Active Vibration Control of Cantilever Structures by Integrating the Closed Loop Control Action into Transient Solution of Finite Element Model and an Application to Aircraft Wing

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

An active vibration control (AVC) of a cantilever beam is studied in this paper . The disturbance is considered as an impulse to the end mass. The controlling action is considered as the velocity actutation to the base, which can be generated with servo motors and servo valves. Displacement feedback is used in simulations because of the difficulty to obtain strain signals in the transient solution stage in ANSYS. Finite element model of cantilever beam with end mass is developed for AVC analysis with Laplace transform and Newmark methods. The control action is integrated to the transient solution in Newmark method.

This paper has high theoretical significance and engineering application value. It is recommended to revise and accept it.

There are the following questions that need to be explained or supplemented：

1 What are the application scenarios of using the motion of the root of a cantilever beam as the input position for control? What is the significance of the project?

2Is it a special case that the position of the external disturbance excitation used in the paper coincides with the position of the response target point? If there is no overlap, verification and analysis are required;

3 The goal of the basic control algorithm is not clear enough, as shown in Figure 4. What is the goal to achieve the minimum?

4  What is the relationship between Laplace method, Newmark method, and APDL method? What algorithm is used in APDL method;

5 The cantilever beam example in the paper only uses the first-order mode, and the second-order bending mode is about 50-80Hz, which also needs to be controlled and the results of the example need to be expanded;

6 Suggest deleting the research content in section 5.4, which is no different from the cantilever beam example and repetitive work;

7 What is the specific time-domain data for the initial impulse response? It needs to be provided.

Author Response

Please see the attached document.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this manuscript, a cantilever beam system with end masses is explored. The end masses are subjected to impulse interference and the control action is realized by basal velocity excitation generated by servo motors and valves. Strain signals amplified by load cell amplifiers are used as feedback in the experiments. Displacement feedback is used in the simulation because it is difficult to obtain the strain signal in the ANSYS transient solving stage. Experimentally comparing the strain and displacement feedback signals, it is found that they are approximately linearly correlated. A finite element model of the cantilever beam for active vibration control (AVC) analysis is established by Laplace transform and Newmark method. Some comments are given by:

• In section 2.1, the assembled relationships between the overall mass and stiffness matrices and the unit mass and stiffness matrices are given (The assembled system matrices can be obtained using Table 1 as given below as examples:), but only two examples are given, and it is hoped that the authors can give specific assembly methods. In addition, the content of the article lacks innovation, the finite unit method used for theoretical analysis and the proportional control used for control are very mature methods in the field of vibration control of beams, and the authors just combine them with ANSYS to realize the vibration control in software, and the models and methods lack novelty.
• The paper mentions the use of strain feedback for active control of vibration and suggests in section 5.1 that the results obtained from simulations using displacement feedback can be used in applications using strain feedback by means of experiments, but does not analyze the relationship between the two theoretically, and suggests that the relationship between displacement and strain during vibration of cantilever beams should be analyzed theoretically. By comparing Figures 10-13 in the text, it is found that the control effect of the experiment is even better than that of the theory and simulation, and it is hoped that the authors will further analyze the reasons for the appearance of this result.
• The authors mentioned in section 5.1 that the disturbance signal in the experiment is input by human beings with randomness, but the subsequent experimental process and theoretical and numerical analyses of the working conditions are relatively single, just changing the proportional control parameter Kp, and it is recommended to design several more groups of working conditions to eliminate the factors of human interference.
• The font size of the formulas in the article is inconsistent (for example, Formula 10 and Table 2 in the article), some of the formula numbers are not right-aligned (for example, Formulas 1 and 3 in the article), most of the formulas are not centered or left-aligned, and some of the titles of the pictures have not been formatted uniformly, and in general, the formulas in the article are more randomly laid out. There are some strange sentence structures in the article, such as the strange line break between the ninth and eighth penultimate lines of section 2.3, and the spaces between the words “is constructed” and “strain gauges” in the second paragraph of section 3. The spaces between words should not be there, in short, the sentences of the article need to be revised carefully, in addition, the program seems to be cumbersome to put in the text, it is recommended to put it in the appendix for explanation.

Comments on the Quality of English Language

 The manuscript needs to be improved and enhanced in terms of its writing. For example，the font size of the formulas in the article is inconsistent (for example, Formula 10 and Table 2 in the article), some of the formula numbers are not right-aligned (for example, Formulas 1 and 3 in the article), most of the formulas are not centered or left-aligned, and some of the titles of the pictures have not been formatted uniformly, and in general, the formulas in the article are more randomly laid out. There are some strange sentence structures in the article, such as the strange line break between the ninth and eighth penultimate lines of section 2.3, and the spaces between the words “is constructed” and “strain gauges” in the second paragraph of section 3. The spaces between words should not be there, in short, the sentences of the article need to be revised carefully, in addition, the program seems to be cumbersome to put in the text, it is recommended to put it in the appendix for explanation.

Author Response

Please see the attached document.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper discusses the active vibration control (AVC) of cantilever structures, integrating multiple methods including experimental study, Laplace transform analytical method, Newmark numerical method, and finite element analysis, ANSYS. Particularly, it incorporates closed-loop control into ANSYS transient analysis, which is not a direct feature of the software itself, contributing to its academic value.

Experiments and simulations demonstrate a high consistency between the simulation results obtained from the Newmark method, ANSYS, and the Laplace transform analytical method. The behavior of AVC with varying control gains Kp also shows consistency.

The paper attempts to apply the research findings to the complex structure of aircraft wing AVC simulations. However, there are significant differences from the original cantilever-beam model, and more explanation is recommended to substantiate their equivalence.

The paper is somewhat lengthy. Considerations in the experiments for sensor linearity and accuracy, experimental determination of damping coefficients, and the mathematical derivation of the matrix are relatively mature techniques and could be appropriately simplified.

Are the conditions for impulse disturbance consistent every time? A detailed explanation of the loading method and the impact of its variations should be provided.

Why does the control strategy only consider proportional (P) control? The most basic approach generally includes proportional-integral-derivative control (PID), or possibly other advanced control methods.

The paper mentions difficulties in directly obtaining strain signals during the transient analysis in ANSYS, which appears inaccurate. The authors (researchers) should further investigate the operational use of the software. Even though strain values are obtained in the post-processing stage using the etable command, these are somewhat processed results.

The damping coefficient for the aircraft wing is determined through a "visual estimation" method to obrain the Rayleigh damping coefficient. Compared with experimental measurement, this method might lack precision. While the paper aims to solve aircraft wing AVC through simulation without physical implementation, using literature to support the data would be more appropriate.

Although the ANSYS was illustrated on the use of element types, it does not clarify the accurate criteria for mesh numbers and time increments in convergence. Further explanation is needed to validate the generality and applicability of the ANSYS procedure for other structural types or structures with different vibration characteristics.

Author Response

Please see the attached document.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

In this manuscript, closed-loop control of a cantilever beam system with an end mass block is achieved by strain and displacement feedback and verified experimentally and by ANSYS finite elements. The manuscript is logically organized. With minor revisions addressing the points below, this work is recommended for acceptance.

1. Section 5.1 states that disturbance signals are "manually input," but the experiments only vary the proportional control parameter Kp. This single-factor approach may introduce bias from artificial randomness, limiting the generalizability of conclusions. Suggest some additional control groups.
2. There are still some minor issues regarding layout and expression.

Author Response

Please see the attached document.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The reviewers' comments have been appropriately addressed and incorporated into the manuscript. This paper can be accepted for publication.

Author Response

Please see the attached document.

Author Response File: Author Response.pdf