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The post-buckling behavior of a beam that is subjected to lateral constraints is of relevance to a range of medical and engineering applications, such as endoscopic examination of internal organs, the insertion of a guidewire into an artery in-stent procedures, root growth, deep-drilling, and more. In this paper, we address a disconnect between the existing literature and the reality of these systems, in which the lateral constraints are flexible and experience nonlinear deformations. As a step towards bridging this gap, we consider a beam undergoing planar deformations that is laterally constrained by a nonlinear springy wall, i.e., a wall that is laterally pushed by the beam against a nonlinear spring. Based on a simplified mathematical model, we obtain closed-form analytical solutions, which provide valuable insights and intuition. For example, we show that important features of the behavior, such as the transition from point contact to line contact and switching to the next mode, are dictated solely by a non-dimensional force, regardless of all other parameters of the system, and that the full description of the behavior is possible by means of two non-dimensional quantities that describe the relative stiffness of the nonlinear spring compared to that of the beam. The results also highlight the fundamental differences between the behavior with a stiffening spring or with a softening spring, such as the number of attainable modes and the monotonicity of the overall force-displacement relation. These results are then validated by experiments. [ABSTRACT FROM AUTHOR]

Face gear drive has been widely investigated in the aviation field as a power split device on the helicopter main reducer. However, high-speed and heavy-load condition makes the face gear prone to tooth surface pitting, leading to deterioration of transmission performance. To improve the load-bearing capacity of face gear, this paper proposes a design and modification method based on gear skiving process for face gear drives. First, gear skiving mathematical models for a face gear pair are established, and a continuously profile-shifted modification method is presented based on these mathematical models. Then, the load-bearing capacity of the modified face gear pair is minutely analyzed and discussed through contact analysis. The contact stress of the modified face gear is reduced by 47.78% on the right side and 41.1% on the left side compared with an unmodified face gear. Finally, gear skiving experiments and meshing performance tests of face gear pairs are conducted. The measurement results show consistency with the calculation results. Thus, the proposed design and continuously profile-shifted modification method based on the gear skiving process is feasible and contributes to load-bearing capacity improvement. [ABSTRACT FROM AUTHOR]

In this paper, we show how autonomous vehicles performing a certain task can be controlled from one command center in order to achieve certain goals. The command center provides individual feedback gains to each vehicle in the form of one compounded feedback gain that in fact carries feedback gain information for each individual vehicle. Vehicles may be of different nature: satellites, cars, tanks, drowns, robots, unmanned aircraft, underwater vehicles, and ships. It is assumed that their dynamic is weakly coupled, namely, dynamics of each individual vehicle is weakly coupled to dynamics of all other vehicles and that they have the same control input. The weak coupling among the vehicles is represented either by physical interactions among vehicles or coordinating or communication signals. The results obtained are applicable to vehicles having different mathematical linear/linearized state space models. In the case when no interaction/coordination/communication among vehicles is present, and all feedback signals come from the command center (central controller) controller, the vehicle mathematical models can be identical. An important feature of the presented results is that different local feedback controllers can be facilitated for different vehicles using a unique global feedback controller signal designed by the command center. In this paper, we will consider cases of two and three vehicles, but the presented multistage feedback design methodology can be potentially extended to N vehicles. The presentation is done in continuous time. Similar derivations hold in the discrete-time domain. [ABSTRACT FROM AUTHOR]

This paper presents a physics-constrained data-driven method that variationally embeds measured data in the modeling and analysis framework. The physics-based model is augmented with sparse but high-fidelity data through a variationally derived loss function. The structure of the loss function is analyzed in the context of variational correction to the modeled response wherein loss function penalizes the difference in the modeled response from the measured data that represents the local response of the system. The variationally embedded measured data (VEMD) method results in forward simulations that are not only driven by boundary and initial conditions but are also augmented by real measurements taken at only a small number of observation points. In the context of forward simulations, the proposed approach can be seen as inducing inductive biases that exploit the difference between the computed and measured quantities in the parametric space. With the help of a model problem, we show that the proposed method learns from the sparse high-fidelity datasets while preserving conservation properties of the balance laws. Method is applied to a non-smooth model problem and the mathematical attributes of the formulation are investigated in the context of high-fidelity sparse datasets. [ABSTRACT FROM AUTHOR]

Researchers have been studying the pain sensation extensively in the past few decades. Quantitative simulation and theoretical modeling of pain sensation based on experimental results are necessary for pain research. Many theories have been proposed to explain the mechanism of pain from molecular, cellular, and neuron network perspectives. But some phenomena in pain sensation are not fully understood, including wind-up and ramp-off. This paper focused on the theoretical model of wind-up and ramp-off phenomena in the pain sensation. With the addition of the transduction model, the generation mechanism of wind-up and ramp-off is better explained. The simulations were carried out to analyze the skin pain sensation under the mechanical stimulus, consisting of four different parts: the mechanical model of skin, transduction, transmission, modulation, and perception. The stress distribution on the skin was obtained based on the elastic theory. And the modified Hodgkin and Huxley model and the mathematical model of gate control theory were utilized to analyze the process of transduction, modulation, and perception, respectively. The numerical experiments demonstrated the wind-up occurs with a frequent stimulus of 1 Hz and 2 Hz, and ramp-off appears with the withdrawal of constant mechanical stimulus, which could contribute to the understanding of the pain sensation mechanism. [ABSTRACT FROM AUTHOR]

Ultrasonic-assisted magnetic abrasive flow machining (UAMAFM) process shows enhanced finishing performance compared to conventional abrasive flow machining (AFM). In this present research paper, mathematical models for MR and Ra have been developed for the UAMAFM process by considering both steady-state and transient phenomena. The external ultrasonic and magnetic field assistance enhanced the velocity and length of contact of active abrasives, calculated from the kinematic analysis. The resultant finishing forces have also been evaluated by considering these external aids. The steady-state material removal per finishing cycle remains constant and depends on the velocity of motion, length of contact, resulting forces, number of active abrasives, and work material hardness. The transient material removal per finishing cycle was calculated in terms of the volume of irregularities present over the work surface, i.e., initial surface roughness. The mathematical model for surface roughness was developed in terms amount of material removed (MR), and initial (Ra0) and critical surface roughness (Racr)?. The predicted values of material removed and surface roughness from developed mathematical models agreed with experimental results with a deviation of 7.80% and 2.44%, respectively. [ABSTRACT FROM AUTHOR]

The implantation of stents and instruments with capillary action demands super-finished internal surfaces of the manufactured product. Elasto-abrasives magneto-spiral finishing (EAMSF) is the attempt made in this paper to enhance finishing productivity by incorporating the abrasive flow in spiral motion due to the presence of the magnetic field. Here, novel impregnated elasto-magnetic abrasive particles (IMPs) are used in a magnetic field-assisted environment to polish the inner walls of the workpiece. In EAMSF, magnetic force provides excess finishing pressure to the abrasives. In contrast, the high-impact polystyrene (HIPS) elasticity absorbs the extra force of the IMPs on the finishing surface. An Indigenous mathematical relation considering the physics of this superfinishing process indicating material removal shows a close resemblance to the experimental results with an error percentage of 1.03 has been developed. The results of the experimentation reveal that 50% concentration of abrasives and a magnetic field density of 18mT yield a superior surface finish with a Ra value equal to 0.053 µm and maximum material removal of 6.9 mg, while in the absence of a magnetic field, excellent surface finish with a Ra = 0.266 µm and maximum material removal of 5.4 mg is achieved. In the presence of magnetic field density, significant enhancement of material removal, surface finish, and burr removal is observed. Finishing the surface at 50% abrasive concentration with a magnetic field represents regular finishing, and the trench marks on the original surface are removed after finishing. [ABSTRACT FROM AUTHOR]