Authors:Nemati A; Yousefi S. Abstract: Our paper presents a new method to solve a class of fractional optimal control problems (FOCPs) based on the numerical polynomial approximation. In the proposed method, the fractional derivative in the dynamical system is considered in the Caputo sense. The approach used here is to approximate the state function by the Legendre orthonormal basis by using the Ritz method. Next, we apply a new constructed operational matrix to approximate fractional derivative of the basis. After transforming the problem into a system of algebraic equations, the problem is solved via the Newton's iterative method. Finally, the convergence of the new method is investigated and some examples are included to illustrate the effectiveness and applicability of the proposed methodology. PubDate: Thu, 25 Feb 2016 00:00:00 GMT

Authors:Shafei AM; Shafei HR. Abstract: This work presents a systematic method for the dynamic modeling of flexible multiple links that are confined within a closed environment. The behavior of such a system can be completely formulated by two different mathematical models. Highly coupled differential equations are employed to model the confined multilink system when it has no impact with the surrounding walls; and algebraic equations are exploited whenever this open kinematic chain system collides with the confining surfaces. Here, to avoid using the 4 × 4 transformation matrices, which suffers from high computational complexities for deriving the governing equations of flexible multiple links, 3 × 3 rotational matrices based on the recursive Gibbs-Appell formulation has been utilized. In fact, the main aspect of this paper is the automatic approach, which is used to switch from the differential equations to the algebraic equations when this multilink chain collides with the surrounding walls. In this study, the flexible links are modeled according to the Euler–Bernoulli beam theory (EBBT) and the assumed mode method. Moreover, in deriving the motion equations, the manipulators are not limited to have only planar motions. In fact, for systematic modeling of the motion of a multiflexible-link system in 3D space, two imaginary links are added to the n real links of a manipulator in order to model the spatial rotations of the system. Finally, two case studies are simulated to demonstrate the correctness of the proposed approach. PubDate: Thu, 25 Feb 2016 00:00:00 GMT

Authors:Ansari RR; Faghih Shojaei MM, Shakouri AH, et al. Abstract: Based on Mindlin's strain gradient elasticity and first-order shear deformation plate theory, a size-dependent quadrilateral plate element is developed in this paper to study the nonlinear static bending of microplates. In comparison with the classical first-order shear deformable quadrilateral plate element, the proposed element needs 15 additional nodal degrees-of-freedom (DOF) including derivatives of lateral deflection and rotations with respect to coordinates, which means a total of 20DOFs per node. Also, the developed strain gradient-based finite-element formulation is general so that it can be reduced to that on the basis of modified couple stress theory (MCST) and modified strain gradient theory (MSGT). In the numerical results, the nonlinear bending response of microplates for different boundary conditions, length-scale factors, and geometrical parameters is studied. It is revealed that by the developed nonclassical finite-element approach, the nonlinear behavior of microplates with the consideration of strain gradient effects can be accurately studied. PubDate: Thu, 25 Feb 2016 00:00:00 GMT

Authors:Balaji SS. Abstract: In this paper, a new method is presented for solving generalized nonlinear singular Lane–Emden type equations arising in the field of astrophysics, by introducing Bernoulli wavelet operational matrix of derivative (BWOMD). Bernoulli wavelet expansions together with this operational matrix method, by taking suitable collocation points, converts the given Lane–Emden type equations into a system of algebraic equations. Solution to the problem is identified by solving this system of equations. Further applicability and simplicity of the proposed method has been demonstrated by some examples and comparison with other recent methods. The obtained results guarantee that the proposed BWOMD method provides the good approximate solution to the generalized nonlinear singular Lane–Emden type equations. PubDate: Fri, 05 Feb 2016 00:00:00 GMT

Authors:Skruch P. Abstract: The paper presents a terminal sliding mode controller for a certain class of disturbed nonlinear dynamical systems. The class of such systems is described by nonlinear second-order differential equations with an unknown and bounded disturbance. A sliding surface is defined by the system state and the desired trajectory. The control law is designed to force the trajectory of the system from any initial condition to the sliding surface within a finite time. The trajectory of the system after reaching the sliding surface remains on it. A computer simulation is included as an example to verify the approach and to demonstrate its effectiveness. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Sandeep Reddy BB; Ghosal A. Abstract: A feedback controlled robot manipulator with positive controller gains is known to be asymptotically stable at a set point and for trajectory following in the sense of Lyapunov. However, when the end-effector of a robot or its joints are made to follow a time-dependent trajectory, the nonlinear dynamical equations modeling the feedback controlled robot can also exhibit chaotic motions and as a result cannot follow a desired trajectory. In this paper, using the example of a simple two-degree-of-freedom robot with two rotary (R) joints, we take a relook at the asymptotic stability of a 2R robot following a desired time-dependent trajectory under a proportional plus derivative (PD) and a model-based computed torque control. We demonstrate that the condition of positive controller gains is not enough and the gains must be large for chaos not to occur and for the robot to asymptotically follow a desired trajectory. We apply the method of multiple scales (MMS) to the two nonlinear second-order ordinary differential equations (ODEs), which describes the dynamics of the feedback controlled 2R robot, and derive a set of four first-order slow flow equations. At a fixed point, the Routh–Hurwitz criterion is used to obtain values of proportional and derivative gains at which the controller is asymptotically stable or indeterminate. For the model-based control, a parameter representing model mismatch is used and the controller gains for a chosen mismatch parameter value are obtained. From numerical simulations with controller gain values in the indeterminate region, it is shown that for some values, the nonlinear dynamical equations are chaotic, and hence, the 2R robot cannot follow the desired trajectory and be asymptotically stable. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Krishnasamy VS; Razzaghi MM. Abstract: In this paper, a numerical method for solving the fractional Bagley–Torvik equation is given. This method is based on using fractional Taylor vector approximation. The operational matrix of the fractional integration for fractional Taylor vector is given and is utilized to reduce the solution of the Bagley–Torvik equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Luo R; Zeng Y. Abstract: This paper investigates the control and synchronization of a class of chaotic systems with external disturbance. The chaotic systems are assumed that only the output state variable is available. By using the output state variable, two types synchronization schemes, i.e., the chaos-based synchronization and the observer-based synchronization schemes, are discussed. Some novel criteria for the control and synchronization of a class of chaotic systems with external disturbance are proposed. The unified chaotic system is taken as an example to demonstrate the efficiency of the proposed approach. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Pappalardo CM; Yu Z, Zhang X, et al. Abstract: In this paper, a rational absolute nodal coordinate formulation (RANCF) thin plate element is developed and its use in the analysis of curved geometry is demonstrated. RANCF finite elements are the rational counterpart of the nonrational absolute nodal coordinate formulation (ANCF) finite elements which employ rational polynomials as basis or blending functions. RANCF finite elements can be used in the accurate geometric modeling and analysis of flexible continuum bodies with complex geometrical shapes that cannot be correctly described using nonrational finite elements. In this investigation, the weights, which enter into the formulation of the RANCF finite element and form an additional set of geometric parameters, are assumed to be nonzero constants in order to accurately represent the initial geometry and at the same time preserve the desirable ANCF features, including a constant mass matrix and zero centrifugal and Coriolis generalized inertia forces. A procedure for defining the control points and weights of a Bezier surface defined in a parametric form is used in order to be able to efficiently create RANCF/ANCF FE meshes in a straightforward manner. This procedure leads to a set of linear algebraic equations whose solution defines the RANCF coordinates and weights without the need for an iterative procedure. In order to be able to correctly describe the ANCF and RANCF gradient deficient FE geometry, a square matrix of position vector gradients is formulated and used to calculate the FE elastic forces. As discussed in this paper, the proposed finite element allows for describing exactly circular and conic sections and can be effectively used in the geometry and analysis modeling of multibody system (MBS) components including tires. The proposed RANCF finite element is compared with other nonrational ANCF plate elements. Several numerical examples are presented in order to demonstrate the use of the proposed RANCF thin plate element. In particular, the FE models of a set of rational surfaces, which include conic sections and tires, are developed. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Abstract: Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Simo Domguia UU; Abobda LT, Woafo PP. Abstract: A capacitive microelectromechanical system (MEMS) powered by a Hindmarsh–Rose (HR)-like electronic oscillator is considered not only for actuation purposes but also to mimic the action of a natural pacemaker and nerves on a cardiac assist device or artificial heart. It is found that the displacement/flexion of the MEMS undergoes bursting and spiking oscillations resulting from the transfer of the electronic signal, when one varies the damping coefficient and the applied DC current. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Trigeassou J; Maamri N, Oustaloup A. Abstract: Lyapunov stability of linear commensurate order fractional systems is revisited with the energy balance principle. This methodology is based on the concept of fractional energy stored in inductor and capacitor components, where natural decrease of the stored energy is caused by internal Joule losses. Previous stability results are interpreted, thanks to an equivalent fictitious fractional RLC circuit. Energy balance is used to analyze the usual Lyapunov function and to provide a physical interpretation to the weighting positive matrix. Moreover, the classical linear matrix inequality (LMI) condition is interpreted in terms of internal and external Joule losses. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Wasfy TM; Yildiz C, Wasfy HM, et al. Abstract: A necessary condition for high-fidelity dynamic simulation of belt-drives is to accurately predict the belt stresses, pulley angular velocities, belt slip, and belt-drive energy efficiency. In previous papers, those quantities were predicted using thin shell, beam, or truss elements along with a Coulomb friction model. However, flat rubber belts have a finite thickness and the reinforcements are typically located near the top surface of the belt. In this paper, the effect of the belt thickness on the aforementioned response quantities is studied using a two-pulley belt-drive. The belt rubber matrix is modeled using three-dimensional brick elements. Belt reinforcements are modeled using one-dimensional truss elements at the top surface of the belt. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Cao W; Hua S, Zhang S, et al. Abstract: Different from conventional injection molding (CIM), injection/compression molding (ICM) evolves boundary variation in gapwise direction. In order to describe melt flow characteristics in ICM correctly, a new material derivative based on arbitrary Lagrangian Eulerian (ALE) description was introduced to modify the material derivatives in the governing and constitutive equations. To avoid large amount of calculation and weak stability of integral numerical method, an iterative approach employing twofold iterations was proposed to decouple the interdependence between velocity, stress, and temperature. The initial values of material parameters in constitutive equations were obtained or fitted by rheological experiments. The ICM experiments for an iso-thick and a var-thick rectangular panel were carried out to validate the proposed method and find the special characteristics of ICM. In addition, the photoelastic tests on a quarter of spherical part processed by ICM were conducted to identify the relationship between residual flow-induced stress distributions and flow fields. Both simulations and experiments show that the pressure profile displays a plateau during compression, temperature decreases with time according to exponential law, large flow-induced stress originates in thick transitional region, flow start, and flow end areas, and gravity has significant effect on meltfront for thick part ICM. The good agreement between experiments and simulations indicates that the current method can properly describe the flow characteristics of ICM. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Nguyen-Van T; Hori N. Abstract: A discretization method is proposed for a rather general class of nonlinear continuous-time systems, which can have a piecewise-constant input, such as one under digital control via a zero-order-hold device. The resulting discrete-time model is expressed as a product of the integration-gain and the system function that governs the dynamics of the original continuous-time system. This is made possible with the use of the delta or Euler operator and makes comparisons of discrete and continuous time systems quite simple, since the difference between the two forms is concentrated into the integration-gain. This gain is determined in the paper by using the Riccati approximation of a certain gain condition that is imposed on the discretized system to be an exact model. The method is shown to produce a smaller error norm than one uses the linear approximation. Simulations are carried out for a Lotka–Volterra and an averaged van der Pol nonlinear systems to show the superior performance of the proposed model to ones known to be online computable, such as the forward-difference, Kahan's, and Mickens' methods. Insights obtained should be useful for developing digital control laws for nonlinear continuous-time systems, which is currently limited to the simplest forward-difference model. PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Authors:Recuero AM; Escalona JL. Abstract: This work is devoted to the validation of a computational dynamics approach previously developed by the authors for the simulation of moving loads interacting with flexible bodies through arbitrary contact modeling. The method has been applied to the modeling and simulation of the coupled dynamics of railroad vehicles moving on deformable tracks with arbitrary undeformed geometry. The procedure presented makes use of a fully arbitrary Lagrangian–Eulerian (ALE) description of the long flexible solid (track) whose mechanical properties may be captured using a dynamics-preserving selection of modes, e.g., via a Padé approximation of a transfer function. The modes accompany the contact interaction rather than being referred to a fixed frame, as it occurs in the finite-element floating frame of reference formulation. In the method discussed in this paper, the mesh, which moves through the long flexible solid, is defined in the trajectory coordinate system (TCS) used to describe the dynamics of the set of bodies (vehicle) that interact with the long flexible structure. For this reason, the selection of modes can be focused on the preservation of the dynamics of the structure instead of having to ensure the structure's static displacement convergence due to the motion of the load. In this paper, the validation of the so-called trajectory coordinate system/moving modes (TCS/MM) method is performed in four different aspects: (a) the analytical mechanics approach is used to obtain the equations of motion in a nonmaterial volume, (b) the resulting equations of motion are compared to the classical discretization procedures of partial differential equations (PDE), (c) the suitability of the moving modes (MM) to describe deformation due to variable-velocity moving loads, and (d) the capability of the finite nonmaterial volume to describe the dynamics of an infinitely long flexible body. Validation (a) is completely general. However, the particular example of a moving load applied to a straight beam resting on a Winkler foundation, with known semi-analytical solution, is used to perform validations (b), (c), and (d). PubDate: Wed, 03 Feb 2016 00:00:00 GMT

Abstract: This paper presents a method for solving the dynamic equations of multibody systems containing both rigid and flexible bodies. The proposed method uses independent coordinates and projects the dynamic equations on the constraint tangent manifold by means of a velocity transformation matrix. It can be used with a wide variety of integration formulae, considering both fixed and variable stepsizes. Topological semirecursive methods are used to take advantage of the relatively small number of parameters needed. An in depth implementation analysis is performed in order to evaluate the terms involved in the integration process. Numerical and stability issues are also discussed. PubDate: Wed, 03 Feb 2016 00:00:00 GMT