“…In contrast, for c cr < 0, the mode of instability switches frequently and randomly for the entire range of γ ∈ [0.2, 0.9]. Within each band, where the mode of instability remains fixed, the critical stability curve has the shape of a catenary for both positive and negative c cr ; such catenary shapes have been reported earlier in the literature in the context of critical stability curves [12,17]. Although the catenary shape gives rise to local maxima and minima, the overall trend shows a decrease in the magnitude of c cr as the location of the measurement of curvature changes from the revolute joint end to the distal end of the beam for both positive and negative c cr .…”
Section: Critical Stability Surface and Modes Of Flutter Instabilitysupporting
confidence: 60%
“…Feedback between the state of the continuous body and its terminal end can be used to generate flutter instability [12] and earlier works [5,11] have demonstrated that flutter oscillations in a fluid environment can generate an efficient traveling waveform. The salient features of both [12] and [5,11] are exploited to generate flutter instability through feedback. Similar to [5,11], we consider a flexible beam pinned to a rigid body but a motor at the pinned joint provides the actuation forces instead of internal flow.…”
Section: Introductionmentioning
confidence: 99%
“…Similar to [5,11], we consider a flexible beam pinned to a rigid body but a motor at the pinned joint provides the actuation forces instead of internal flow. The motor provides a torque proportional to the strain in the beam, but unlike [12] the motor is located at the base and not at the terminal end. The physical system is described in section 2 along with a set of assumptions that simplify the mathematical model.…”
Oscillating propulsors can provide both propulsive and maneuvering forces to an underwater vehicle. Because the working area is the same, it is possible to provide maneuvering forces that are similar in magnitude to that of the propulsive forces. An oscillating propulsor in the form of a flexible beam is investigated; the flexible beam is appended to an underwater vehicle by a pin joint and actuated by a motor. It is shown that the flexible propulsor can be driven into post-flutter limit cycle oscillations using feedback of the state of the propulsor. The limit cycle oscillations result in traveling waves, which in turn generate propulsive forces. The elastic strain of the propulsor is used to provide feedback; it is shown that changing the location of strain measurement can result in a rich set of stability transitions, each stability transition is associated with a specific mode of flutter-based propulsion with unique thrust and efficiency characteristics.
“…In contrast, for c cr < 0, the mode of instability switches frequently and randomly for the entire range of γ ∈ [0.2, 0.9]. Within each band, where the mode of instability remains fixed, the critical stability curve has the shape of a catenary for both positive and negative c cr ; such catenary shapes have been reported earlier in the literature in the context of critical stability curves [12,17]. Although the catenary shape gives rise to local maxima and minima, the overall trend shows a decrease in the magnitude of c cr as the location of the measurement of curvature changes from the revolute joint end to the distal end of the beam for both positive and negative c cr .…”
Section: Critical Stability Surface and Modes Of Flutter Instabilitysupporting
confidence: 60%
“…Feedback between the state of the continuous body and its terminal end can be used to generate flutter instability [12] and earlier works [5,11] have demonstrated that flutter oscillations in a fluid environment can generate an efficient traveling waveform. The salient features of both [12] and [5,11] are exploited to generate flutter instability through feedback. Similar to [5,11], we consider a flexible beam pinned to a rigid body but a motor at the pinned joint provides the actuation forces instead of internal flow.…”
Section: Introductionmentioning
confidence: 99%
“…Similar to [5,11], we consider a flexible beam pinned to a rigid body but a motor at the pinned joint provides the actuation forces instead of internal flow. The motor provides a torque proportional to the strain in the beam, but unlike [12] the motor is located at the base and not at the terminal end. The physical system is described in section 2 along with a set of assumptions that simplify the mathematical model.…”
Oscillating propulsors can provide both propulsive and maneuvering forces to an underwater vehicle. Because the working area is the same, it is possible to provide maneuvering forces that are similar in magnitude to that of the propulsive forces. An oscillating propulsor in the form of a flexible beam is investigated; the flexible beam is appended to an underwater vehicle by a pin joint and actuated by a motor. It is shown that the flexible propulsor can be driven into post-flutter limit cycle oscillations using feedback of the state of the propulsor. The limit cycle oscillations result in traveling waves, which in turn generate propulsive forces. The elastic strain of the propulsor is used to provide feedback; it is shown that changing the location of strain measurement can result in a rich set of stability transitions, each stability transition is associated with a specific mode of flutter-based propulsion with unique thrust and efficiency characteristics.
“…Interestingly, these structural models do not only display flutter instability but, similarly to the 'Ziegler's double pendulum', also counterintuitive behaviours, often referred as 'paradoxes' [37][38][39][40][41][42][43][44][45][46][47][48][49].…”
Section: (A) the Counterintuitive Character Of Flutter Instabilitymentioning
confidence: 99%
“…Among the many, the following ones are recalled (figure 2): Reut’s double pendulum [29], differing from the ‘Ziegler’s double pendulum’ only in the load application. More specifically, the constant magnitude load P slides along a rigid bar to maintain its application line always coincident with the undeformed state;Beck’s column [30], an elastic cantilever rod differing from the ‘Ziegler’s double pendulum’ only for the continuous and uniform distribution of mass, bending stiffness and dissipation;Pflüger’s column [31,32], which enhances the Beck’s column by considering the presence of a lumped mass at the application point of the follower load;Leipholz’s column [33,34], an elastic cantilever rod subject to a uniform distribution of follower tangential load acting along its axis;Nicolai’s column [35,36], an elastic cantilever rod with a follower twist load applied at the free end, so that three-dimensional motion is realized, instead of a planar one.Interestingly, these structural models do not only display flutter instability but, similarly to the ‘Ziegler’s double pendulum’, also counterintuitive behaviours, often referred as ‘paradoxes’ [37–49]. Figure 2Discrete and continuous structural models displaying flutter instability when subject to non-conservative loads.…”
The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.
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