Abstract
Bistable compliant elements offer excellent advantages in many applications ranging from high precision sensing to energy harvesting. The essential nonlinear mechanics of such elements are strongly coupled with their buckling mode, geometric parameters, and loading conditions. The force–displacement plot of bistable curved beams could contain a displacement limit point, which cannot be well modeled by the commonly used smooth cubic function and would cause operational problems due to incorrect predictions of the bistability. In this technical brief, the nonlinear bistable mechanics of a compliant curved beam with both ends fixed is analyzed based on the large deflection finite element theory. By using the multistep displacement loading method, the deformation behaviors and their transition from symmetric to asymmetric modes are numerically studied, which provides insights into the force–displacement curve and the multiple snapping pathways. Furthermore, the influences of the structure parameters on bistable mechanics are analyzed, and a quality factor for identifying the occurrence of displacement limit points is introduced for different loading conditions. Finally, a method for achieving a single smooth snapping pathway is proposed, providing a theoretical basis to the design and control of the bistable compliant structures.
Issue Section:
Technical Brief
References
1.
Chen
, G.
, Aten
, Q. T.
, Zirbel
, S.
, Jensen
, B. D.
, and Howell
, L. L.
, 2010
, “A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms
,” ASME J. Mech. Rob.
, 2
(1
), p. 014501
. 10.1115/1.40005292.
Holst
, G. L.
, Teichert
, G. H.
, and Jensen
, B. D.
, 2011
, “Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms
,” ASME J. Mech. Des.
, 133
(5
), p. 051002
. 10.1115/1.40039223.
Zhao
, J.
, Jia
, J.
, He
, X.
, and Wang
, H.
, 2008
, “Post-Buckling and Snap-Through Behavior of Inclined Slender Beams
,” ASME J. Appl. Mech.
, 75
(4
), p. 041020
. 10.1115/1.28709534.
Pedersen
, C. B. W.
, Buhl
, T.
, and Sigmund
, O.
, 2001
, “Topology Synthesis of Large-Displacement Compliant Mechanisms
,” Int. J. Numer. Methods. Eng.
, 50
(12
), pp. 2683
–2705
. 10.1002/nme.1485.
Hao
, G.
, and Mullins
, J.
, 2016
, “On the Comprehensive Static Characteristic Analysis of a Translational Bistable Mechanism
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 230
(20
), pp. 3803
–3817
. 10.1177/09544062156164186.
Yu
, Y. Q.
, Howell
, L. L.
, Lusk
, C.
, Yue
, Y.
, and He
, M. G.
, 2005
, “Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model
,” ASME J. Mech. Des.
, 127
(4
), pp. 760
–765
. 10.1115/1.19007507.
Jensen
, B. D.
, and Howell
, L. L.
, 2004
, “Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints
,” ASME J. Mech. Des.
, 126
(4
), pp. 657
–666
. 10.1115/1.17607768.
Ohsaki
, M.
, Katoh
, N.
, Kinoshita
, T.
, Tanigawa
, S.
, Avis
, D.
, and Streinu
, I.
, 2009
, “Enumeration of Optimal Pin-Jointed Bistable Compliant Mechanisms With Non-Crossing Members
,” Struct. Multidisc. Optim.
, 37
(6
), pp. 645
–651
. 10.1007/s00158-008-0258-z9.
Su
, H. J.
, and McCarthy
, J. M.
, 2007
, “Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy
,” ASME J. Mech. Des.
, 129
(10
), pp. 1094
–1098
. 10.1115/1.275719210.
Pucheta
, M. A.
, and Cardona
, A.
, 2010
, “Design of Bistable Compliant Mechanisms Using Precision-Position and Rigid-Body Replacement Methods
,” Mech. Mach. Theory
, 45
(2
), pp. 304
–326
. 10.1016/j.mechmachtheory.2009.09.00911.
Zhao
, J.
, Yang
, Y. T.
, Wang
, H. X.
, and Jia
, J. Y.
, 2010
, “A Novel Magnetic Actuated Bistable Acceleration Switch With Low Contact Resistance
,” IEEE Sensors J.
, 10
(4
), pp. 869
–876
. 10.1109/JSEN.2009.203644212.
Freudenreich
, M.
, Mescheder
, U.
, and Somogyi
, G.
, 2004
, “Simulation and Realization of a Novel Micromechanical bi-Stable Switch
,” Sens. Actuators, A
, 114
(2–3
), pp. 451
–459
. 10.1016/j.sna.2004.01.03413.
Gerson
, Y.
, Schreiber
, D.
, Grau
, H.
, and Krylov
, S.
, 2014
, “Meso Scale MEMS Inertial Switch Fabricated Using an Electroplated Metal-on-Insulator Process
,” J. Micromech. Microeng.
, 24
(2
), p. 025008
. 10.1088/0960-1317/24/2/02500814.
Qiu
, J.
, Lang
, J. H.
, Slocum
, A. H.
, and Weber
, A. C.
, 2005
, “A Bulk-Micromachined Bistable Relay With U-Shaped Thermal Actuators
,” J. Microelectromech. Syst.
, 14
(5
), pp. 1099
–1109
. 10.1109/JMEMS.2005.85667615.
Miao
, X. D.
, Dai
, X. H.
, Wang
, P. H.
, Ding
, G. F.
, and Zhao
, X. L.
, 2011
, “Design, Fabrication and Characterization of a Bistable Electromagnetic Microrelay With Large Displacement
,” Microelectron. J.
, 42
(8
), pp. 992
–998
. 10.1016/j.mejo.2011.05.00416.
Wu
, Y. B.
, Ding
, G. F.
, Zhang
, C. C.
, Wang
, J. A.
, Mao
, S. P.
, and Wang
, H.
, 2010
, “Design and Implementation of a Bistable Microcantilever Actuator for Magnetostatic Latching Relay
,” Microelectron. J.
, 41
(6
), pp. 325
–330
. 10.1016/j.mejo.2010.03.00617.
Chen
, T.
, and Shea
, K.
, 2018
, “An Autonomous Programmable Actuator and Shape Reconfigurable Structures Using Bistability and Shape Memory Polymers
,” 3D Print. Addit. Manuf.
, 5
(2
), pp. 91
–101
. 10.1089/3dp.2017.011818.
Chouinard
, P.
, and Plante
, J. S.
, 2012
, “Bistable Antagonistic Dielectric Elastomer Actuators for Binary Robotics and Mechatronics
,” IEEE/ASME Trans. Mechatron.
, 17
(5
), pp. 857
–865
. 10.1109/TMECH.2011.213586219.
Zaidi
, S.
, Lamarque
, F.
, Favergeon
, J.
, Carton
, O.
, and Prelle
, C.
, 2011
, “Wavelength-Selective Shape Memory Alloy for Wireless Microactuation of a Bistable Curved Beam
,” IEEE Trans. Ind. Electron.
, 58
(12
), pp. 5288
–5295
. 10.1109/TIE.2010.204660920.
Armanini
, C.
, Dal Corso
, F.
, Misseroni
, D.
, and Bigoni
, D.
, 2017
, “From the Elastica Compass to the Elastica Catapult: An Essay on the Mechanics of Soft Robot Arm
,” Proc. Math. Phys. Eng. Sci.
, 473
(2198
), p. 20160870
. 10.1098/rspa.2016.087021.
Sneller
, A. J.
, Cette
, P.
, and Mann
, B. P.
, 2011
, “Experimental Investigation of a Post-Buckled Piezoelectric Beam With an Attached Central Mass Used to Harvest Energy
,” Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng.
, 225
(I4
), pp. 497
–509
. 10.1177/095965181140195422.
Harne
, R. L.
, and Wang
, K. W.
, 2013
, “A Review of the Recent Research on Vibration Energy Harvesting via Bistable Systems
,” Smart Mater. Struct.
, 22
(2
), p. 023001
. 10.1088/0964-1726/22/2/02300123.
Charlot
, B.
, Sun
, W.
, Yamashita
, K.
, Fujita
, H.
, and Toshiyoshi
, H.
, 2008
, “Bistable Nanowire for Micromechanical Memory
,” J. Micromech. Microeng.
, 18
(4
), p. 045005
. 10.1088/0960-1317/18/4/04500524.
Roodenburg
, D.
, Spronck
, J. W.
, van der Zant
, H. S. J.
, and Venstra
, W. J.
, 2009
, “Buckling Beam Micromechanical Memory With On-Chip Readout
,” Appl. Phys. Lett.
, 94
(18
), p. 183501
. 10.1063/1.312919525.
Hansen
, B. J.
, Carron
, C. J.
, Jensen
, B. D.
, Hawkins
, A. R.
, and Schultz
, S. M.
, 2007
, “Plastic Latching Accelerometer Based on Bistable Compliant Mechanisms
,” Smart Mater. Struct.
, 16
(5
), pp. 1967
–1972
. 10.1088/0964-1726/16/5/05526.
Zhao
, J.
, Jia
, J.
, Wang
, H.
, and Li
, W.
, 2007
, “A Novel Threshold Accelerometer With Postbuckling Structures for Airbag Restraint Systems
,” IEEE Sensors J.
, 7
(7–8
), pp. 1102
–1109
. 10.1109/JSEN.2007.89793627.
Harne
, R. L.
, and Wang
, K. W.
, 2017
, Harnessing Bistable Structural Dynamics: For Vibration Control,” Energy Harvesting and Sensing
, John Wiley & Sons Ltd.
, Hoboken, NJ
.28.
Chen
, J. S.
, Ro
, W. C.
, and Lin
, J. S.
, 2009
, “Exact Static and Dynamic Critical Loads of a Sinusoidal Arch Under a Point Force at the Midpoint
,” Int. J. Non Linear Mech.
, 44
(1
), pp. 66
–70
. 10.1016/j.ijnonlinmec.2008.08.00629.
Chen
, J. S.
, and Ro
, W. C.
, 2010
, “Deformations and Stability of an Elastica Subjected to an Off-Axis Point Constraint
,” ASME J. Appl. Mech.
, 77
(3
), p. 031006
. 10.1115/1.400042630.
Chen
, J. S.
, and Hung
, S. Y.
, 2011
, “Snapping of an Elastica Under Various Loading Mechanisms
,” Eur. J. Mech. A. Solids
, 30
(4
), pp. 525
–531
. 10.1016/j.euromechsol.2011.03.00631.
Cazzolli
, A.
, and Dal Corso
, F.
, 2019
, “Snapping of Elastic Strips With Controlled Ends
,” Int. J. Solids Struct.
, 162
(4
), pp. 285
–303
. 10.1016/j.ijsolstr.2018.12.00532.
Patrício
, P.
, Adda-Bedia
, M.
, and Ben Amar
, M.
, 1998
, “An Elastica Problem: Instabilities of an Elastic Arch
,” Physica D
, 124
(1–3
), pp. 285
–295
. 10.1016/S0167-2789(98)00203-633.
Chen
, G. M.
, and Ma
, F. L.
, 2015
, “Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model
,” ASME J. Mech. Des.
, 137
(2
), p. 022301
. 10.1115/1.402902434.
Han
, Q.
, Jin
, K.
, Chen
, G.
, and Shao
, X.
, 2017
, “A Novel Fully Compliant Tensural-Compresural Bistable Mechanism
,” Sens. Actuators, A
, 268
(16
), pp. 72
–82
. 10.1016/j.sna.2017.10.01235.
Magnusson
, A.
, Ristinmaa
, M.
, and Ljung
, C.
, 2001
, “Behaviour of the Extensible Elastica Solution
,” Int. J. Solids Struct.
, 38
(46–47
), pp. 8441
–8457
. 10.1016/S0020-7683(01)00089-036.
Vangbo
, M.
, 1998
, “An Analytical Analysis of a Compressed Bistable Buckled Beam
,” Sens. Actuators, A
, 69
(3
), pp. 212
–216
. 10.1016/S0924-4247(98)00097-137.
Camescasse
, B.
, Fernandes
, A.
, and Pouget
, J.
, 2013
, “Bistable Buckled Beam: Elastica Modeling and Analysis of Static Actuation
,” Int. J. Solids Struct.
, 50
(19
), pp. 2881
–2893
. 10.1016/j.ijsolstr.2013.05.00538.
Camescasse
, B.
, Fernandes
, A.
, and Pouget
, J.
, 2014
, “Bistable Buckled Beam and Force Actuation: Experimental Validations
,” Int. J. Solids Struct.
, 51
(9
), pp. 1750
–1757
. 10.1016/j.ijsolstr.2014.01.01739.
Huang
, Y.
, Zhao
, J.
, and Liu
, S.
, 2016
, “Design Optimization of Segment-Reinforced Bistable Mechanisms Exhibiting Adjustable Snapping Behavior
,” Sens. Actuators, A
, 252
(16
), pp. 7
–15
. 10.1016/j.sna.2016.10.01440.
Cazottes
, P.
, Fernandes
, A.
, Pouget
, J.
, and Hafez
, M.
, 2009
, “Bistable Buckled Beam: Modeling of Actuating Force and Experimental Validations
,” ASME J. Mech. Des.
, 131
(10
), p. 101001
. 10.1115/1.317900341.
Pham
, H. T.
, and Wang
, D. A.
, 2011
, “A Quadristable Compliant Mechanism With a Bistable Structure Embedded in a Surrounding Beam Structure
,” Sens. Actuators, A
, 167
(2
), pp. 438
–448
. 10.1016/j.sna.2011.02.04442.
Danso
, L. A.
, and Karpov
, E. G.
, 2017
, “Cusp Singularity-Based Bistability Criterion for Geometrically Nonlinear Structures
,” Extreme Mech. Lett.
, 13
(4
), pp. 135
–140
. 10.1016/j.eml.2017.01.00143.
Virgin
, L. N.
, Wiebe
, R.
, Spottswood
, S. M.
, and Eason
, T. G.
, 2014
, “Sensitivity in the Structural Behavior of Shallow Arches
,” Int. J. Non Linear Mech.
, 58
, pp. 212
–221
. 10.1016/j.ijnonlinmec.2013.10.00344.
Cox
, B. S.
, Groh
, R. M. J.
, Avitabile
, D.
, and Pirrera
, A.
, 2018
, “Exploring the Design Space of Nonlinear Shallow Arches With Generalised Path-Following
,” Finite Elem. Anal. Des.
, 143
(4
), pp. 1
–10
. 10.1016/j.finel.2018.01.00445.
Pi
, Y. L.
, Bradford
, M. A.
, and Guo
, Y. L.
, 2016
, “Revisiting Nonlinear In-Plane Elastic Buckling and Postbuckling Analysis of Shallow Circular Arches Under a Central Concentrated Load
,” J. Eng. Mech.
, 142
(8
), pp. 1
–10
. 10.1061/(asce)em.1943-7889.000109846.
Arena
, G.
, Groh
, R. M. J.
, Brinkmeyer
, A.
, Theunissen
, R.
, Weaver
, P. M.
, and Pirrera
, A.
, 2017
, “Adaptive Compliant Structures for Flow Regulation
,” Proc. Math. Phys. Eng. Sci.
, 473
(2204
), p. 20170334
. 10.1098/rspa.2017.033447.
Eriksson
, A.
, 1997
, “Equilibrium Subsets for Multi-Parametric Structural Analysis
,” Comput. Meth. Appl. Mech. Eng.
, 140
(3–4
), pp. 305
–327
. 10.1016/S0045-7825(96)01096-148.
Harne
, R. L.
, and Wang
, K. W.
, 2014
, “A Bifurcation-Based Coupled Linear-Bistable System for Microscale Mass Sensing
,” J. Sound. Vib.
, 333
(8
), pp. 2241
–2252
. 10.1016/j.jsv.2013.12.01749.
Romeo
, F.
, Manevitch
, L. I.
, Bergman
, L. A.
, and Vakakis
, A.
, 2015
, “Transient and Chaotic Low-Energy Transfers in a System With Bistable Nonlinearity
,” Chaos
, 25
(5
), p. 053109
. 10.1063/1.492119350.
Manevitch
, L. I.
, Sigalov
, G.
, Romeo
, F.
, Bergman
, L. A.
, and Vakakis
, A.
, 2014
, “Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Analytical Study
,” ASME J. Appl. Mech.
, 81
(4
), p. 041011
. 10.1115/1.402515051.
Mattei
, P. O.
, Poncot
, R.
, Pachebat
, M.
, and Côte
, R.
, 2016
, “Nonlinear Targeted Energy Transfer of Two Coupled Cantilever Beams Coupled to a Bistable Light Attachment
,” J. Sound Vib.
, 373
(14
), pp. 29
–51
. 10.1016/j.jsv.2016.03.00852.
Groh
, R. M. J.
, Avitabile
, D.
, and Pirrera
, A.
, 2018
, “Generalised Path-Following for Well-Behaved Nonlinear Structures
,” Comput. Meth. Appl. Mech. Eng.
, 331
(4
), pp. 394
–426
. 10.1016/j.cma.2017.12.00153.
Bathe
, K. J.
, 1996
, Finite-Element Procedures
, Prentice Hall, Inc.
, Englewood Cliffs, NJ
.Copyright © 2019 by ASME
You do not currently have access to this content.
