs Varszegi, Denes Takacs and Gabor Stepan
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036482
A simple mechanical model of the skateboard-skater system is analyzed, in which a linear proportional-derivative (PD) controller with delay is included to mimic the effect of human control. The equations of motion of the nonholonomic system are derived with the help of the Gibbs-Appell method. The linear stability analysis of the rectilinear motion is carried out analytically in closed form. It is shown how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as functions of the speed, the position of the skater on the board and the damping of the skateboard suspension system. Based on these, an explanation is given for the experimentally observed dynamic behavior of the skateboard-skater system at high speed.
TOPICS: Dynamics (Mechanics), Stability, Control equipment, Suspension systems, Equations of motion, Damping, Delays
Lindsay Moir, Davide Piovesan and Anne Schmitz
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036483
Musculoskeletal simulations can be used to determine loads experienced by the ligaments and cartilage during athletic motions such as impact from a drop landing, hence investigating mechanisms for injury. An open-source discrete element knee model was used to perform a forward dynamic simulation of the impact phase of a drop landing. Since the cartilage contact loads are largely depending on the elastic moduli of the cartilage, the analysis was performed for varying moduli: nominal stiffness based on the literature, stiffness increased by 10%, and decreased by 10%. As the cartilage stiffness increased, the medial compartment contact load decreased. Conversely, the lateral compartment load and MCL force increased, causing a shift in the load distribution. However, these changes were insignificant compared to the overall magnitude of the contact forces (<4% change). The ACL, PCL, and LCL loads remain unchanged between varying cartilage stiffness values. The medial compartment bears a majority of the load (860 N in medial compartment versus 540 N in lateral) during the impact phase of a drop landing, which agrees with physiological data that the medial side of the knee is more affected by osteoarthritis than the lateral side. This is one of the few models to quantify this load distribution and show the results are invariant to changes in cartilage stiffness.
TOPICS: Stress, Stiffness, Cartilage, Knee, Simulation, Osteoarthritis, Anterior cruciate ligament, Musculoskeletal system, Wounds, Physiology, Elastic moduli
Arnaud Malher, Cyril Touzé, Olivier Doaré, Giuseppe Habib and Gaëtan Kerschen
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036420
The influence of a Nonlinear Tuned Vibration Absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subcriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. Large amplitude motions of the airfoil are taken into account with nonlinear restoring forces for the pitch and plunge degrees of freedom. The two cases of a hardening and a softening spring behavior are investigated. The influence of each NLTVA parameter is studied and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to shift the instability, avoid its possible subcriticality and reduce the LCOs amplitude.
TOPICS: Flutter (Aerodynamics), Vibration absorbers, Airfoils, Bifurcation, Springs, Degrees of freedom, Stress, Hardening
Technical Brief  
Auni Aslah Mat Daud
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036418
A Galton board, also referred to as quincunx, is an instrument invented in 1873 by Francis Galton (1822-1911). It is a box with a glass front and many horizontal nails or pins embedded in the back, and a funnel. Galton and many modern statisticians claimed that a lead ball descending to the bottom of the Galton board would display random walk. In this study, a new mathematical model of Galton board is developed, to further improve three very recently proposed models. The novel contribution of this paper is the introduction of the velocity dependent coefficient of restitution. The developed model is then analyzed using symbolic dynamics. The results of the symbolic dynamics analysis prove that the developed Galton board model does not behave the way Galton envisaged. This study also confirms that the details of the of the deterministic models of Galton board are not essential for demonstrating deviations from the statistical models.
TOPICS: Dynamics (Mechanics), Glass, Pins (Engineering), Instrumentation
Ali Ahmadian, Soheil Salahshour, Chee Seng Chan and Dumitru Baleanu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036419
In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well know that the usage of fuzzy differential equations (FDEs) is a natural way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge-Kutta methods is generalized that are for solving first order fuzzy dynamical systems An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduces substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.
TOPICS: Computer simulation, Dynamic systems, Uncertainty, Stability, Robustness, Runge-Kutta methods, Differential equations
Qing Wu, Colin Cole, Maksym Spiryagin, Yucang Wang, Weihua Ma and Chongfeng Wei
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036421
This paper developed a detailed fluid dynamics model and a parallel computing scheme for air brake systems on long freight trains. The model consists of sub-system models for pipes, locomotive brake valves and wagon brake valves. A new efficient hose connection boundary condition that considers pressure loss across the connection was developed. Simulations with 150 sets of wagon brake systems were conducted and validated against experimental data; the simulated results and measured results reached an agreement with the maximum difference of 15%; all important air brake system features were well simulated. Computing time was compared for simulations with and without parallel computing. The computing time for the conventional sequential computing scheme was about 6.7 times slower than real-time. Parallel computing using four computing cores decreased the computing time by 70 %. Real-time simulations were achieved by parallel computing using eight computer cores.
TOPICS: Railroads, Brakes, Simulation, Engineering simulation, Valves, Computers, Boundary-value problems, Locomotives, Pipes, Pressure, Fluid dynamics, Trains
Dumitru Baleanu, Tamás Kalmár-Nagy, Themistoklis P. Sapsis and Hiroshi Yabuno
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036422
Nonlinear dynamical systems have wide relevance to many fields, including engineering. Many techniques, including analytical and numerical ones, have been developed to qualitatively and quantitatively study the properties of nonlinear dynamical systems. With the rapid development of computational methods and tools, the interest in studies on nonlinear dynamical systems has grown substantially. The new computational resources have helped gain new insights into nonlinear phenomena across a range of systems. The main focus of this special issue is to promote the exchange of new ideas, methods (primarily analytical and numerical) and their use in studies of nonlinear dynamics. Applications encompassing real-world problems related to the fields of engineering, in particular, aerospace, mechanical, ocean and civil engineering fields are welcome.
TOPICS: Nonlinear dynamics, Nonlinear dynamical systems, Oceans, Civil engineering, Aerospace industry, Computational methods
Muhammad Saif Ullah Khalid and Imran Akhtar
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036346
For the present study, setting Strouhal Number as the control parameter, we perform numerical simulations for the flow over oscillating NACA-0012 airfoil at Reynolds Number 1,000. This study reveals that aerodynamic forces produced by the oscillating airfoils are independent of the initial kinematic conditions that proves existence of the limit cycle. Frequencies present in the oscillating lift force are composed of the fundamental harmonics, and its odd harmonics. Using these numerical simulations, we observe the shedding frequencies nearly equal to the excitation frequencies in all the cases. Hence, considering it as a primary resonance case, we model the unsteady lift force through a modified van der Pol oscillator. Using the method of multiple scales and spectral analysis of the steady-state CFD solutions, we estimate the frequencies and the damping terms in the reduced-order model. We prove the applicability of this model to all the planar motions of airfoil; heaving, pitching and flapping. With the increasing Strouhal number, the nonlinear damping terms for all types of motion approach similar magnitudes. Another important aspect in one of the currently-proposed model is capturing the time-averaged value of the aerodynamic lift force. We also notice that increase in the magnitude of the lift force is due to effect of destabilizing linear damping parameter.
TOPICS: Lift (Fluid dynamics), Airfoils, Damping, Computer simulation, Steady state, Limit cycles, Excitation, Reynolds number, Emission spectroscopy, Fluid-dynamic forces, Computational fluid dynamics, Kinematics, Resonance, Flow (Dynamics), Aerodynamics, Spectroscopy
Mohammad Sharif Shourijeh, Reza Sharif Razavian and John McPhee
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036288
A model for forward dynamic simulation of the rapid tapping motion of an index finger is presented. The finger model was actuated by two muscle groups: one flexor and one extensor. The goal of this analysis was to estimate the maximum tapping frequency that the index finger can achieve using forward dynamics simulations. To this goal, each muscle excitation signal was parameterized by a seventh-order Fourier series as a function of time. Simulations found that the maximum tapping frequency was 6~Hz, which is reasonably close to the experimental data. Amplitude attenuation (37% at 6Hz) due to excitation/activation filtering, as well as the inability of muscles to produce enough force at high contractile velocities, are factors that prevent the finger from moving at higher frequencies. Musculoskeletal models have the potential to shed light on these restricting mechanisms and help to better understand human capabilities in motion production.
TOPICS: Simulation, Muscle, Musculoskeletal system, Excitation, Engineering simulation, Fourier series, Dynamics (Mechanics), Filtration, Signals
A. M. Shafei and H. R. Shafei
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036197
In this article, a recursive approach is used to dynamically model a tree-type robotic system with floating-base. Two solution procedures are developed to obtain the time responses of the mentioned system. A set of highly nonlinear differential equations is employed to obtain the dynamic behavior of the system when it has no contact with the ground or any object in its environment (flying phase); and a set of algebraic equations is exploited when this tree-type robotic system collides with the ground (impact phase). The Gibbs-Appell (G-A) formulation in recursive form and the Newton's impact law are applied to derive the governing equations of the aforementioned robotic system for the flying and impact phases, respectively. The main goal of this article is a systematic algorithm that is used to divide any tree-type robotic system into a specific number of open kinematic chains and derive the forward dynamic equations of each chain, including its inertia matrix and right hand side vector. Then, the inertia matrices and the right hand side vectors of all these chains are automatically integrated to construct the global inertia matrix and the global right-hand-side vector of the whole system. Finally, to show the effectiveness of the suggested algorithm in deriving the motion equations of multi-chain robotic systems, a ten-link tree-type robotic system with floating base is simulated.
TOPICS: Inertia (Mechanics), Collisions (Physics), Equations of motion, Algorithms, Chain, Robotics, Manipulators, Nonlinear differential equations, Algebra, Open kinematic chains
Yuwen Li, Jiancheng Ji, Shuai Guo and Fengfeng (Jeff) Xi
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036196
This paper proposes a method for process parameter optimization of a mobile robotic percussive riveting system with flexible joints to guarantee the rivet gun alignment during the operation. This development is motivated by the increasing interest in using industrial robots to replace human operators for percussive impact riveting in aerospace assembly. In percussive riveting, the rivet gun generates repetitive impacts acting on the rivet. These impacts not only deform the rivet but also induce forced vibration to the robot, and thus the robot must hold the gun firmly during riveting. The process parameters for the mobile robotic riveting system include those related to the impact force generation for planning the rivet gun input and those related to the robot pose with respect to the joined panels for planning the mobile platform motion. These parameters are incorporated into a structural dynamic model of the robot under a periodic impact force. Then an approximate analytical solution is formulated to calculate the displacement of the rivet gun mounted on the end-effector for its misalignment evaluation. It is found that both the force frequency and the mobile platform position have strong influence on the robotic riveting performance in terms of alignment during operation. Global optimization of these process parameters is carried out to demonstrate the practical application of the proposed method for the planning of the robotic percussive riveting system.
TOPICS: Robotics, Optimization, Riveting, Rivets, Robots, Manufacturing, Structural dynamics, Aerospace industry, Vibration, Displacement, End effectors
Kazuya Sakamoto, Ryosuke Kan, Akihiro Takai and Shigehiko Kaneko
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036115
A free-standing rack (FS rack) is a type of a spent nuclear fuel rack, which is just placed on a floor of a pool. For this characteristic, seismic loads can be reduced by fluid force and friction force, but a collision between a rack and another rack or a wall must be avoided. Therefore, it is necessary for designing an FS rack to figure out how it moves under seismic excitation. In this research, a dynamic model of an FS rack is developed considering seismic inertial force, friction force and fluid force. This model consists of two sub-models: a translation model, which simulates planar translational and rotational motion; and a rocking model, which simulates non-slide rocking motion. First, simulations with sinusoidal inertial force were conducted, changing values of a friction coefficient. Next, to validate this dynamic model, a miniature experiment was conducted. Finally, the model is applied to a real-size FS rack and actually observed seismic acceleration. It is found that translational movement of a rack varies depending on the value of friction coefficient in the simulation with sinusoidal and actual acceleration. Also, simulation results are similar to the experimental results in the aspects of translational and rocking motion provided friction coefficient is selected properly. Through this research, the knowledge is acquired that friction force plays a significant role in a motion of FS rack so that estimating and controlling a friction coefficient is important in designing an FS rack.
TOPICS: Fuels, Dynamic models, Excitation, Friction, Fluids, Design, Simulation, Stress, Collisions (Physics), Simulation results, Rotation, Spent nuclear fuels
Antonio Simon Chong Escobar, Piotr Brzeski, Marian Wiercigroch and Przemyslaw Perlikowski
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036114
In this paper we perform a path following bifurcation analysis of church bell to gain an insight into the governing dynamics of the yoke-bell-clapper system. We use an experimentally validated hybrid dynamical model based on the detailed measurements of a real church bell. Numerical analysis is performed both by a direct numerical integration and a path-following methods using a new numerical toolbox ABESPOL (Chong, Numerical modelling and stability analysis of non-smooth dynamical systems via ABESPOL) based on Coco (Dankowicz et al., Recipes for continuation). We constructed one-parameter diagrams that allow to characterize the most common dynamical states and to investigate the mechanisms of their dynamic stability. A novel method allowing to locate the regions in the parameters space ensuring robustness of bells effective performance is presented.
TOPICS: Dynamic systems, Bifurcation, Dynamic stability, Robustness, Dynamics (Mechanics), Stability, Modeling, Non-smooth dynamics, Numerical analysis
Van-Du Nguyen, Huu-Cong Nguyen, Nhu-Khoa Ngo and Ngoc-Tuan La
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035933
This paper presents a development in design, mathematical modeling and experimental study of a vibro-impact moling device which was invented by the author before. A vibratory unit deploying electro-mechanical interactions of a conductor with oscillating magnetic field has been realized and developed. The combination of resonance in an RLC circuit including a solenoid is found to create a relative oscillatory motion between the metal bar and the solenoid. This results in impacts of the solenoid on an obstacle block, which causes the forward motion of the system. Compared to the former model which employs impact from the metal bar, the improved rig can offer a higher progression rate of six times when using the same power supply. The novel geometrical arrangement allows for future optimization in terms of system parametric selection and adaptive control. This implies a very promising deployment of the mechanism in ground moling machines as well as other self-propelled mobile systems. In this paper, insight to the design development based on physical and mathematical models of the rig is presented. Then the obtained coupled electro-mechanical equations of motion are solved numerically, and a comparison between experimental results and numerical predictions is presented.
TOPICS: Design, Solenoids, Metals, Machinery, Magnetic fields, Adaptive control, Equations of motion, Modeling, Optimization, Circuits, Resonance

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