Mathematical modelling of a beam-like flexible structure in slewing motion assuming non-linear curvature

Fenili, André; Balthazar, José Manoel; Brasil, Reyolando Manoel Lopes Rebello da Fonseca

doi:10.1016/s0022-460x(03)00370-5

Cited by 11 publications

(6 citation statements)

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“…The influence of the energy source i.e. DC motor supplied torque to the hub-beam rotor was investigated in [9] for a few selected resonance conditions. The derived partial differential equations have been reduced to ordinary differential equations and then solved by the multiple scale method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibrations of an extensional beam with tip mass in slewing motion

2020

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Dynamics of a rotor composed of a flexible beam attached to a slewing rigid hub is presented in the paper. Dynamics of the structure is studied for a slender beam model, based on extended Bernoulli–Euler theory, which takes into account a nonlinear curvature, coupled transversal and longitudinal oscillations and non-constant angular velocity of the hub. Moreover, to demonstrate a general case for dynamical boundary conditions, lumped mass fixed at the beam tip is added. The partial differential equations (PDEs) are derived from Hamilton principle of the least action. The analytical solutions of the PDEs are obtained by the multiple time scale method applied directly to PDEs. Forced vibrations around selected resonance zones are studied and the influence of beam rotation, preset angle, hub radius, tip mass is presented. Hardening and softening phenomena, respectively for the first and the second mode, are obtained for various angular velocity values.

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Section: Introductionmentioning

confidence: 99%

Nonlinear vibrations of an extensional beam with tip mass in slewing motion

2020

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“…We substitute the order e (0) solution, Eq. (24), and the solution for q 11 obtained from e (1) equation into the order e (2) expansion, and then set the secular terms to zero.…”

Section: Steady-state Solutionmentioning

confidence: 99%

Stability analysis of a nonlinear rotating blade with torsional vibrations

Wang

Zhang

2012

Journal of Sound and Vibration

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“…For this method, the kinetic and potential energy expression need to be written. The kinetic energy of the rotating beam is given by (Fenili et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Motion and vibration control of a slewing flexible structure by SMA actuators and parameter sensitivity analysis

Janzen

Tusset

Piccirillo

et al. 2015

Eur. Phys. J. Spec. Top.

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This work presents two approaches to the problem of vibration and positioning control of a flexible structural beam driven by a DC motor. The position is controlled by the current applied to the DC motor armature. A Shape Memory Alloy (SMA) actuator controls vibrations of the flexible structural beam. The State Dependent Riccati Equation (SDRE) technique is used to provide a control action which uses sub-optimal control and system local stability search. The robustness of these two controllers is tested by sensitivity analysis to parametric uncertainties. Numerical simulations results are presented to demonstrate the effectiveness of the proposed control strategy.

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Mathematical modelling of a beam-like flexible structure in slewing motion assuming non-linear curvature

Cited by 11 publications

References 0 publications

Nonlinear vibrations of an extensional beam with tip mass in slewing motion

Nonlinear vibrations of an extensional beam with tip mass in slewing motion

Stability analysis of a nonlinear rotating blade with torsional vibrations

Motion and vibration control of a slewing flexible structure by SMA actuators and parameter sensitivity analysis

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