Approximate solutions for vibrations of deploying appendages

Misra, A. K.; Kalaycioglu, S.

doi:10.2514/3.20639

Cited by 35 publications

(7 citation statements)

References 13 publications

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“…Crawley and de Luis [1] proposed an analytical approach for a static case including several actuator geometries to be bonded on flexible substrates. A dynamic modeling technique for the vibration suppression of plate structures by using piezo patches is detailed in [2]. The first real applications in aerospace structures were made by [3,4].…”

Section: Literature Backgroundmentioning

confidence: 99%

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SISO Piezo Based Circuit Development for Active Structural Vibration Control

Arena

Viscardi

2020

Fluids

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This paper deals with the issue of developing a smart vibration control platform following an innovative model-based approach. As a matter of fact, obtaining accurate information on system response in pre-design and design phases may reduce both computational and experimental efforts. From this perspective, a multi-degree-of-freedom (MDOF) electro-mechanical coupled system has been numerically schematized implementing a finite element formulation: a robust simulation tool integrating finite element model (FEM) features with Simulink® capabilities has been developed. Piezo strain actuation has been modelled with a 2D finite element description: the effects exerted on the structure (converse effect) have been applied as lumped loads at the piezo nodes interface. The sensing (direct effect) has instead been modelled with a 2D piezoelectric constitutive equation and experimentally validated as well. The theoretical study led to the practical development of an integrated circuit which allowed for assessing the vibration control performance. The analysis of critical parameters, description of integrated numerical models, and a discussion of experimental results are addressed step by step to get a global overview of the engineering process. The single mode control has been experimentally validated for a simple benchmark like an aluminum cantilevered beam. The piezo sensor-actuator collocated couple has been placed according to an optimization process based on the maximum stored electrical energy. Finally, a good level of correlation has been observed between the forecasting model and the experimental application: the frequency analysis allowed for characterizing the piezo couple behavior even far from the resonance peak.

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Section: Literature Backgroundmentioning

confidence: 99%

“…The following feedback formulation was developed in [27] for a passive absorber problem and in [28] for piezoceramic actuators. Considering a new variable basis ηi, the physical coordinates representing the nodal displacement and velocity can be reported as Equations (2) and 3:…”

Section: State-space Representation Of Structural Modelmentioning

confidence: 99%

SISO Piezo Based Circuit Development for Active Structural Vibration Control

Arena

Viscardi

2020

Fluids

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“…, is appropriate shape function satisfying at least the geometric boundary conditions. 12 n is the number of terms in the series expansions. Considering the parameter ¼ x L , the shape function is chosen as follows: 30…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…8,9 On the other hand, Hakak and Khoddam 10 and Walker and Aglietti 11 have investigated the design parameters of satellite deployable structures. Moreover, Kalaycioglu and Misra 12 have presented approximate analytical solution for dynamics of spacecraft appendages and tethered systems without tip mass while assumed modes method has been employed. The analytical solutions for dynamics of beams with constant length under base excitation have been developed by Esmailzadeh and Nakhaie-Jazar 13 and Esmailzadeh and Jalili, 14 where Green's function and Schauder's fixed-point theorem have been applied.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytical solutions of an axially moving spacecraft appendage subjected to tip mass

Ghaleh

Khayyat

Farjami

et al. 2013

Proceedings of the Institution of Mechanical Engineers, Part G:

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Approximate solutions for vibrations of flexible beam-type appendages subjected to tip mass are studied while uniform and exponential profiles for arm deployment are simulated. Applying an equivalent dynamical system and following Lagrangian approach, the equations of motion of the system are derived as nonlinear ordinary differential equations (ODEs) (with time-varying coefficients), in which the effect of the tip mass can be considered as some nonlinearity added to the 'no tip mass' case dynamics. The approximate closed-form solutions are obtained through a novel methodology using a computer algorithm, in which the solutions of the 'no tip mass' case are expanded by imposing quadratic perturbations on the independent variable. The mean square of errors (MSEs) for the obtained approximate analytical solution is computed. Using this method, the amplitude and frequency of the arm response are presented by the algebraic equations, which help the parametric design of such systems. In addition, effects of tip mass as an indicator of nonlinearities added to the system dynamics, on the amplitude and frequency of the beam response, are investigated during arm deployment.

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“…As one example, this study analyzes the deployment dynamics of a spinstabilized solar sail, in which the folded membrane bundles being released are modeled as extending beams. Since analytical methods are only applicable to significantly simplified models [6][7][8][9], this study develops a numerical method in a geometrically nonlinear finite element (FE) framework, in order to simulate a more realistic spacecraft.…”

Section: Introductionmentioning

confidence: 99%

Transient Dynamic Analysis of Gossamer-Appendage Deployment Using Nonlinear Finite Element Method

Sakamoto

Miyazaki

Mori

2011

Journal of Spacecraft and Rockets

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The present study develops a new three-dimensional Timoshenko beam finite element whose length can be varied during transient dynamic analysis. The variable-length element enables the dynamic deployment analysis of flexible appendages with nonnegligible bending stiffness. In addition, the developed scheme employs an implicit time integration whereby energy and momentum in the system are properly conserved, and no artificial numerical dissipation is introduced. The developed beam element is then used in an finite element model of a solar sailcraft, and its deployment dynamics are analyzed allowing for the nonzero bending stiffness of the bundled membranes, as well as the effect of some realistic design imperfections. Nomenclature A = beam cross-sectional area A r = 3 3 matrix defined in Eq. (13) d CM = vector pointing from the geometrical center to the center of mass of a satellite bus E = Young's modulus of beam E r i , e r i = nodal base vector in undeformed and deformed configurations at node r (i 1; 2; 3) f p xE = nodal elastic force for translational degrees of freedom at node p f p xI = nodal inertial force for translational degrees of freedom at node p f r E = nodal elastic force for rotational degrees of freedom at node r f r I = nodal inertial force for rotational degrees of freedom at node r G = shear modulus of beam G i , g i = covariant base vector in undeformed and deformed configurations (i 1; 2; 3) h = beam height I = 3 3 identity matrix I ij = moment-of-inertia components of rigid body I = beam second moment of area i i = local reference unit vector (i 1; 2; 3) J rs = elemental inertia matrix K i , D i = beam stiffness parameters defined in Eq. (35) K pq I , K rs I = stiffness matrix corresponding to inertial force vector at translational and rotational nodes L 0 , L f = initial and final length of cantilevered beam ' = beam length in undeformed configuration M, M pq = elemental mass matrix and its component m = mass of rigid body N= number of beam elements in convergence study N p , N r = shape functions n = unit eigenaxis vector R r I , R r = nodal base matrix in undeformed and deformed configurations at node r T = kinetic energy t = time U in = strain energy w = beam width X, x = position vector in undeformed and deformed configurations X p , x p = nodal position vector in undeformed and deformed configurations at node p _ x p = nodal velocity vector at node p Y i = three-dimensional local coordinate embedded to beam (i 1; 2; 3) r = nodal modified Rodrigues vector at node r ij = components of Green-Lagrange strain t = time-step size x p = incremental nodal position vector at node p r = incremental nodal modified Rodrigues vector at node r " i , i = beam strain parameters defined in Eq. (35) " ij = components of infinitesimal strain = in-plane phase angle of tip mass = beam density ij = components of stress = out-of-plane phase angle of tip mass = pseudo velocity vector for rotational degree of freedom = eigenaxis rotation angle = element domain ! r = nodal angular velocity vector at node r Subsc...

show abstract

Approximate solutions for vibrations of deploying appendages

Cited by 35 publications

References 13 publications

SISO Piezo Based Circuit Development for Active Structural Vibration Control

SISO Piezo Based Circuit Development for Active Structural Vibration Control

Approximate analytical solutions of an axially moving spacecraft appendage subjected to tip mass

Transient Dynamic Analysis of Gossamer-Appendage Deployment Using Nonlinear Finite Element Method

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