We use molecular mechanics simulations with the MM3 potential to study instabilities in clampedclamped single-walled carbon nanotubes (SWCNTs) deformed in torsion and axial compression. The following are the two criteria employed to find the critical buckling strain: (i) a sudden drop in the potential energy and (ii) an eigenvalue of the mass weighted Hessian of the deformed configuration becoming zero. The instability under axial compression is investigated for zigzag and armchair SWCNTs, and that under torsional deformations is also studied for chiral tubes. In general, values of critical strains from the 2nd criterion are found to be substantially less than those from the 1st criterion. For chiral SWCNTs, the critical strains from the 2nd criterion and the potential energies at the onset of instability markedly depend upon the twisting direction. Values of buckling strains predicted from the column and the shell buckling theories are found to agree well with those obtained using the 2nd criterion. Published by AIP Publishing.
The dynamics of space structures is significantly impacted by the presence of power and electronic cables. Robust physical model is essential to investigate how the host structure dynamics is influenced by cable harnessing. All the developed models only considered the decoupled bending motion. Initial studies by authors point out the importance of coordinate coupling in structures with straight longitudinal cable patterns. In this article, an experimentally validated mathematical model is developed to analyze the fully coupled dynamics of beam with a more complex cable wrapping pattern which is periodic in nature. The effects of cable wrapping pattern and geometry on the system dynamics are investigated through the proposed coupled model. Homogenization-based mathematical modeling is developed to obtain an analogous solid beam that represents the cable wrapped system. The energy expressions obtained for fundamental repeating segment are transferred into the global coordinates consisting of several periodic elements. The coupled partial differential equations (PDE) are obtained for an analogous solid structure. The advantage of the proposed analytical model over the existing models to analyze the vibratory motion of beam with complex cable wrapping pattern has been shown through experimental validation.
Recent developments in the aerospace industry have driven focus towards accurately modeling the effects of the cables and electronic cords on space structures. In the past, researchers have modeled the mass and stiffness effects of these cables but primarily overlooked their damping effects through careful analytical model developments. The objective of the current work is to present analytical models for cable-harnessed structures that also include the damping effects in their vibration response. Obtaining simple, low-order and high-fidelity models are highly advantageous in designing robust vibration real-time control algorithms for structures. Additionally, the analytical models are useful tools in providing insight and better understanding the dynamics of space structures as they are often difficult to be tested prior to launch due to their large size and at best only a few components may be tested. Motivated by the space applications, this work considers beam structures wrapped with cables which are modeled using beam and string theory assumptions. Two different damping models namely Kelvin-Voigt and hysteretic damping are considered. The homogenization approach is used as a starting point for structures of periodic wrapping patterns. Using the variational principle, the governing partial differential equation for the transverse coordinate of vibrations is found for three cable patterns and the results are compared to those from the Distributed Transfer Function Method (DTFM). Finally, the effects of several structural parameters are studied on the overall system damping.
In this technical brief, the experimental study and model validations for the damping mechanisms of cable-harnessed beam structures are presented. The structure consists of cables wrapped around a host beam in a periodic zigzag pattern. A special case of cable attached along the beam length over its centerline is also considered. Firstly, material damping in the cables is characterized using dynamic tests and the relevant cable damping factors are calculated for both the Kelvin-Voigt and hysteretic damping models. Experimental modal testing is then performed on the fabricated cable-harnessed beams to obtain the frequency response functions (FRFs). Finally, the experimental FRFs are compared with the damped analytical models. The test and model results are shown to be in very good agreements in predicting the structural damping induced by the cables.
Over the past decade, modeling of cable-harnessed space structures has received special attention due to the need for better accuracies than the existing models. As these structures become more lightweight upon the advancements in the materials science it is imperative to further consider accurate models in which the dynamic effects of the added cables are better accounted for. Researchers have heavily focused on creating models for cable-harnessed beam-like structures, while very few works have considered plate-like structures. The proposed research aims at the development of an analytical model for cable-harnessed plate-like structures. Cables are assumed to be periodic in geometry to allow for the application of an energy-equivalent homogenization technique. To begin with, a linear displacement field and a second-order Green-Lagrange strain tensor for strain-displacement relationships are considered. The strain and kinetic energies of the fundamental element are found using these relations. The repeated pattern of the fundamental element over the area of the plate structure allows for the employment of the homogenization approach in which the kinetic and strain energies per area of the fundamental element are found and assumed to remain the same as an equivalent homogenized solid plate-like element. The governing dynamic Partial Differential Equations (PDEs) are found using the Hamilton’s principle. The results are validated using finite element analysis. A detailed parametric analysis is also performed to investigate the effects of various cable parameters and wrapping patterns on the dynamics of the host structure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.