ON THE FORESHORTENING EFFECTS OF A ROTATING FLEXIBLE BEAM USING DIFFERENT MODELING METHODS<sup>*</sup>

Piedbœuf, Jean-Claude; Moore, B. D.

doi:10.1081/sme-120001478

Cited by 13 publications

(4 citation statements)

References 6 publications

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“…This is due to the computational advantages associated with B-splines including ease of implementation and smoothness. In multibody dynamics, the use of interpolating cubic splines has been studied in [21, 22], while others have hinted towards their potential applications in modeling multi-flexible body systems [23, 24]. However, a detailed analysis of interpolating spline-based algorithms is lacking, including a study of their performance compared to traditional modeling approaches.…”

Section: Introductionmentioning

confidence: 99%

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

Khan

Ahn

Anderson

et al. 2013

International Journal of Non-Linear Mechanics

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An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel.

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Section: Introductionmentioning

confidence: 99%

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

Khan

Ahn

Anderson

et al. 2013

International Journal of Non-Linear Mechanics

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“…Although this formulation lacks full mathematical consistency because of neglecting other higher-order terms, it is often encountered in the literature and is essential to represent the centrifugal stiffening effect [14]. For further reading on other centrifugal effect treatments please consult, for example, [32–34].…”

Section: Mathematical Model Of the Structurementioning

confidence: 99%

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

Latalski

Warmiński

Rega

2016

Mathematics and Mechanics of Solids

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The dynamics of a system consisting of a rotating rigid hub and a flexible composite thin-walled beam is discussed. The nonclassical effects like material anisotropy, rotary inertia and transverse shear are considered in the mathematical model of the structure. Moreover, the hub mass moment of inertia is taken into account. The differential equations of motion featuring beam bending–twist elastic coupling are derived using the Hamilton principle, and the Galerkin method is applied in order to reduce the partial differential governing equations to the ordinary differential equations. Parametric studies are conducted to evaluate beam stiffness coefficients depending on the fiber lamination angle. Next, numerical results are obtained to investigate the impact of hub to beam relative inertia on the natural frequencies of the structure. Cases of forced vibrations of the system are examined where the driving torque is considered as the sum of a constant (mean value) and a periodic component. Simulations show the importance of the hub inertia on the complete system dynamics. A shift of the resonance zones and a vibration absorption are observed.

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“…Yoo et al 24 established dynamic equations of a beam undergoing overall motions incorporating geometric stiffening. Piedboeuf and Moore 25 presented six methods of modeling a flexible rotating beam, including geometric stiffening, by taking into account foreshortening in the beam model. Behzad and Bastami 26 studied the effect of axial forces produced by the Poisson effect on the natural frequency of a shaft rotating its longitudinal axis.…”

Section: Introductionmentioning

confidence: 99%

Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed

2009

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SUMMARYThe effect of axial forces on the dynamic properties is formulated and investigated for a 3-PRR planar parallel manipulator with three flexible intermediate links. A dynamic model of the manipulator system is developed based on the assumed mode method with the consideration of the effect of longitudinal forces on lateral stiffness is included. The flexible intermediate links are modeled as Euler–Bernoulli beams with pinned-pinned boundary conditions, which are verified by experimental modal tests. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic behavior including the effect of axial forces on lateral deformation is investigated, and configuration-dependant frequencies are analyzed. Numerical simulations of configuration-dependent frequency properties and axial forces are performed to illustrate the effect of axial forces on the dynamic behaviors of the flexible parallel manipulator. Simulation results of mode amplitudes, deformations, axial forces, inertial, and coupling forces are presented, and further validate the theoretical derivations. These analyses and results provide a new and valuable insight to the design and control of the parallel manipulators with flexible intermediate links.

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ON THE FORESHORTENING EFFECTS OF A ROTATING FLEXIBLE BEAM USING DIFFERENT MODELING METHODS^*

Cited by 13 publications

References 6 publications

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed

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ON THE FORESHORTENING EFFECTS OF A ROTATING FLEXIBLE BEAM USING DIFFERENT MODELING METHODS*

Cited by 13 publications

References 6 publications

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed

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ON THE FORESHORTENING EFFECTS OF A ROTATING FLEXIBLE BEAM USING DIFFERENT MODELING METHODS^*