Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: (a) A schematic diagram showing the dimensions of the beam, side electrodes, bottom electrode, and the actuation voltages Vs and Vg; (b) schematic of electric field lines under the influence of fringing force and direct force, respectively; (c) sectional side view of the cantilever beam and the bottom electrode; and (d) sectional side view of the fixed–fixed beam and the bottom electrode

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: Variation of approximate static deflection versus the dc-voltage parameter between the beam and the bottom electrode, i.e., η¯dcBb2 for different values of the dc voltage parameter between the beam and the side electrodes η¯dcBs2=0,0.2,0.4,0.6,0.8, and 1 for (a) the fixed–fixed beam and (b) the cantilever beam. Figures shown inside (a) and (b) represent the variation of pull-in point with the dc voltage parameter of the beam and the side electrodes (here, “LP” indicates the start of unstable solution, i.e., the pull-in point).

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: Comparison of solutions based on MMS and the numerical simulation for the fixed–fixed microbeam under (a) the direct force excitation (η¯dcBs = 0,η¯dcBb = 0.02,η¯acBs = 0,η¯acBb = 0.07), (b) the fringing force excitation (η¯dcBs = 0.02,η¯dcBb = 0,η¯acBs = 0.07,η¯acBb = 0), and (c) the combined effect of the direct and fringing force excitation (η¯dcBs = 0.02,η¯dcBb = 0.02,η¯acBs = 0.07,η¯acBb = 0.07). Here, β = 1.84,μNL = 0.9,μL = 0.001, α = 1.

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: Comparison of solutions based on MMS and the numerical simulation for the cantilever microbeam under (a) the direct force excitation (η¯dcBs = 0,η¯dcBb = 0.02,η¯acBs = 0,η¯acBb = 0.2), (b) the fringing force excitation (η¯dcBs = 0.02,η¯dcBb = 0,η¯acBs = 0.2,η¯acBb = 0), and (c) the combined effect of the direct and fringing force excitation (η¯dcBs = 0.02,η¯dcBb = 0.02,η¯acBs = 0.2,η¯acBb = 0.2). Here, β = 0.3,μNL = 0.5,μL = 0.001, α = 1.

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: Frequency response of fixed–fixed microbeam for different ac voltages under the influence of (a) direct force excitation (η¯dcBs = 0,η¯dcBb = 0.2,η¯acBs = 0,η¯acBb = 0.4,0.6,0.8); (b) fringing force excitation (parametric excitation) (η¯dcBs = 0.2,η¯dcBb = 0,η¯acBs = 0.4,0.6,0.8,η¯acBb = 0); and (c) the combined (direct + fringing) force excitation (η¯dcBs = 0.2,η¯dcBb = 0.2,η¯acBs = 0.4,0.6,0.8,η¯acBb = 0.4,0.6,0.8). Here, β = 1.84,μL = 0.001,μNL = 0.5,α = 1. Solid lines represent stable solutions and dash lines represents unstable solutions.

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: Frequency response of cantilever microbeam for different ac voltages under the influence of (a) direct force excitation (η¯dcBs = 0,η¯dcBb = 0.2,η¯acBs = 0,η¯acBb = 0.4,0.6,0.8); (b) fringing force excitation (parametric excitation) (η¯dcBs = 0.2,η¯dcBb = 0,η¯acBs = 0.4,0.6,0.8,η¯acBb = 0); and (c) the combined (direct + fringing) force excitation (η¯dcBs = 0.2,η¯dcBb = 0.2,η¯acBs = 0.4,0.6,0.8,η¯acBb = 0.4,0.6,0.8). Here, β = 0.3,μL = 0.001,μNL = 0.5,α = 1. Solid lines represent stable solutions and dash lines represents unstable solutions.

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: The variation of frequency response of the beam for different values of nonlinear damping parameter μNL under (a) the direct force excitation, (b) the fringing force excitation (parametric excitation), and (c) the combined (direct + fringing) force excitation (here, β = 0,μL = 0.001,α = 1,η¯dcBb = η¯dcBs = 0.2, and η¯acBb = η¯acBs = 0.35)

Date of download: 12/29/2017 Copyright © ASME. All rights reserved. From: Nonlinear Response of a Microbeam Under Combined Direct and Fringing Field Excitation J. Comput. Nonlinear Dynam. 2015;10(5):051010-051010-10. doi:10.1115/1.4029700 Figure Legend: Effect of nonlinear stiffness, β, on the frequency response of the beam under (a) the direct force excitation, (b) the fringing force excitation (parametric excitation), and (c) the combined (direct + fringing) force excitation for the following parameter values μNL = 0.5,μL = 0.001,α = 1,η¯dcBb = η¯dcBs = 0.2,η¯acBb = η¯acBs = 0.8