Abstract: One of the major challenges in dynamics of multibody systems is to handle redundant constraints appropriately. The box friction model is one of the existing approaches to formulate the contact and friction phenomenon as a mixed linear complementarity problem (MLCP). In this setting, the contact redundancy can be handled by relaxing the constraints, but such a technique might suffer from certain drawbacks, specially in the case of large number of redundant constraints. Most of the common pivoting algorithms used to solve the resulting mixed complementarity problem might not converge when the relaxation terms are chosen as small as they should be. To overcome the aforementioned shortcoming, we propose a novel approach which takes advantage of the sparse structure of the formulated MLCP. This novel approach reduces the sensitivity of the solution of the problem to the relaxation terms and decreases the number of required pivots to obtain the solution, leading to shorter computational times. Furthermore, as a result of the proposed approach, much smaller relaxation terms can be used while the solution algorithms converge. PubDate: Fri, 16 Sep 2016 00:00:00 GMT

Authors:Jamroziak K; Bocian M, Kulisiewicz M. Abstract: The paper presents a new way to determine some dynamical properties of materials modeled by the so-called degenerate system. The system is an element (subsystem) of any complex multidegree-of-freedom system. This subsystem follows from assumption of standard rheological model of stress–strain law of the materials. It is assumed that on the complex system act a set of random excitation forces. For this coincidence, a so-called energy balance equation was developed and was used to create a suitable identification method. The equations were derived for any differentiable function of elasticity. The stationary random process of the system response was assumed in the whole algorithm. As it was proved, in this case, instead of calculating appropriate fields of the hysteresis loop of suitable signals, an application of average values of the input and output signals and their proper combinations can be used. It is assumed that the elastic damping interaction force in the complex dynamical subsystem is described by the function F(x,x˙), in which x is a deformation of the identified degenerated element and denotes a relative displacement between some appropriate neighboring masses of the system. Some numerical examples of the application are shown. PubDate: Fri, 16 Sep 2016 00:00:00 GMT

Authors:Singh AK; Yadav VK, Das SS. Abstract: In this article, the authors have proposed a novel scheme for the dual combination synchronization among four master systems and two slave systems for the fractional order complex chaotic systems. Dual combination synchronization for the integer order has already been investigated in real space; but for the case of fractional order in complex space, it is the first of its kind. Due to complexity and presence of additional variable, it will be more secure and interesting to transmit and receive signals in communication theory. Based on the Lyapunov stability theory, six complex chaotic systems are considered and corresponding controllers are designed to achieve synchronization. The special cases, such as combination synchronization, projective synchronization, complete synchronization, and many more, can be derived from the proposed scheme. The corresponding theoretical analysis and numerical simulations are shown to verify the feasibility and effectiveness of the proposed dual combination synchronization scheme. PubDate: Fri, 16 Sep 2016 00:00:00 GMT

Authors:Sharifi M; Salarieh H, Behzadipour S. Abstract: In this paper, the optimal performance of a planar humanlike musculoskeletal arm is investigated during reaching movements employing an optimal control policy. The initial and final states (position and velocity) are the only known data of the response trajectory. Two biomechanical objective functions are taken into account to be minimized as the central nervous system (CNS) strategy: (1) a quadratic function of muscle stresses (or forces), (2) total time of movement plus a quadratic function of muscle stresses. A two-degress of freedom (DOF) nonlinear musculoskeletal arm model (for planar movements) with six muscle actuators and four state variables is used in order to evaluate the proposed optimal policy, while the constraints of the arm motion and muscle forces are considered mathematically. The nonlinear differential equations of this optimal control problem with the first objective function are solved using the method of variation of extremals (VE). For the second objective function, a modified version of the VE method is employed. Accordingly, the optimal total time of the motion is predicted via the second objective function in addition to the optimal trajectory and forces that are also predicted using the first objective function. The influence of the motion time duration on the optimal trajectory is shown and discussed. Finally, the obtained optimal trajectories are compared to the experimental trajectories of the human arm movements. PubDate: Fri, 09 Sep 2016 00:00:00 GMT

Authors:Moghadasi A; Held A, Seifried R. Abstract: In recent years, topology optimization has been used for optimizing members of flexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for flexible multibody systems is presented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between flexible members in a multibody system using revolute joints is seen in many applications. Moreover, the modeling accuracy of the bearing area is shown to be influential on the shape of the optimized structure. In this work, the flexible bodies are incorporated in the multibody simulation using the floating frame of reference formulation, and their elastic deformation is approximated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints using Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Furthermore, an application example of a flexible multibody system with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization result is performed with an equivalent system which is modeled with nonlinear finite elements. PubDate: Fri, 09 Sep 2016 00:00:00 GMT

Authors:Veldman DM; Fey RB, Zwart H. Abstract: Single-degree-of-freedom (single-DOF) nonlinear mechanical systems under periodic excitation may possess multiple coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. In energy-harvesting applications, the large-amplitude periodic solutions are preferred, and in vibration reduction problems, the small-amplitude periodic solutions are desired. We propose a method to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution, which requires only limited information about the applied force. We illustrate our method for a single-degree-of-freedom model of a rectangular plate with geometric nonlinearity, which takes the form of a monostable forced Duffing equation with hardening nonlinearity. PubDate: Tue, 06 Sep 2016 00:00:00 GMT

Authors:Chang S. Abstract: A structure-dependent integration method may experience an unusual overshooting behavior in the steady-state response of a high frequency mode. In order to explore this unusual overshooting behavior, a local truncation error is established from a forced vibration response rather than a free vibration response. As a result, this local truncation error can reveal the root cause of the inaccurate integration of the steady-state response of a high frequency mode. In addition, it generates a loading correction scheme to overcome this unusual overshooting behavior by means of the adjustment the difference equation for displacement. Apparently, these analytical results are applicable to a general structure-dependent integration method. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Just LW; DeLuca AM, Palazotto AN. Abstract: The research question addressed is whether a lighter than air vehicle (LTAV), which uses an internal vacuum to become positively buoyant, can be designed to provide extended loiter for U.S. Air Force applications. To achieve a vacuum, internal gases are evacuated from the vessel, which creates a dynamic response in the supporting structural frame. This paper considers the frame of an icosahedron shaped LTAV subject to external atmospheric pressure evacuated at varying rates. A static finite element analysis documented in previous research revealed a snapback phenomenon in the frame members under certain loading conditions. A nonlinear chaotic response was observed when a dynamic analysis was conducted with the same boundary conditions used in the static analysis. The chaotic response for a variety of boundary conditions, generated by varying the rate of evacuation, similar to a ramp input, is determined. An analysis of the dynamic response is determined nonlinearly using a method that relies on a reference point distribution of external pressures to distribute the surface force across the frame. A novel method of combining the power spectral density with a Lyapunov exponent was used to determine the degree of nonlinearity and chaotic response for each boundary condition examined. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Zhong H; Wang Q, Yu J, et al. Abstract: A novel characteristic model-based discrete adaptive sliding mode control (SMC) scheme is proposed for vibration attenuation of the space frame. First, this paper establishes a characteristic model as real time model for the space structure. The characteristic model is simple and accurate. Furthermore, a novel discrete sliding mode control strategy is proposed with low chattering and strong robustness. In addition, the stability of the closed-loop control system is proved. Finally, simulation results show the effectiveness and strong robustness of the proposed scheme. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Li Z; Jiang J, Tian Z. Abstract: In this paper, stochastic responses and behaviors of a nonlinear rotor system with the fault of uncertain parallel misalignment and under random fluid-induced forces are investigated. First, the equations of motion of the rotor system are derived by taking into account the nonlinear journal bearings, the unsymmetrical section of the shaft, and the displacement constraint between the two adjacent rotors. Then, the modeling on uncertainties of misalignment and random fluid-induced forces are developed based on the polynomial chaos expansion (PCE) technique, where the misalignment is modeled as a bounded random variable with parameter η distribution and the fluid-induced force as a random variable with standard white noise process. Finally, examples on the stochastic dynamic behaviors of the nonlinear generator-rotor system are studied, and the influences of the uncertainties on the effects of shaft misalignment, the stochastic behaviors near bifurcation point as well as the distribution of the system responses are well demonstrated. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Kim J; Harne RL, Wang KW. Abstract: Accurately predicting the onset of large behavioral deviations associated with saddle-node bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and ever-present influences. As a result, it is critical to simultaneously account for these two factors toward the estimation of parameters that may induce sudden bifurcations. Here, a new analytical formulation is presented to accurately determine the probable time at which a system undergoes an escape event as governing parameters are swept toward a saddle-node bifurcation point in the presence of noise. The double-well Duffing oscillator serves as the archetype system of interest since it possesses a dynamic saddle-node bifurcation. The stochastic normal form of the saddle-node bifurcation is derived from the governing equation of this oscillator to formulate the probability distribution of escape events. Non-stationarity is accounted for using a time-dependent bifurcation parameter in the stochastic normal form. Then, the mean escape time is approximated from the probability density function (PDF) to yield a straightforward means to estimate the point of bifurcation. Experiments conducted using a double-well Duffing analog circuit verifies that the analytical approximations provide faithful estimation of the critical parameters that lead to the non-stationary and noise-activated saddle-node bifurcation. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Abstract: We study the dynamics of targeted energy transfers in suppressing chatter instability in a single-degree-of-freedom (SDOF) machine tool system. The nonlinear regenerative (time-delayed) cutting force is a main source of machine tool vibrations (chatter). We introduce an ungrounded nonlinear energy sink (NES) coupled to the tool, by which energy transfers from the tool to the NES and efficient dissipation can be realized during chatter. Studying variations of a transition curve with respect to the NES parameters, we analytically show that the location of the Hopf bifurcation point is influenced only by the NES mass and damping coefficient. We demonstrate that application of a well-designed NES renders the subcritical limit cycle oscillations (LCOs) into supercritical ones, followed by Neimark–Sacker and saddle-node bifurcations, which help to increase the stability margin in machining. Numerical and asymptotic bifurcation analyses are performed and three suppression mechanisms are identified. The asymptotic stability analysis is performed to study the domains of attraction for these suppression mechanisms which exhibit good agreement with the bifurcations sets obtained from the numerical continuation methods. The results will help to design nonlinear energy sinks for passive control of regenerative instabilities in machining. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Saghir S; Younis MI. Abstract: This article presents and compares different approaches to develop reduced-order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First, we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced-order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches is made for this case. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Zhang Y; Vakakis AF. Abstract: We study the transient responses of linear and nonlinear semi-infinite periodic media on linear elastic foundations under suddenly applied, high-frequency harmonic excitations. We show that “dynamic overshoot” phenomena are realized whereby, due to the high-rate of application of the high-frequency excitations, coherent traveling responses are propagating to the far fields of these media; and this, despite the fact that the high frequencies of the suddenly applied excitations lie well within the stop bands of these systems. For the case of a linear one-dimensional (1D) spring-mass lattice, a leading-order asymptotic approximation in the high frequency limit of the suddenly applied harmonic excitation shows that the transient dynamic overshoot is expressed in terms of the Green's function at its free end. Then, a two-dimensional (2D) strongly nonlinear granular network is considered, composed of two semi-infinite, ordered homogeneous granular lattices mounted on linear elastic foundations and coupled by weak linear coupling terms. A high-frequency harmonic excitation is applied to one of the granular lattices—designated as the “excited lattice”, with the other lattice designated as the “absorbing” one. The resulting dynamic overshoot phenomenon consists of a “pure” traveling breather, i.e., of a single propagating oscillatory wavepacket with a localized envelope, resulting from the balance of discreteness, dispersion, and strong nonlinearity. The pure breather is asymptotically studied by a complexification/averaging technique, showing nearly complete but reversible energy exchanges between the excited and absorbing lattices as the breather propagates to the far field. Verification of the analytical approximations with direct numerical simulations is performed. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Chen YM; Lv ZR, Liu JK. Abstract: Fourier series expansion (FSE) plays a pivotal role in frequency domain analysis of a wide variety of nonlinear dynamical systems. To the best of our knowledge, there are two general approaches for FSE, i.e., a collocation method (CM) previously proposed by the authors and the classical discrete FSE. Though there are huge applications of these methods, it still remains much less understood in their relationship and error estimation. In this study, we proved that they are equivalent if time points are uniformly chosen. Based on this property, more importantly, the error was analytically estimated for both discrete Fourier expansion (DFE) and CM. Furthermore, we revealed that the accuracy of frequency domain solutions cannot be improved by increasing the number of time points alone, whereas it absolutely depends upon the truncated number of harmonics. It indicates that an appropriate number of time points should be chosen in FSE if frequency domain solutions are targeted for nonlinear dynamical systems, especially those with complicated functions. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Kim P; Rogers J, Sun J, et al. Abstract: Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Authors:Shah VV; Goyal S, Palanthandalam-Madapusi HJ. Abstract: Parkinson's disease (PD) is a neurodegenerative disorder characterized by increased response times leading to a variety of biomechanical symptoms, such as tremors, stooping, and gait instability. Although the deterioration in biomechanical control can intuitively be related to sluggish response times, how the delay leads to such biomechanical symptoms as tremor is not yet understood. Only recently has it been explained from the perspective of feedback control theory that delay beyond a threshold can be the cause of Parkinsonian tremor (Palanthandalam-Madapusi and Goyal, 2011, “Is Parkinsonian Tremor a Limit Cycle?” J. Mech. Med. Biol., 11(5), pp. 1017–1023). The present paper correlates several observations from this perspective to clinical facts and reinforces them with simple numerical and experimental examples. Thus, the present work provides a framework toward developing a deeper conceptual understanding of the mechanism behind PD symptoms. Furthermore, it lays a foundation for developing tools for diagnosis and progress tracking of the disease by identifying some key trends. PubDate: Thu, 01 Sep 2016 00:00:00 GMT

Abstract: The effect of impulsive stiffness variation to the modal energy content of dynamical systems is investigated in this contribution. Therefore, the overall number of modes of vibration is divided into a set of lower and a set of higher modes. It is shown analytically that impulsive stiffness variation, applied in a state-dependent, nonlinear manner allows a targeted transfer of discrete amounts of energy across mode sets. Analytical conditions are presented, holding for a transfer from the lower to the higher mode set or vice versa. The existence of transfer cases where no energy crosses the system boundary, i.e., the energy-neutral case, is investigated in a comprehensive manner. Some numerical investigations underline that shifting vibration energy to higher modes causes a faster decay of vibration amplitudes, as the damping properties of a mechanical system can be utilized more effectively. Moreover, it is demonstrated that the proposed approach allows to eliminate vibration frequencies from the frequency spectrum of mechanical systems. PubDate: Thu, 01 Sep 2016 00:00:00 GMT