0


Research Papers

J. Comput. Nonlinear Dynam. 2017;12(5):051001-051001-7. doi:10.1115/1.4035880.

In this work, a mathematical model is developed for simulating the vibrations of a single flexible cylinder under crossflow. The flexible tube is subjected to an axial load and has loose supports. The equation governing the dynamics of the tube under the influence of fluid forces (modeled using quasi-steady approach) is a partial delay differential equation (PDDE). Using the Galerkin approximation, the PDDE is converted into a finite number of delay differential equations (DDE). The obtained DDEs are used to explore the nonlinear dynamics and stability characteristics of the system. Both analytical and numerical techniques were used for analyzing the problem. The results indicate that, with high axial loads and for flow velocities beyond certain critical values, the system can undergo flutter or buckling instability. Post-flutter instability, the amplitude of vibration grows until it impacts with the loose support. With a further increase in the flow velocity, through a series of period doubling bifurcations the tube motion becomes chaotic. The critical flow velocity is same with and without the loose support. However, the loose support introduces chaos. It was found that when the axial load is large, the linearized analysis overestimates the critical flow velocity. For certain high flow velocities, limit cycles exist for axial loads beyond the critical buckling load.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051002-051002-12. doi:10.1115/1.4035214.

This paper aims at analyzing the size-dependent nonlinear dynamical behavior of a geometrically imperfect microbeam made of a functionally graded (FG) material, taking into account the longitudinal, transverse, and rotational motions. The size-dependent property is modeled by means of the modified couple stress theory, the shear deformation and rotary inertia are modeled using the Timoshenko beam theory, and the graded material property in the beam thickness direction is modeled via the Mori–Tanaka homogenization technique. The kinetic and size-dependent potential energies of the system are developed as functions of the longitudinal, transverse, and rotational motions. On the basis of an energy method, the continuous models of the system motion are obtained. Upon application of a weighted-residual method, the reduced-order model is obtained. A continuation method along with an eigenvalue extraction technique is utilized for the nonlinear and linear analyses, respectively. A special attention is paid on the effects of the material gradient index, the imperfection amplitude, and the length-scale parameter on the system dynamical response.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051003-051003-10. doi:10.1115/1.4035671.

This paper concerns the dynamic simulation of constrained mechanical systems in the context of real-time applications and stable integrators. The goal is to adaptively find a balance between the stability of an over-damped implicit scheme and the energetic consistency of the symplectic, semi-implicit Euler scheme. As a starting point, we investigate in detail the properties of a recently proposed timestepping scheme, which approximates a full nonlinear implicit solution with a single linear system, without compromising stability. This scheme introduces a geometric stiffness term that improves numerical stability up to a certain time-step size, but it does so at the cost of large mechanical dissipation in comparison to the traditional constrained dynamics formulation. Dissipation is sometimes undesirable from a mechanical point of view, especially if the dissipation is not quantified. In this paper, we propose to use an additional control parameter to regulate “how implicit” the Jacobian matrix is, and change the degree to which the geometric stiffness term contributes. For the selection of this parameter, adaptive schemes are proposed based on the monitoring of energy drift. The proposed adaptive method is verified through the simulation of open-chain systems.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051004-051004-6. doi:10.1115/1.4035896.

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051005-051005-6. doi:10.1115/1.4036195.

Static optimization (SO) has been used extensively to solve the muscle redundancy problem in inverse dynamics (ID). The major advantage of this approach over other techniques is the computational efficiency. This study discusses the possibility of applying SO in forward dynamics (FD) musculoskeletal simulations. The proposed approach, which is entitled forward static optimization (FSO), solves the muscle redundancy problem at each FSO time step while tracking desired kinematic trajectories. Two examples are showcased as proof of concept, for which results of both dynamic optimization (DO) and FSO are presented for comparison. The computational costs are also detailed for comparison. In terms of simulation time and quality of muscle activation prediction, FSO is found to be a suitable method for solving forward dynamic musculoskeletal simulations.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051006-051006-8. doi:10.1115/1.4036116.

This paper describes a very simple beam model, amenable to be used in multibody applications, for cases where the effects of torsion and shear are negligible. This is the case of slender rods connecting different parts of many space mechanisms, models useful in polymer physics, computer animation, etc. The proposed new model follows a lumped parameter method that leads to a rotation-free formulation. Axial stiffness is represented by a standard nonlinear truss model, while bending is modeled with a force potential. Several numerical experiments are carried out in order to assess accuracy, which is usually the main drawback of this type of approach. Results reveal a remarkable accuracy in nonlinear dynamical problems, suggesting that the proposed model is a valid alternative to more sophisticated approaches.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051007-051007-12. doi:10.1115/1.4036118.

A modified two-timescale incremental harmonic balance (IHB) method is introduced to obtain quasi-periodic responses of nonlinear dynamic systems with combinations of two incommensurate base frequencies. Truncated Fourier coefficients of residual vectors of nonlinear algebraic equations are obtained by a frequency mapping-fast Fourier transform procedure, and complex two-dimensional (2D) integration is avoided. Jacobian matrices are approximated by Broyden's method and resulting nonlinear algebraic equations are solved. These two modifications lead to a significant reduction of calculation time. To automatically calculate amplitude–frequency response surfaces of quasi-periodic responses and avoid nonconvergent points at peaks, an incremental arc-length method for one timescale is extended for quasi-periodic responses with two timescales. Two examples, Duffing equation and van der Pol equation with quadratic and cubic nonlinear terms, both with two external excitations, are simulated. Results from the modified two-timescale IHB method are in excellent agreement with those from Runge–Kutta method. The total calculation time of the modified two-timescale IHB method can be more than two orders of magnitude less than that of the original quasi-periodic IHB method when complex nonlinearities exist and high-order harmonic terms are considered.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051008-051008-13. 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 known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) 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 reduce 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051009-051009-7. 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 achieve 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 6 Hz) 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051010-051010-4. doi:10.1115/1.4035718.

In this manuscript, we have used the recently developed Fα-calculus to calculate the energy straggling function through the fractal distributed structures. We have shown that such a fractal structure of space causes the fractal pattern of the energy loss. Also, we have offered Fα-differential Fokker–Planck equation for thick fractal absorbers.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051011-051011-9. 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 1 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 this 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051012-051012-17. doi:10.1115/1.4036481.

This paper investigates the vibration control of a towerlike structure with 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051013-051013-10. 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 pseudopenetration 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051014-051014-7. 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 that 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, position of the skater on the board, and 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051015-051015-5. doi:10.1115/1.4036519.

A novel synchronization scheme called special hybrid projective synchronization (SHPS), in which different state variables can synchronize up to same 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. Taking 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051016-051016-11. 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 limit cycle oscillations (LCOs) amplitude.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051017-051017-11. doi:10.1115/1.4036421.
FREE TO VIEW

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 subsystem 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051018-051018-7. doi:10.1115/1.4036520.

To increase measurement throughput of atomic force microscopy (AFM), 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 show 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 macroscale 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.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051019-051019-8. 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 a Reynolds number of 1000. This study reveals that aerodynamic forces produced by oscillating airfoils are independent of the initial kinematic conditions suggesting the existence of limit cycle. Frequencies present in the oscillating lift force are composed of the fundamental harmonics and its odd harmonics. Using these numerical simulations, we analyze the shedding frequencies close to the excitation frequencies. Hence, considering it as a primary resonance case, we model the unsteady lift force with a modified van der Pol oscillator. Using the method of multiple scales and spectral analysis of the steady-state computational fluid dynamics (CFD) solutions, we estimate the frequencies and the damping terms in the reduced-order model (ROM). We show the applicability of this model to all planar motions of the airfoil; heaving, pitching, and flapping. With increasing the Strouhal number, the nonlinear damping terms for all types of motion approach similar magnitudes. Another important aspect in one of the proposed model is its ability to capture the time-averaged value of the aerodynamic lift force. We also notice that increase in the magnitude of the lift force is due to the effect of destabilizing linear damping parameter.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051020-051020-7. doi:10.1115/1.4036710.

Since the solutions of the fractional differential equations (FDEs) have unbounded derivatives at zero, their numerical solutions by piecewise polynomial collocation method on uniform meshes will lead to poor convergence rates. This paper presents a piecewise nonpolynomial collocation method for solving such equations reflecting the singularity of the exact solution. The entire domain is divided into several small subdomains, and the nonpolynomial pieces are constructed using a block-by-block scheme on each subdomain. The method is applied to solve linear and nonlinear fractional differential equations. Numerical examples are given and discussed to illustrate the effectiveness of the proposed approach.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051021-051021-5. doi:10.1115/1.4036813.

In this paper, a Green’s function based iterative algorithm is proposed to solve strong nonlinear oscillators. The method’s essential part is based on finding an appropriate Green’s function that will be incorporated into a linear integral operator. An application of fixed point iteration schemes such as Picard’s or Mann’s will generate an iterative formula that gives reliable approximations to the true periodic solutions that characterize these kinds of equations. The applicability and stability of the method will be tested through numerical examples. Since exact solutions to these equations usually do not exist, the proposed method will be tested against other popular numerical methods such as the modified homotopy perturbation, the modified differential transformation, and the fourth-order Runge–Kutta methods.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051022-051022-10. doi:10.1115/1.4036913.

In this paper, a novel controller is developed for control of turning and milling dynamics. The controller design benefits from the use of time-delays in controlling a dynamic system. The gains of the controller are determined by using the discrete optimal control method. Numerical simulations are carried out in order to verify the efficiency of the controller. The findings show that the designed controller can be effective in suppressing chatter in both turning and milling processes as well as improve the stability of the cutting processes with the introduced time-delay. The authors discuss the influence of designed time-delay on control performance and robustness, and point out the advantages of using a time-delayed controller for controlling cutting dynamics.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051023-051023-7. doi:10.1115/1.4037103.

Oscillatory behavior and transfer properties of relay feedback systems with a linear plant including a fractional-order integrator are studied in this paper. An expression for system response in the time domain is obtained by means of short memory principle, Poincare return map, and Mittag–Leffler functions. On the basis of this expression, the frequency of self-excited oscillations is approximated. In addition, the locus of perturbed relay system (LPRS) is derived to analyze the input–output properties of the relay system. The presented analysis is supported by a numerical example.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051024-051024-12. doi:10.1115/1.4036814.

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay-coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Here, nearest-neighbor statistics are studied for uncorrelated random time series and contrasted with the corresponding deterministic and stochastic statistics. New composite FNN metrics are constructed and their performance is evaluated for deterministic, correlates stochastic, and white random time series. In addition, noise-contaminated deterministic data analysis shows that these composite FNN metrics are robust to noise. All FNN results are also contrasted with surrogate data analysis to show their robustness. The new metrics clearly identify random time series as not having a finite embedding dimension and provide information about the deterministic part of correlated stochastic processes. These metrics can also be used to differentiate between chaotic and random time series.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051025-051025-11. doi:10.1115/1.4036815.

The nonlinear modal coupling between the vibration modes of an arch-shaped microstructure is an interesting phenomenon, which may have desirable features for numerous applications, such as vibration-based energy harvesters. This work presents an investigation into the potential nonlinear internal resonances of a microelectromechanical systems (MEMS) arch when excited by static (DC) and dynamic (AC) electric forces. The influences of initial rise and midplane stretching are considered. The cases of one-to-one and three-to-one internal resonances are studied using the method of multiple scales and the direct attack of the partial differential equation of motion. It is shown that for certain initial rises, it is possible to activate a three-to-one internal resonance between the first and third symmetric modes. Also, using an antisymmetric half-electrode actuation, a one-to-one internal resonance between the first symmetric and the second antisymmetric modes is demonstrated. These results can shed light on such interactions that are commonly found on micro and nanostructures, such as carbon nanotubes.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051026-051026-7. doi:10.1115/1.4036761.

In this paper, explicit Runge–Kutta methods are investigated for numerical solutions of nonlinear dynamical systems with conserved quantities. The concept, ε-preserving is introduced to describe the conserved quantities being approximately retained. Then, a modified version of explicit Runge–Kutta methods based on the optimization technique is presented. With respect to the computational effort, the modified Runge–Kutta method is superior to implicit numerical methods in the literature. The order of the modified Runge–Kutta method is the same as the standard Runge–Kutta method, but it is superior in preserving the conserved quantities to the standard one. Numerical experiments are provided to illustrate the effectiveness of the modified Runge–Kutta method.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051027-051027-8. doi:10.1115/1.4037075.

The gyroscopic exercise tool called the “Power Ball,” used to train the antebrachial muscle, is focused on. The basin of attraction of the synchronous rolling motion in the state space of initial condition is investigated. The reduced model governing the synchronous rolling motion is used and its averaged equation is deduced. The first integral for the dynamical behavior of the synchronous rolling motion occurring in the power ball is obtained. The separatrix, which identifies the basin of attraction of the synchronous rolling motion, is derived, and the ranges of initial precession angle and the initial spin angular velocity for realizing the synchronous rolling motion are clarified. These theoretically obtained results are then experimentally confirmed. Furthermore, the influences of parameters to the basin of attraction are also clarified.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051028-051028-8. doi:10.1115/1.4037076.

In this paper, the trajectory controllability (T-controllability) of a nonlinear fractional-order damped system with time delay is studied. Existence and uniqueness of solution are obtained by using the Banach fixed point theorem and Green's function. Necessary and sufficient conditions of trajectory controllable for the nonlinear system are formulated and proved under a predefined trajectory. Modified fractional finite difference method is applied to the system for numerical approximation of its solution. The applicability of this technique is demonstrated by numerical simulation of two scientific models such as neuromechanical interaction in human snoring and fractional delayed damped Mathieu equation.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051029-051029-8. doi:10.1115/1.4036831.

The paper proposes a time-delayed hyperchaotic system composed of multiscroll attractors with multiple positive Lyapunov exponents (LEs), which are described by a three-order nonlinear retarded type delay differential equation (DDE). The dynamical characteristics of the time-delayed system are far more complicated than those of the original system without time delay. The three-order time-delayed system not only generates hyperchaotic attractors with multiscroll but also has multiple positive LEs. We observe that the number of positive LEs increases with increasing time delay. Through numerical simulations, the time-delayed system exhibits a larger number of scrolls than the original system without time delay. Moreover, different numbers of scrolls with variable delay and coexistence of multiple attractors with a variable number of scrolls are also observed in the time-delayed system. Finally, we setup electronic circuit of the proposed system, and make Pspice simulations to it. The Pspice simulation results agree well with the numerical results.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051030-051030-9. doi:10.1115/1.4037105.

A new non-Gaussian linearization method is developed for extending the analysis of Gaussian white-noise excited nonlinear oscillator to incorporate sinusoidal excitation. The non-Gaussian linearization method is developed through introducing a modulated correction factor on the linearization coefficient which is obtained by Gaussian linearization. The time average of cyclostationary response of variance and noise spectrum is analyzed through the correction factor. The validity of the present non-Gaussian approach in predicting the statistical response is supported by utilizing Monte Carlo simulations. The present non-Gaussian analysis, without imposing restrictive analytical conditions, can be obtained by solving nonlinear algebraic equations. The non-Gaussian solution effectively predicts accurate sinusoidal and noise response when the nonlinear system is subjected to both sinusoidal and white-noise excitations.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051031-051031-9. doi:10.1115/1.4037104.

The paper presents dynamic optimization methods used to calculate the optimal braking torques applied to wheels of an articulated vehicle in the lane following/changing maneuver in order to prevent a vehicle rollover. In the case of unforeseen obstacles, the nominal trajectory of the articulated vehicle has to be modified, in order to avoid collisions. Computing the objective function requires an integration of the equation of motions of the vehicle in each optimization step. Since it is rather time-consuming, a modification of the classical gradient method—variable metric method (VMM)—was proposed by implementing parallel computing on many cores of computing unit processors. Results of optimization calculations providing stable motion of a vehicle while performing a maneuver and a description and results of parallel computing are presented in this paper.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):051032-051032-12. doi:10.1115/1.4036989.

In order to achieve a correct representation of jointed structures within multibody dynamic simulations, an accurate computation of the nonlinear contact and friction forces between the contact surfaces is required. In recent history, trial vectors based on trial vector derivatives, the so-called joint modes, have been presented, which allow an accurate and efficient representation of this joint contact. In this paper, a systematic adaption of this method for preloaded bolted joints is presented. The new strategy leads to a lower number of additional joint modes required for accurate results and hence to lower computational time. Further, a major reduction of the computational effort for joint modes can be achieved. The potential and also possible limitations of the method are investigated using two numerical examples of a preloaded friction bar and a bolted piston rod bearing cap.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Comput. Nonlinear Dynam. 2017;12(5):054501-054501-5. doi:10.1115/1.4036117.

The control of the motion of nonholonomic systems is of practical importance from the perspective of robotics. In this paper, we consider the dynamics of a cartlike system that is both propelled forward by motion of an internal momentum wheel. This is a modification of the Chaplygin sleigh, a canonical nonholonomic system. For the system considered, the momentum wheel is the sole means of locomotive thrust as well the only control input. We first derive an analytical expression for the change in the heading angle of the sleigh as a function of its initial velocity and angular velocity. We use this solution to design an open-loop control strategy that changes the orientation of sleigh to any desired angle. The algorithm utilizes periodic impulsive torque inputs via the motion of the momentum wheel.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):054502-054502-5. doi:10.1115/1.4036547.

A complementary metal oxide semiconductor-operational transconductance amplifier (CMOS-OTA)-based implementation of fractional-order Newton–Leipnik chaotic system is introduced in this paper. The proposed circuit offers the advantages of electronic tunability of system order and on-chip integration due to MOS only design. The double strange attractor chaotic behavior of the system in consideration for an order of 2.9 has been demonstrated, and effectiveness of this chaotic system in preliminary secure message communication has also been presented. The theoretical predictions of the proposed implementation have been verified by hspice simulator using Austrian Microsystem (AMS) 0.35 μm CMOS process and subsequently compared with matlab simulink results. The power consumption of the system was 103.6 μW for standalone Newton–Leipnik chaotic generator.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2017;12(5):054503-054503-9. doi:10.1115/1.4036914.

General differential equations of motion in nonlinear forced vibration analysis of multilayered composite beams are derived by using the higher-order shear deformation theories (HSDT's). Viscoelastic properties of fiber-reinforced plastic composite materials are considered according to the Kelvin–Voigt viscoelastic model for transversely isotropic composite materials. The method of multiple scales is employed to perform analytical frequency amplitude relationships for superharmonic resonance. Parametric study is conducted by considering various geometrical and material parameters, employing HSDT's and first-order deformation theory (FSDT).

Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In