Effect of intermediate support on critical stability of a cantilever with non-conservative loading: Some new results

Abdullatif, Mahmoud; Mukherjee, Ranjan

doi:10.1016/j.jsv.2020.115564

Cited by 9 publications

(5 citation statements)

References 29 publications

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“…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: 59%

“…Each point on an Euler-Bernoulli beam undergoes a purely transverse displacement; therefore, using trial and error we scale the initial conditions such that the maximum elongation of the beam, irrespective of the mode of flutter, does not exceed 5%. Mathematically, the complex amplitudes A n , n = 1, 2, 3, 4, in (17) are scaled such that sup τ ∈[0,2π/Ωcr]…”

Section: Motion Scaling For Computation Of Thrust and Efficiencymentioning

confidence: 99%

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Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow

Abdullatif¹,

Mukherjee²,

Hellum³

2021

Preprint

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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.

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Section: Critical Stability Surface and Modes Of Flutter Instabilitysupporting

confidence: 59%

Section: Motion Scaling For Computation Of Thrust and Efficiencymentioning

confidence: 99%

Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow

Abdullatif¹,

Mukherjee²,

Hellum³

2021

Preprint

Self Cite

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“…Beam, plate, and shell structures can be found in various engineering systems [1,2,3,4,5,6,7,8]. As a sub-class of these structures, cantilevers are present in numerous engineering applications ranging from macro [9,10,2] to nano scale, such as micro/nano-electromechanical systems, micro gyroscopes, vibration energy harvesters, and scanning probe microscopy [11,12,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional nonlinear extreme vibrations of cantilevers based on a geometrically exact model

Farokhi

Ertürk

2021

Journal of Sound and Vibration

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“…For Euler-Bernoulli beams containing elastic support, Roncevic et al [18] investigated the frequency equation and mode forms. Abdullatif [19] analyzed the effect of intermediate support on the critical stability of a cantilever with non-conservative loading.…”

Section: Introductionmentioning

confidence: 99%

Minimum stiffness and optimal position of intermediate elastic support to maximize the fundamental frequency of a vibrating Timoshenko beam

2023

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The optimal position and minimum support stiffness of a vibrating Timoshenko beam are investigated to maximize the fundamental frequency. The Finite element method is employed. According to the maximum-minimum theorem of Courant, the optimum position is at the zero of the second mode shape function. The intermediate support's position and minimal stiffness for a wide variety of slenderness proportions were achieved. It was observed that the ideal position of intermediate support and its minimum stiffness are sensitive to the slenderness ratio. Also, for thick cantilever beams with intermediate support at the optimal location, the minimum support stiffness is less than 266.9, which was reported in the literature for the Euler-Bernoulli beam. The minimum stiffness of familiar end conditions of an optimally located beam is presented for a wide range of slenderness ratios. Since, in many practical applications, it is impossible to locate support at the optimal position, the minimum support stiffness for a beam in which its intermediate support is not located at the optimal position is obtained for various boundary conditions and slenderness ratios. Furthermore, empirical evaluations were carried out, and the findings were contrasted with hypothetical estimates of the initial two natural frequencies.

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Effect of intermediate support on critical stability of a cantilever with non-conservative loading: Some new results

Cited by 9 publications

References 29 publications

Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow

Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow

Three-dimensional nonlinear extreme vibrations of cantilevers based on a geometrically exact model

Minimum stiffness and optimal position of intermediate elastic support to maximize the fundamental frequency of a vibrating Timoshenko beam

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