Accepted Manuscripts

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
Beibei Guo, Wei Jiang and Chiping Zhang
J. Comput. Nonlinear Dynam   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 equation. 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 the smaller computational work and higher precision
TOPICS: Differential equations, Numerical analysis, Algorithms
Anwar Sadath, Vinu V. and Chandrika Prakash Vyasarayani
J. Comput. Nonlinear Dynam   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 over-estimates the critical flow velocity. For certain high flow velocities, limit cycles exist for axial loads beyond the critical buckling load.
TOPICS: Stress, Heat exchangers, Vibration, Cross-flow, Flow (Dynamics), Delay differential equations, Buckling, Flutter (Aerodynamics), Bifurcation, Fluids, Dynamics (Mechanics), Stability, Chaos, Cylinders, Galerkin method, Nonlinear dynamics, Limit cycles
Louay S. Yousuf and Dan B. Marghitu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035824
A cam is a mechanical device used to transmit motion to a follower by direct contact. In this study a cam and follower mechanism is analyzed. The proposed cam can be used for controlling valve and also on motor car camshafts to operate the engine valves. The dynamic analysis presents follower displacement driven by a cam rotating at a uniform angular velocity. There is a clearance between the follower and the guide. The mechanism is analyzed using computer simulations taking into account the impact and the friction between the flat-faced follower and the guide. Four different follower guide's clearances have been used in the simulations and the Largest Lyapunov Exponents have been calculated. An experimental set up is developed to capture the general planar motion of the cam and follower. The measures of the cam and the follower positions are obtained through high-resolution optical encoders (markers) mounted on the cam and follower shaft. The effect of guide clearance is investigated for different angular velocities of the cam. The largest Lyapunov exponents for the simulated and experimental data are analyzed and selected.
TOPICS: Friction, Computer simulation, Engines, Simulation, Resolution (Optics), Clearances (Engineering), Dynamic analysis, Engineering simulation, Valves, Camshafts, Displacement, Simulation results
Saleh Ashrafi and Ali Khalili Golmankhaneh
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035718
In this manuscript we have used the recently developed Fα-calculus for calculating the energy straggling function in the fractal distributed structures. We have shown that such 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.
TOPICS: Energy dissipation, Fokker-Planck equation, Fractals
Joseph Hewlett, Laszlo Kovacs, Alfonso Callejo, Paul G. Kry, Jozsef Kovecses and Jorge Angeles
J. Comput. Nonlinear Dynam   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 new time-stepping scheme proposed by Tournier et al., ``Stable constrained dynamics,'' ACM transactions on Graphics, 2015, which approximates a full non-linear 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.
TOPICS: Dynamics (Mechanics), Stability, Simulation, Energy dissipation, Chain, Jacobian matrices, Linear systems, Numerical stability, Stiffness
Mergen H. Ghayesh, Hamed Farokhi, Alireza Gholipour, Shahid Hussain and Maziar Arjomandi
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035214
This paper aims at analysing the size-dependent nonlinear dynamical behaviour of a geometrically imperfect microbeam made of a functionally graded material, taking into account the longitudinal, transverse, and rotational motions. The size-dependent property is modelled by means of the modified couple stress theory, the shear deformation and rotary inertia are modelled using the Timoshenko beam theory, and the graded material property in the beam thickness direction is modelled via the Mori-Tanaka homogenisation 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 utilised 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.
TOPICS: Resonance, Microbeams, Rotation, Stress, Rotational inertia, Materials properties, Eigenvalues, Functionally graded materials, Shear deformation, Timoshenko beam theory
Jeremy Kolansky and Corina Sandu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4031194
The Generalized Polynomial Chaos mathematical technique, when integrated with the Extended Kalman Filter method, provides a parameter estimation and state tracking method. The truncation of the series expansions degrades the link between parameter convergence and parameter uncertainty which the filter uses to perform the estimations. An empirically derived correction for this problem is implemented, that maintains the original parameter distributions. A comparison is performed to illustrate the improvements of the proposed approach. The method is demonstrated for parameter estimation on a regression system, where it is compared to the Recursive Least Squares method.
TOPICS: Kalman filters, Parameter estimation, Polynomials, Chaos, Filters, Uncertainty

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