Reconfiguring smart structures using phase space connections

McInnes, Colin R.; Waters, Thomas J.

doi:10.1088/0964-1726/17/2/025030

Cited by 11 publications

(22 citation statements)

References 24 publications

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“…A smooth control time history is obtained at the same time. The results demonstrate that the control effort can compensate for parameter errors to generate a heteroclinic connection between two unstable equilibria [10], which transit from an unstable equilibrium E 9 through a stable equilibrium E 1 to the neighbouring unstable equilibrium E 10 .…”

Section: Numerical Solutionmentioning

confidence: 93%

“…In previous work, McInnes and Waters report a simple model of a smart structure, which is constructed by a two mass chain with three springs subject to clamping at both ends [10]. Then, the model is simplified to a cubic nonlinearity and dynamical system theory used to investigate the characteristics of the simplified model.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, trajectories exist between these configurations which in principle do not require the addition of or dissipation of energy. This prior work has illustrated that the use of such heteroclinic connections between unstable equilibria can in principle be energetically efficient compared to reconfiguring a structure between stable configurations, which require the addition of and then dissipation of energy [10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reconfiguring Smart Structures Using Approximate Heteroclinic Connections in a Spring-Mass Model

Zhang

McInnes

2015

Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling,

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Several new methods are proposed to reconfigure smart structures with embedded computing, sensors and actuators. These methods are based on heteroclinic connections between equal-energy unstable equilibria in an idealised spring-mass smart structure model. Transitions between equal-energy unstable (but actively controlled) equilibria are considered since in an ideal model zero net energy input is required, compared to transitions between stable equilibria across a potential barrier. Dynamical system theory is used firstly to identify sets of equal-energy unstable configurations in the model, and then to connect them through heteroclinic connection in the phase space numerically. However, it is difficult to obtain such heteroclinic connections numerically in complex dynamical systems, so an optimal control method is investigated to seek transitions between unstable equilibria, which approximate the ideal heteroclinic connection. The optimal control method is verified to be effective through comparison with the results of the exact heteroclinic connection. In addition, we explore the use of polynomials of varying order to approximate the heteroclinic connection, and then develop an inverse method to control the dynamics of the system to track the polynomial reference trajectory. It is found that high order polynomials can provide a good approximation to true heteroclinic connections and provide an efficient means of generating such trajectories. The polynomial method is envisaged as being computationally efficient to form the basis for real-time reconfiguration of real, complex smart structures with embedded computing, sensors and actuators.

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Section: Numerical Solutionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reconfiguring Smart Structures Using Approximate Heteroclinic Connections in a Spring-Mass Model

Zhang

McInnes

2015

Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling,

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“…where full details of the development of the simple smart structure model are provided by McInnes and Waters [18].…”

Section: ̇=mentioning

confidence: 99%

“…In this paper, previous work by McInnes and Waters [18] is firstly summarised. We use dynamical system theory to investigate the characteristics of their double mass-spring problem as a simple model of a smart structure.…”

Section: Introductionmentioning

confidence: 99%

Reconfiguring smart structures using approximate heteroclinic connections

Zhang

McInnes

2015

Smart Mater. Struct.

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Abstract.A new method is investigated to reconfigure smart structures by the technique of polynomial series, used to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to firstly approximate the heteroclinic connection between two equalenergy unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used firstly in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

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Collapse characterization and shock mitigation by elastomeric metastructures

Vuyk

Harne

2020

Extreme Mechanics Letters

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Reconfiguring smart structures using phase space connections

Cited by 11 publications

References 24 publications

Reconfiguring Smart Structures Using Approximate Heteroclinic Connections in a Spring-Mass Model

Reconfiguring Smart Structures Using Approximate Heteroclinic Connections in a Spring-Mass Model

Reconfiguring smart structures using approximate heteroclinic connections

Collapse characterization and shock mitigation by elastomeric metastructures

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