On the Structural Behavior of MEMS Shallow Arch under Combined Effects of In-Plane Parallel Fields and Out-of-Plane Fringing-Fields
Round 1
Reviewer 1 Report
The authors investigated the nonlinear stroke and modal interactions of a shallow arch flexible micro-electrode by inducing in-plane parallel and out-of-plane fringing fields separately and combinedly. Detailed simulation results were presented for different types of field actuation. Overall, the paper is well-written and well-presented. However, the following issues need to be addressed in the revised manuscript. I therefore cannot recommend publication of the work in this present form.
- The Numerical reduced-order model section is not self-contained. They provided a general overview of mathematical steps to obtain a set 'N' of ODE from a nonlinear partial equation. It would be completed and more insightful if they provide a little more about the obtained formula for their MEMS case without showing any detailed calculations. For example, what the basic functions were and what criteria they used to replace the modal amplitude u_i(t) by unknown constants c_i (line no. 130-131).
2. Simulation results have been demonstrated by varying different parameters. For example, voltage V_pp and V_FF, gap b_0, horizontal offset g, electrode size L_e, etc. have been varied, and the corresponding measurements have been recorded. Authors should clarify for the readers how w(x,t) varies with the flexible arch electrode's varying surface area (Lb). For example, the surface area can be (L/4)b, (L/2)b, and Lb, where L/4 >> h, and the corresponding deflection can be measured to understand how the size of the flexible electrode influences the deflection.
3. There are some typos, such as in line 48 in line 162. All the typos should be corrected in the revised manuscript.
4. The phrase 'the in-plane parallel field' seems missing in line 99. Please check whether the sentence expresses your intended idea.
5. Authors should add mathematical value in the abstract and conclusion should be sound and strong support to the experiments.
Author Response
We are very much thankful to the reviewer for the deep and thorough review. We have revised our present research paper in the light of the reviewer useful suggestions and comments. We hope our revision has improved the paper to the level of the reviewer satisfaction and the required quality for the journal.
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The authors investigated the nonlinear stroke and modal interactions of a shallow arch flexible micro-electrode by inducing in-plane parallel and out-of-plane fringing fields separately and combinedly. Detailed simulation results were presented for different types of field actuation. Overall, the paper is well-written and well-presented. However, the following issues need to be addressed in the revised manuscript. I therefore cannot recommend publication of the work in this present form.
1. The Numerical reduced-order model section is not self-contained. They provided a general overview of mathematical steps to obtain a set 'N' of ODE from a nonlinear partial equation. It would be completed and more insightful if they provide a little more about the obtained formula for their MEMS case without showing any detailed calculations. For example, what the basic functions were and what criteria they used to replace the modal amplitude u_i(t) by unknown constants c_i (line no. 130-131).
We concur with the reviewer's assessment that the reduced-order model section may lack clarity in terms of its self-explanatory nature. Our intention was to avoid overwhelming this section with an abundance of equations and monotonous explanations readily available in standard textbooks within this field (kindly refer to [A, B]). Indeed, the governing equations, known as N-ODEs, are inherently time-varying and interconnected. To facilitate static simulations, we nullify all time-dependent components within these ODEs, encompassing elements such as inertia, damping, and variable forcing. We then substitute the time-dependent modal variables with unknown constants (which vary with time) denoted as Ci. This transformation results in a set of nonlinear algebraic equations, necessitating numerical solutions through the application of the Newton–Raphson method.
[A] Reddy J N (2002) Energy Principles and Variational Methods in Applied Mechanics.Wiley and Sons, NewYork
[B] Younis, M. I. (2011). MEMS linear and nonlinear statics and dynamics (Vol. 20). Springer Science & Business Media.
2. Simulation results have been demonstrated by varying different parameters. For example, DC voltages, initial rise, horizontal offset, and electrode size, have been varied, and the corresponding static results have been recorded. Authors should clarify for the readers how w(x,t) varies with the flexible arch electrode's varying surface area (Lb). For example, the surface area can be (L/4)b, (L/2)b, and Lb, where L/4 >> h, and the corresponding deflection can be measured to understand how the size of the flexible electrode influences the deflection.
We agree the feedback provided by the reviewer regarding the need to express both the parallel and fringing-fields electrostatic forces in terms of the flexible electrode surface area. In the case of the parallel-plates force, we adopt the Euler-Bernoulli beam equation model, which inherently considers forces per unit length. Therefore, the oversight of the electrode length in the expression of Coulomb's law is a reflection of this consideration.
Regarding the fringing-fields expression, we rely on Finite-Element numerical data and subsequently normalize the results by dividing by the length to obtain the respective force per unit length. This normalization process ensures that the forces are appropriately represented per unit length as required.
3. There are some typos, such as in line 48 in line 162. All the typos should be corrected in the revised manuscript.
We have carefully checked the original manuscript and corrected language errors to improve the readability of this paper while taking into account the reviewer recommendations.
4. The phrase 'the in-plane parallel field' seems missing in line 99. Please check whether the sentence expresses your intended idea.
We modified the phrase.
5. Authors should add mathematical value in the abstract and conclusion should be sound and strong support to the experiments.
Thanks for your suggestion. We took it into account in the abstract and conclusion.
Reviewer 2 Report
The authors have performed a theoretical study on the electromechanical behaviour of fixed-fixed MEMS beams with initial curvature. The study appears to be sound and comprehensive and the authors should consider the following comments:
1. My preference would have been to see the results compared against experimental measurement. As a minimum, it would be good to compare the theoretical modelling against a multiphysics simulation software (e.g. COMSOL or ANSYS).
2. The authors should think about a design that is more amenable to actual fabrication. The design shown in Fig 1 is not suitable for most fabrication processes.
3. It is not easy to track the data point against the axes for the plots in Fig. 12
Generally OK but more verbose than it needs to be and can be repetitive across sections. The authors should consider making the writing more concise and to the point.
Typo "deferential" in the Abstract
Author Response
We are very much thankful to the reviewer for the deep and thorough review. We have revised our present research paper in the light of the reviewer useful suggestions and comments. We hope our revision has improved the paper to the level of the reviewer satisfaction and the required quality for the journal. Number wise answers to his specific comments/suggestions/queries are as follows.
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The authors have performed a theoretical study on the electromechanical behaviour of fixed-fixed MEMS beams with initial curvature. The study appears to be sound and comprehensive and the authors should consider the following comments:
- My preference would have been to see the results compared against experimental measurement. As a minimum, it would be good to compare the theoretical modelling against a multiphysics simulation software (e.g. COMSOL or ANSYS).
Completely agree with the above reviewer comment, and we re-assure him that we have compared, in previously published papers, the PP (refer to [A] and FF (refer to [B]) static deflections with experimental data.
[A] Ouakad, H. M. (2014). Static response and natural frequencies of microbeams actuated by out-of-plane electrostatic fringing-fields. International Journal of Non-Linear Mechanics, 63, 39-48.
[B] Ouakad, H. M. (2018). Electrostatic fringing-fields effects on the structural behavior of MEMS shallow arches. Microsystem Technologies, 24, 1391-1399.
- The authors should think about a design that is more amenable to actual fabrication. The design shown in Fig 1 is not suitable for most fabrication processes.
We really thank the reviewer for his valuable comment on the design's suitability for fabrication. We do understand the importance of suggesting designs that are practical and feasible with the micro-fabrication processes. In response to your comment, we have thoroughly reviewed our design, particularly the one presented in Figure 1, and will take the above feedback into account. We have a future plan to restructure the proposed system while simplifying the design, minimizing elaborate features, and ensuring compatibility with standard micro-fabrication processes commonly used in the MEMS field. This would not be doable without consultation with certain micro-fabrication experts. We will ensure to seek the expertise of micro-fabrication specialists to ensure that our new design aligns with the capabilities of fabrication technologies available. Their insights will certainly be instrumental in refining the practical design.
We are committed to producing a design that is not only scientifically sound but also practically implementable. The reviewer feedback has been instrumental in guiding us toward this goal, and we are confident that these adjustments will lead to a more fabrication-friendly design. The possible adjustment of the MEMS design is pointed in section 2.
- It is not easy to track the data point against the axes for the plots in Fig. 12
Fig. 12 is modified in the revised version.
Comments on the Quality of English Language
- Generally OK but more verbose than it needs to be and can be repetitive across sections. The authors should consider making the writing more concise and to the point.
- Typo "deferential" in the Abstract
We have carefully checked the original manuscript and corrected language errors to improve the readability of this paper while taking into account the reviewer recommendations.
Round 2
Reviewer 1 Report
I have carefully reviewed author's response, and revised manuscript. Authors addressed all comments in the revised manuscript. I therefore, recommended the revised manuscript for publication in Actuators journal.
Author Response
We are very much thankful to the reviewer for the deep and thorough review.
Reviewer 2 Report
The authors have addressed my comments and suggestions.
Author Response
We are very much thankful to the reviewer for the deep and thorough review.
