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Academic literature on the topic 'Bistable arches'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Bistable arches"

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Pontecorvo, Michael E., Silvestro Barbarino, Gabriel J. Murray, and Farhan S. Gandhi. "Bistable arches for morphing applications." Journal of Intelligent Material Systems and Structures 24, no. 3 (August 31, 2012): 274–86. http://dx.doi.org/10.1177/1045389x12457252.

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This article examines the bistable behavior of an arch for morphing applications. The arch has a cosine profile, is clamped at both ends, and is restrained axially by a spring at one end. Fabrication and testing of several Delrin and NiTiNOL arch specimens (with varying arch height, thickness, and spring stiffness) were followed by ANSYS finite element modeling, and the ANSYS simulation results showed good overall agreement with the test results. A parametric study was conducted using the ANSYS model to assess the influence of arch thickness, height, and spring stiffness on the bistable behavior. The results indicated that lower arch thickness, larger arch height, and higher spring stiffness tend to promote bistability; lower arch thickness and height reduce peak strains as the arch moves between equilibrium states, but increasing spring stiffness has a smaller effect; and higher arch thickness, height, and spring stiffness increase the snap-through force, which in turn increases the actuation force requirement as well as load carrying capability of the bistable morphing arch. If the arch slenderness ratio is unchanged, change in arch span (size) does not change the maximum stress while increasing the peak snap-through force proportionally.
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Palathingal, Safvan, and G. K. Ananthasuresh. "Analytical modelling of spatial deformation pathways in planar and spatial shallow bistable arches." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2227 (July 2019): 20190164. http://dx.doi.org/10.1098/rspa.2019.0164.

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We analyse spatial bistable arches and present an analytical model incorporating axial, two transverse bending and torsion energy components. We extend the St. Venant and Michell relationship used in flexural-torsional buckling of planar arches and use it in modelling spatial arches. We study deformation pathways in spatial arches and their effect on critical characteristics of bistability such as back and forth switching forces, and the distance travelled by a point of the arch. We show that not considering spatial deformation leads to incorrect inferences concerning the bistability of planar arches too. Thus, this model serves as a generalized framework for the existing analysis on planar arches since they belong to a subset of spatial arches. Additionally, the effects of eccentric loading on spatial deformations are explored for arches with a range of as-fabricated shapes and boundary conditions, and the results are validated with finite-element analysis.
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Avetisov, Vladik A., Maria A. Frolkina, Anastasia A. Markina, Alexander D. Muratov, and Vladislav S. Petrovskii. "Short Pyridine-Furan Springs Exhibit Bistable Dynamics of Duffing Oscillators." Nanomaterials 11, no. 12 (November 30, 2021): 3264. http://dx.doi.org/10.3390/nano11123264.

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The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose dynamics are similar to those of bistable mechanical systems, such as Euler arches and Duffing oscillators. Of particular interest are the molecular structures capable of spontaneous vibrations and stochastic resonance. Recently, oligomeric molecules that were a few nanometers in size and exhibited the bistable dynamics of an Euler arch were identified through molecular dynamics simulations of short fragments of thermo-responsive polymers subject to force loading. In this article, we present molecular dynamics simulations of short pyridine-furan springs a few nanometers in size and demonstrate the bistable dynamics of a Duffing oscillator with thermally-activated spontaneous vibrations and stochastic resonance.
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Cai, Jianguo, Xiaowei Deng, and Jian Feng. "Effects of symmetric imperfections on the behavior of bistable struts." Mathematics and Mechanics of Solids 22, no. 12 (August 23, 2016): 2240–52. http://dx.doi.org/10.1177/1081286516664565.

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The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.
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Sabale, Aditya, and K. V. Nagendra Gopal. "Nonlinear In-Plane Stability of Deep Parabolic Arches Using Geometrically Exact Beam Theory." International Journal of Structural Stability and Dynamics 18, no. 01 (January 2018): 1850006. http://dx.doi.org/10.1142/s0219455418500062.

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In this paper, we investigate the in-plane stability and post-buckling response of deep parabolic arches with high slenderness ratios subjected to a concentrated load on the apex, using the finite element implementation of a geometrically exact rod model and the cylindrical version of the arc-length continuation method enabled with pivot-monitored branch-switching. The rod model used here includes geometrically exact kinematics of the cross-section, exact kinetics, and a linear elastic constitutive law; and advantageously employs quaternion parameters to treat the cross-sectional rotations and to compute the exponential map in the configurational update of rotations. The evolution of the Frenet frame along the centroidal curve is used to determine the initial curvature of the rod. Three sets of boundary conditions, i.e. fixed–fixed (FF), fixed–pinned (FP) and pinned–pinned (PP), are considered, and arches with a wide range of rise-to-span ratios are analyzed for each set. Complete post-buckling response has been derived for all cases. The results reveal that although all the PP arches and all the FF arches (with the exception of FF arches with rise-to-span ratio less than 0.3) considered in this study buckle via bifurcation, the nature of stability of the different solution branches in the post-buckling regime differs from case to case. All FP slender parabolic arches exhibit limit-point buckling, again with several markedly different post-buckling behaviors. Also, some arches in the FF and PP case are shown to exhibit a clear bistable behavior in the post-buckled state.
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Palathingal, Safvan, and G. K. Ananthasuresh. "A bilateral relationship between stable profiles of pinned–pinned bistable shallow arches." International Journal of Solids and Structures 143 (June 2018): 183–93. http://dx.doi.org/10.1016/j.ijsolstr.2018.03.006.

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Palathingal, Safvan, and G. K. Ananthasuresh. "Design of bistable arches by determining critical points in the force-displacement characteristic." Mechanism and Machine Theory 117 (November 2017): 175–88. http://dx.doi.org/10.1016/j.mechmachtheory.2017.07.009.

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Librandi, Gabriele, Eleonora Tubaldi, and Katia Bertoldi. "Programming nonreciprocity and reversibility in multistable mechanical metamaterials." Nature Communications 12, no. 1 (June 8, 2021). http://dx.doi.org/10.1038/s41467-021-23690-z.

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AbstractNonreciprocity can be passively achieved by harnessing material nonlinearities. In particular, networks of nonlinear bistable elements with asymmetric energy landscapes have recently been shown to support unidirectional transition waves. However, in these systems energy can be transferred only when the elements switch from the higher to the lower energy well, allowing for a one-time signal transmission. Here, we show that in a mechanical metamaterial comprising a 1D array of bistable arches nonreciprocity and reversibility can be independently programmed and are not mutually exclusive. By connecting shallow arches with symmetric energy wells and decreasing energy barriers, we design a reversible mechanical diode that can sustain multiple signal transmissions. Further, by alternating arches with symmetric and asymmetric energy landscapes we realize a nonreciprocal chain that enables propagation of different transition waves in opposite directions.
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Palathingal, Safvan, and G. K. Ananthasuresh. "Analysis and Design of Fixed–Fixed Bistable Arch-Profiles Using a Bilateral Relationship." Journal of Mechanisms and Robotics 11, no. 3 (April 8, 2019). http://dx.doi.org/10.1115/1.4043044.

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Arch-profiles of bistable arches, in their two force-free equilibrium states, are related to each other. This bilateral relationship is derived for arches with fixed–fixed boundary conditions in two forms: a nonlinear single-variable equation for analysis and a closed-form analytical expression for design. Some symmetrical features of shape as well as necessary and sufficient conditions for bistability are presented as corollaries. Analysis and design of arch-profiles using the bilateral relationship are illustrated through examples.
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Alqasimi, Jihad E., and Hassen M. Ouakad. "Vibrational Response of Initially Deformed Bistable Microbeams Under the Combined Effect of Mechanical Shock Loads and Electrostatic Forces." Journal of Vibration and Acoustics 140, no. 2 (October 27, 2017). http://dx.doi.org/10.1115/1.4038107.

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This paper focuses on the influence of sudden drop tests on the nonlinear structural behavior of electrically actuated bi-table shallow microelectromechanical system (MEMS) arches. The assumed structure consists of an initially bell-shaped doubly clamped microbeam with a rectangular cross section. The Euler–Bernoulli beam theory is assumed to model the nonlinear structural behavior of the bistable system under the combined effect of both the direct current (DC) actuating load and the shaking waves. Moreover, the structural model takes into account both geometric midplane stretching and electric actuation nonlinear terms. A multimode Galerkin-based decomposition is used to discretize the beam equations to extract a reduced-order model (ROM). The convergence of the ROM simulations are first verified and furthermore compared to published experimental data. A thorough ROM parametric study showed that the effect of increasing the shallow arch initial rise alter drastically the system behavior from undergoing a uninterrupted snap-through motion to a sudden snap-through instability. Moreover, the arch rise relationship with its shock spectrum response (SSR) is investigated and it was concluded that as increasing the rise value can cause the system to collapse under the combined DC and shock wave loadings if the shock wave duration is lower or near the system fundamental natural period. All the presented graphs in this investigation represent some robust numerical approaches and design tools to help MEMS designers in improving both the reliability and efficiency of these bistable-based microdevices under shaking dynamic environments.
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Dissertations / Theses on the topic "Bistable arches"

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Palathingal, Safvan. "Statics of Shallow Bistable Arches." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/4626.

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Bistable arches have two force-free stable equilibrium configurations. They also show multimodality by switching between their stable states in multiple deformation pathways. These two attributes and their nonlinear force-displacement characteristic are desirable in a range of engineering applications. The analytical and semi-analytical methods developed in this work enable faster analysis than finite element analysis and also facilitate closed-form relationships for insightful design of arches. We show that arch profiles composed using the basis set of buckling mode shapes of the straight column with the corresponding boundary conditions exhibit bistability. We analyze such arches by expressing their deformed profiles also in the same basis set. We assume that the arches are slender and shallow to derive their potential energy comprising bending and compression strain energies as well as the work potential. We solve the equilibrium equations obtained by minimizing potential energy using a semi-analytical method for analytically intractable general boundary conditions. In this method, we obtain the critical points on the force-displacement curve corresponding to switching and switch back forces and travel of the mid-point of the arch. We use this method to analyze and optimize arches of varying as-fabricated stress-free shapes and boundary conditions. We obtain an analytical relationship between the arch-profiles in the force-free states of the arch by equating the force to zero in the aforementioned equilibrium equations for both fixed-fixed and pinned-pinned boundary conditions. This relationship is bilateral, i.e., in one form it can be a used for analysis and in another for design. We derive necessary and sufficient conditions as well as corollaries from the bilateral relationship pertaining to the shapes of bistable arches. Deformation pathways in bistable arches can also be three-dimensional . These spatial deformation pathways can help reduce the switching and switch-back forces and might also, at times, adversely affect bistability. We model spatial pathways by incorporating additional energy terms due to out-of-plane bending and torsion into analysis of planar arches. We use a geometric relation by St. Venant and Michell to capture the coupling amongst the in-plane and out-of-plane deformations and rotation of the cross-sections. Furthermore, we show that non-planar arches, i.e., spatial arches, can be bistable too. Our analysis is extended to spatial arches by modifying the geometric relation to consider the additional out-of-plane curvature. We also present design of two applications based on bistable arches: an RF-MEMS switch and a mechanical OR gate. RF-MEMS switch utilizes bimodality and a novel initially-retracting electrothermal actuator to realize ON and OFF states with only two electrical terminals. The mechanical OR gate uses the bilateral relationship to design arch-profiles that achieve the OR gate logic. Additionally, we present two studies on bistability in axisymmetric shallow thin shells. In the first study, we optimize the shell-profile for maximum travel by numerical and semi-analytical approaches and compare the results with the shell obtained by revolving the optimal arch for maximum travel. In the second study, we discuss the design of a passive universal gripper based on a bistable shell that can grasp objects of varying shape.
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Book chapters on the topic "Bistable arches"

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Banik, Deepayan, Safvan Palathingal, G. K. Ananthasuresh, and Amitabha Ghosh. "A Mechanical OR Gate Using Pinned-Pinned Bistable Arches." In Lecture Notes in Mechanical Engineering, 861–74. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-4477-4_61.

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Maharana, Priyabrata, Jyoti Sonawane, Pavan Belehalli, and G. K. Anathasuresh. "Analysis of Planar Bistable and Snap-through Arches for Contact and Dynamic Loads." In Advances in Mechanism and Machine Science, 3245–54. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20131-9_320.

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Palathingal, Safvan, and G. K. Ananthasuresh. "Design of Bistable Pinned-Pinned Arches with Torsion Springs by Determining Critical Points." In Lecture Notes in Electrical Engineering, 677–88. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2875-5_56.

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Conference papers on the topic "Bistable arches"

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Smith, Matthew L., M. Ravi Shankar, Ryan Backman, Vincent P. Tondiglia, Kyung Min Lee, Michael E. McConney, David H. Wang, Loon-Seng Tan, and Timothy J. White. "Designing light responsive bistable arches for rapid, remotely triggered actuation." In SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, edited by Nakhiah C. Goulbourne and Hani E. Naguib. SPIE, 2014. http://dx.doi.org/10.1117/12.2044906.

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Krylov, Slava, and Nir Dick. "Pull-In Dynamics of Electrostatically Actuated Bistable Micro Beam." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87236.

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Results of theoretical investigation of the transient dynamics of an initially curved electrostatically actuated clamped-clamped micro beam are presented. A reduced order model of the shallow Euler-Bernoulli arch developed using the Galerkin procedure with eigenmodes of a straight beam as a basis accounts for the distributed electrostatic and inertial loading, fringing electric fields and nonlinear squeeze film damping. Due to the unique combination of mechanical and electrostatic nonlinearities which is intrinsic in micro devices but is not encountered naturally in large-scale structures, the voltage-deflection characteristic of the sufficiently curved beam may have two maxima implying the existence of sequential mechanical (snap-through) and electrostatic (pull-in) instabilities. Phase plane analysis performed for the case of a suddenly applied electrostatic loading along with the simulation results show that critical voltages corresponding to the dynamic snap-through and pull-in instabilities are lower than their static counterparts while the minimal curvature required for the appearance of the dynamic snap-through is higher than in the static case. Clear functional advantages of this kind of structures, namely extended stable deflections and ability to tune the device frequencies in a very large range may result in improved performance of switches, inertial sensors and micromechanical non-volatile memory devices.
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Ruzziconi, Laura, Mohammad I. Younis, and Stefano Lenci. "Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48601.

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This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.
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