Nonlinear Deployment Dynamics and Wrinkling of a Membrane Attached to Two Axially Moving Beams

2021 ◽  
pp. 1-19
Author(s):  
Behrad Vatankhahghadim ◽  
Christopher J. Damaren
Keyword(s):  
Axially Moving Beams ◽  
Axially Moving ◽  
Deployment Dynamics

Deployment of a Membrane Attached to Two Axially Moving Beams

2018 ◽  
Vol 86 (3) ◽  
Author(s):  
Behrad Vatankhahghadim ◽  
Christopher J. Damaren
Keyword(s):  
Equations Of Motion ◽  
Plane Motion ◽  
Rate Of Change ◽  
Coupled Equations ◽  
Cantilevered Beam ◽  
Analytic Expressions ◽  
Axially Moving Beams ◽  
Axially Moving ◽  
Deployment Dynamics ◽  
Time Invariant

The deployment dynamics of a simplified solar sail quadrant consisting of two Euler–Bernoulli beams and a flexible membrane are studied. Upon prescribing the in-plane motion and modeling the tension field based on linearly increasing stresses assumed on the attached boundaries, the coupled equations of motion that describe the system's transverse deflections are obtained. Based on these equations and their boundary conditions (BCs), deployment stability is studied by deriving simplified analytic expressions for the rate of change of system energy. It is shown that uniform extension and retraction result in decreasing and increasing energy, respectively. The motion equations are discretized using expansions in terms of “time-varying quasi-modes” (snapshots of the modes of a cantilevered beam and a clamped membrane), and the integrals needed for the resulting system matrices are rendered time-invariant via a coordinate transformation. Numerical simulation results are provided to illustrate a sample deployment and validate the analytic energy rate expressions.

Vibration Localization in Band/Wheel Systems: Theory and Experiment

1993 ◽  
Author(s):  
A. A. N. Al-jawi ◽  
A. G. Ulsoy ◽  
Christophe Pierre
Keyword(s):  
Simple Model ◽  
Coupling Model ◽  
Complex Model ◽  
Translation Speed ◽  
Mode Localization ◽  
Vibration Localization ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Axially Moving Beams ◽  
Axially Moving

Abstract An investigation of the localization phenomenon in band/wheel systems is presented. The effects of tension disorder, interspan coupling, and translation speed on the confinement of the natural modes of free vibration are investigated both theoretically and experimentally. Two models of the band/wheel system dynamics are discussed; a simple model proposed by the authors [1] and a more complete model originally proposed by Wang and Mote [9]. The results obtained using the simple interspan coupling model reveal phenomena (i.e., eigenvalue crossings and veerings and associated mode localization) that are qualitatively similar to those featured by the more complex model of interspan coupling, thereby confirming the usefulness of the simple coupling model. The analytical predictions of the two models are validated by an experiment. A very good agreement between the experimental results and the theoretical ones for the simple model is observed. While both the experimental observations and the theoretical predictions show that a beating phenomenon takes place for ordered stationary and axially moving beams, beating is destroyed (indicating the occurrence of localization) when any small tension disorder is introduced especially for small interspan coupling (i.e., when localization is strongest).

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

2006 ◽  
Vol 129 (3) ◽  
pp. 380-385 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Müftü
Keyword(s):  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Axial Tension ◽  
Winkler Elastic Foundation ◽  
Critical Tension ◽  
Divergence Instability ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. The natural frequencies and associated mode shapes are obtained. The natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at a critical velocity and a critical tension; and, divergence and flutter instabilities coexist at postcritical speeds, and divergence instability takes place precritical tensions. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams are presented.

Galerkin methods for natural frequencies of high-speed axially moving beams

2010 ◽  
Vol 329 (17) ◽  
pp. 3484-3494 ◽  
Author(s):  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Galerkin Methods ◽  
Axially Moving Beams ◽  
Axially Moving

Investigation of the Stability of Axially Moving Beams With Discrete Masses

2021 ◽  
Author(s):  
Konstantina Ntarladima ◽  
Michael Pieber ◽  
Johannes Gerstmayr
Keyword(s):  
Large Deformations ◽  
Equations Of Motion ◽  
Arbitrary Lagrangian Eulerian ◽  
Axial Motion ◽  
Multibody Modeling ◽  
Conveyor Belts ◽  
Axially Moving Beams ◽  
Concentrated Masses ◽  
Axially Moving ◽  
The Stability

Abstract The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

Multidimensional Lindstedt–Poincaré method for nonlinear vibration of axially moving beams

2007 ◽  
Vol 306 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
S.H. Chen ◽  
J.L. Huang ◽  
K.Y. Sze
Keyword(s):  
Nonlinear Vibration ◽  
Axially Moving Beams ◽  
Axially Moving

scholarly journals Nonlinear Vibrations of Axially Moving Beams

10.5772/6948 ◽  
2010 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Nonlinear Vibrations ◽  
Axially Moving Beams ◽  
Axially Moving

Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

2019 ◽  
Vol 11 (02) ◽  
pp. 1950021 ◽  
Author(s):  
Yuanbin Wang ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Large Amplitude ◽  
Model Equation ◽  
Classical Model ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Governing Equations ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Axially Moving Beams ◽  
Axially Moving

This paper clarified kinematic aspects of motion of axially moving beams undergoing large-amplitude vibration. The kinematics was formulated in the mixed Eulerian–Lagrangian framework. Based on the kinematic analysis, the governing equations of nonlinear vibration were derived from the extended Hamilton principle and the higher-order shear beam theory. The derivation considered the effects of material parameters on the beam deformation. The proposed governing equations were compared with a few previous governing equations. The comparisons show that proposed equations are with higher precision. Besides, the proposed equations can be viewed as the asymptotic governing equations of Lagrange’s equations of motion for large displacement. Finally, the corresponding boundary conditions and the comparison between the presented model equation and classical model equation were provided.

Complex stability boundaries of axially moving beams with interdependent speed and tension

2021 ◽  
Vol 89 ◽  
pp. 208-224
Author(s):  
You-Qi Tang ◽  
Yuan Zhou ◽  
Shuang Liu ◽  
Shan-Ying Jiang
Keyword(s):  
Complex Stability ◽  
Stability Boundaries ◽  
Axially Moving Beams ◽  
Axially Moving
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