An official website of the United States government
Abstract This paper examines the effect of viscoelasticity on the dynamic behavior of a bistable dome-shaped structure represented as a lumped parameter viscoelastic von Mises truss. The viscoelastic system is governed by a third order jerk equation. The presence of viscoelasticity also introduces additional time scales and degrees of freedom into the problem when compared to their viscous counterparts, thus making the study of these systems in the presence of harmonic loading even more interesting. It is highly likely that the system would exhibit non-regular behavior for some combination of forcing frequency and forcing amplitude. With this motivation, we start by studying the dynamics of a harmonically forced von Mises truss in the presence of viscous damping only. This leads to a Duffing type equation with an additional quadratic non-linearity. We demonstrate some of the rich dynamic behavior that this system exhibits in some parameter ranges. This provides useful insight into the possible behavior of the viscoelastic system. The viscous damper is then replaced by a viscoelastic unit. We show that the system can exhibit both regular as well as chaotic behavior. The threshold limit for the chaotic motion has been determined using Melnikov’s criteria and verified through numerical simulations using the largest Lyapunov exponent.
more »
« less
Limit Cycle Analysis and Control of the Dissipative Chaplygin Sleigh
There are many types of systems in both nature and technology that exhibit limit cycles under periodic forcing. Sometimes, especially in swimming robots, such forcing is used to propel a body forward in a plane. Due to the complexity in studying a fluid system it is often useful to investigate the dynamics of an analogous land model. Such analysis can then be useful in gaining insight about and controlling the original fluid system. In this paper we investigate the behavior of the Chaplygin sleigh under the effect of viscous dissipation and sinusoidal forcing. This is shown to behave in a similar manner as certain robotic fish models. We then apply limit cycle analysis techniques to predict the behavior and control the net translational velocity of the sleigh in a horizontal plane.
more »
« less
- Award ID(s):
- 1563315
- PAR ID:
- 10026103
- Date Published:
- Journal Name:
- ASME Dynamic Systems and Control Conference
- Page Range / eLocation ID:
- V002T21A004
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The control and motion planning of bioinspired swimming robots is complicated by the fluid–robot interaction, which is governed by a very high (infinite)-dimensional nonlinear system. Many high dimensional nonlinear systems, often have low-dimensional attractors. From the perspective of swimming robots, such low-dimensional attractors simplify the analysis of the mechanics of swimming and prove to be useful to design controllers. This paper describes such a low-dimensional model for the swimming of a class of robots that are propelled by the motion of an internal reaction wheel. The model of swimming on a low-dimensional attractor is itself motivated by recent work on the dissipative Chaplygin sleigh, a well-known nonholonomic system, that exhibits limit cycle dynamics. We show that the governing equations of the Chaplygin sleigh are a very useful surrogate model for the swimming robot. The Chaplygin sleigh model is used to demonstrate certain maneuvers by the robot through computations. Experiments with such a robot provide evidence of limit cycle dynamics. Computational models based on discrete point vortex–body interaction confirm this behavior. Our work also suggests that there is a close phenomenological and mathematical similarity between the dynamics of swimming robots and those of ground based nonholonomic robots, which could motivate the development of very low-dimensional mathematical models for the motion of other fish-like swimming robots.more » « less
-
The influence of parametric forcing on a viscoelastic fluid layer, in both gravitationally stable and unstable configurations, is investigated via linear stability analysis. When such a layer is vertically oscillated beyond a threshold amplitude, large interface deflections are caused by Faraday instability. Viscosity and elasticity affect the damping rate of momentary disturbances with arbitrary wavelength, thereby altering the threshold and temporal response of this instability. In gravitationally stable configurations, calculations show that increased elasticity can either stabilize or destabilize the viscoelastic system. In weakly elastic liquids, higher elasticity increases damping, raising the threshold for Faraday instability, whereas the opposite is observed in strongly elastic liquids. While oscillatory instability occurs in Newtonian fluids for all gravity levels, we find that parametric forcing below a critical frequency will cause a monotonic instability for viscoelastic systems at microgravity. Importantly, in gravitationally unstable configurations, parametric forcing above this frequency stabilizes viscoelastic fluids, until the occurrence of a second critical frequency. This result contrasts with the case of Newtonian liquids, where under the same conditions, forcing stabilizes a system for all frequencies below a single critical frequency. Analytical expressions are obtained under the assumption of long wavelength disturbances predicting the damping rate of momentary disturbances as well as the range of parameters that lead to a monotonic response under parametric forcing.more » « less
-
null (Ed.)This paper presents a nonlinear control method, which achieves simultaneous fluid flow velocity control and limit cycle oscillation (LCO) suppression in a flexible airfoil. The proposed control design is based on a dynamic model that incorporates the fluid structure interactions (FSI) in the airfoil. The FSI describe how the flow field velocity at the surface of a flexible structure gives rise to fluid forces acting on the structure. In the proposed control method, the LCO are controlled via control of the flow field velocity near the surface of the airfoil using surface-embedded synthetic jet actuators. Specifically, the flow field velocity profile is driven to a desired time-varying profile, which results in a LCO-stabilizing fluid forcing function acting on the airfoil. A Lyapunov-based stability analysis is used to prove that the active flow control system asymptotically converges to the LCO-stabilizing forcing function that suppresses the LCO. Numerical simulation results are provided to demonstrate the performance of the proposed active flow-and-LCO suppression method.more » « less
-
We describe a fluid model with time-varying input that approximates a multiclass many-server queue with general reneging distribution and multiple customer classes (specifically, the multiclass G/GI/N+GI queue). The system dynamics depend on the policy, which is a rule for determining when to serve a given customer class. The class of admissible control policies are those that are head-of-the-line (HL) and nonanticipating. For a sequence of many-server queues operating under admissible HL control policies and satisfying some mild asymptotic conditions, we establish a tightness result for the sequence of fluid scaled queue state descriptors and associated processes and show that limit points of such sequences are fluid model solutions almost surely. The tightness result together with the characterization of distributional limit points as fluid model solutions almost surely provides a foundation for the analysis of particular HL control policies of interest. We leverage these results to analyze a set of admissible HL control policies that we introduce, called weighted random buffer selection (WRBS), and an associated WRBS fluid model that allows multiple classes to be partially served in the fluid limit (which is in contrast to previously analyzed static priority policies).more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/DSCC2017-5193
