Static Loads Influence on Modal Properties of the Composite Cylindrical Shells with Integrated Sensor Network
Round 1
Reviewer 1 Report
This manuscript investigates the modal properties of composite cylindrical shells under axial tension using experimental and numerical methods. The study is within the scope of SENSORS and is of high quality. The reviewer recommends publication of this manuscript after responding to the following comments
- The unit mm was missing from the dimensioning of Fig. 1.
- L133, the height of cylindrical shell was 760 mm, however in figure 1 it was 790mm, please check.
- As the weight was suspended at the centre of the flange, then the flange was subjected to a radial force, which resulted in a small deformation. In this case was the cylindrical shell still subjected to axial tension only? Please provide more discussion.
- L326, more details about the numerical model are expected to be given, such as the final mesh size to be used, the numerical calculation method (explicit or implicit?) etc.
- What was the material constitutive model for composite cylindrical shells in the numerical model, please clarify.
- Perhaps it would be helpful for similar studies if the authors could discuss in more depth the reasons for the differences between numerical simulations and experiments.
- The reviewer also read the authors' preliminary work:
Mironov, A.; Safonovs, A.; Mironovs, D.; Doronkin, P.; Kuzmickis, V. Health Monitoring of Serial Structures Applying Piezoelectric Film Sensors and Modal Passport. Sensors 2023, 23, 1114. https://doi.org/10.3390/s23031114
In this article, the cylindrical shell had no tensile effect. However, the numerical model material parameters in this paper do not appear to be consistent with the material parameters of this study. The reviewers expect the authors to add more details and discussion.
Author Response
1. The unit mm was missing from the dimensioning of Fig. 1.
Thank You for the comment. Dimensions were added in Fig.1.
2. L133, the height of cylindrical shell was 760 mm, however in figure 1 it was 790mm, please check.
Thank You for the comment. In this case the height of cylindrical shell was 760 mm without plywood flanges and before gluing in the recesses of the plywood flange. The deep of recesses in the plywood flange are 15 mm. Therefore, in figure 1 the height of the composite cylinder without the height of the flanges is shown as 730 mm. I added a sentence to the text to explain the difference between the heights of composite shells in the text and in the picture.
“At the last stage of production of serial samples, to ensure the mechanical strength of a tested specimen, its upper and lower edges are glued into the recesses of the plywood flange (30-mm thickness). The deep of recesses are 15 mm. Active height of circular cylindrical shell between plywood flanges is 730 mm.”
3. As the weight was suspended at the centre of the flange, then the flange was subjected to a radial force, which resulted in a small deformation. In this case was the cylindrical shell still subjected to axial tension only? Please provide more discussion.
The follow sentences were added in the text.
“A nonlinear static calculation show that, there are radial forces from flanges that caused by static load. These forces compress ends of the cylinder part leading to compressive strains in the circumferential direction. There is also uneven disribution of strains along the height of cylynder part. So, in the cylinder shell tensile stresses in the axial direction are combined with compressive stresses in the circumferential direction.”
4. L326, more details about the numerical model are expected to be given, such as the final mesh size to be used, the numerical calculation method (explicit or implicit?) etc.
The description of mesh convergence study was added in the text.
“Before numerical calculations, the mesh convergence analysis was carried out to obtain results with acceptable accuracy. The mesh convergence study was carried out for the element sizes of 5x5, 10x10, 15x15, and 20x20 mm on a composite cylinder shell without rigid plywood flanges [38]. Free–free boundary conditions were used for calculation of first 22 natural frequencies in composite cylinder. The mode shapes at the element size of 5x5 and 10x10 mm were similar which testifies the good correlation of the results obtained. During calculation mode shapes changed beginning with the element size of 15x15 mm and 20x20 mm after 9th and 3rd mode shapes, respectively. Thus, the finite element model with element size of 10x10 mm was chosen for ensuring the high accuracy of future research and decreasing the time of calculation.”
A few words about implicit were added in the text
Firstly, a static nonlinear calculation of the model by implicit solver is carried out using the option taking into account the effect of the resulting stresses from the axial load. Then, the natural frequencies and mode of vibrations, taking into account the prestressed state, are determined by modal analysis accounting for the results of the static analysis.
5. What was the material constitutive model for composite cylindrical shells in the numerical model, please clarify.
Thank You for the comment. The properties of composite material in ANSYS software defined as Linear-Elastic-Orthotropic. Geometric nonlinearity of the model is taken into account during calculation.
6. Perhaps it would be helpful for similar studies if the authors could discuss in more depth the reasons for the differences between numerical simulations and experiments.
Thank You for the comment. The follow sentences were added in the text.
“According to the studies, the natural frequencies and vibration modes of a prestressed system differ from those for an unstressed. However, the experimental values of natural frequencies for some vibration modes with an increasing the applied tensile load do not agree with the theoretical and calculated values. The increase and decrease of natural frequencies depending on the mode shape with the tensile load growth suggests that under tensile loads both compressive and tensile stresses simultaneously arise in the cylindrical shell. It is possible to put forward a number of assumptions about the reasons for some discrepancy between the experimental and analytical and numerical results obtained. Due to imperfection of the hand-layup method of manufacturing cylindrical specimens its uneven wall thickness can cause a change in the stress-strain state of the cylinder under the action of an axial tensile load.”
Natural vibration modes depend on the configuration of a structure and the longitudinal and transverse waves propagation in its material. If tensile stresses of structure lead to grow in the speed of wave propagation and increase natural frequencies, when a compress stresses may have an opposite effect. Depending on the mode shape the dual influence of positive and negative values of stresses may have different effects. The specimens considered in this study were manufactured manually, and the wall thickness is irregular. This effect leads to an increase in the uneven distribution of tensile and compressive stresses in axial and circumferential directions.”
7. The reviewer also read the authors' preliminary work:
Mironov, A.; Safonovs, A.; Mironovs, D.; Doronkin, P.; Kuzmickis, V. Health Monitoring of Serial Structures Applying Piezoelectric Film Sensors and Modal Passport. Sensors 2023, 23, 1114. https://doi.org/10.3390/s23031114. In this article, the cylindrical shell had no tensile effect. However, the numerical model material parameters in this paper do not appear to be consistent with the material parameters of this study. The reviewers expect the authors to add more details and discussion.
In the above-mentioned article, another author has made calculations of cylindrical shells that was modelled in conjunction with test bench. It’s know, that determination the elastic constants of laminated composite materials is much more complicated in comparison with isotropic materials and requires more effort and time. Therefore, the values of material properties of unidirectional E-glass fibre/epoxy lamina were taken from publication in which values were close of material used for manufactured composite cylinders. Numerical -experimental method for identification of material properties was used in this publication to improve finite element model for future calculation numerical. Comparative analysis of errors between two finite element models shows that in this publication errors between numerical and experimental frequencies are less.
Reviewer 2 Report
Maniscript: sensors-2280141
Dear authors,
I would like to thanks the authors.
The research sounds like a good idea, please address the following comments:
1- First of all please explain the innovativity of the research clearly in the introduction part.
2- As mentioned in the abstract :”the tensile load influence functions for modal frequency and shape parameters ob-545 tained from the experimental data were not fully consistent with the numerical”, Can you explain why this inconsistency exists?
3- Explain how the equation 11 is generated? If S matrix is added to the relation because of the stresses, then traditional matrix is not changed?
4- Why the final load in Fig 9 is 4817N? which criteria is used to define this load?
5- How did you do the verification process of the numerical model?
6- In eq.3 frequency on temperature, is dependence of the modal parameter on the static load linear?
7- How did you define nonlinear properties of the composoite in Ansys software? The how are the interactions defined?
8- The date of reference No:7 is not specified. The style and the format of references should be revised.
Author Response
First of all please explain the innovation of the research clearly in the introduction part.
Thank You for the comment. The follow sentences were added in the text.
“This study is part of the project developing the technologies for structural health monitoring (SHM) of serial structures using the methods of operational modal analysis. The two main elements of the novelty of this project, implemented in the framework of this study, are the use of piezoelectric films as sensors and the modal passport. This new application of such sensors for SHM is based on their low cost and negligible mass. The modal passport is a set of methods and calculations of diagnostic parameters of working structures. A modal passport enables, using the modal properties common to serial structures, to monitor each particular specimen. As external conditions may vary for different specimen so, the influence functions are used that takes into account actual conditions. Influence functions are general for identical structures and being determined by testing the set of such structures allow taking into account external conditions for health monitoring the particular specimen. The current work is devoted to the study of the influence of a specific factor - tensile load - on the modal properties of the same type specimens. Having generalized this influence over all specimens of the series, we obtained an influence function that can be used for SHM within the framework of the modal passport.”
As mentioned in the abstract: ”the tensile load influence functions for modal frequency and shape parameters obtained from the experimental data were not fully consistent with the numerical”, Can you explain why this inconsistency exists?
Thank You for the comment. The additional sentences about difference between numerical and experimental data were added in the text.
“According to the studies, the natural frequencies and vibration modes of a prestressed system differ from those for an unstressed. However, the experimental values of natural frequencies for some vibration modes with an increasing the applied tensile load do not agree with the theoretical and calculated values. The increase and decrease of natural frequencies depending on the mode shape with the tensile load growth suggests that under tensile loads both compressive and tensile stresses simultaneously arise in the cylindrical shell. It is possible to put forward a number of assumptions about the reasons for some discrepancy between the experimental and analytical and numerical results obtained. Due to imperfection of the hand-layup method of manufacturing cylindrical specimens its uneven wall thickness can cause a change in the stress-strain state of the cylinder under the action of an axial tensile load.”
Natural vibration modes depend on the configuration of a structure and the longitudinal and transverse waves propagation in its material. If tensile stresses of structure lead to grow in the speed of wave propagation and increase natural frequencies, when a compress stresses may have an opposite effect. Depending on the mode shape the dual influence of positive and negative values of stresses may have different effects. The specimens considered in this study were manufactured manually, and the wall thickness is irregular. This effect leads to an increase in the uneven distribution of tensile and compressive stresses in axial and circumferential directions.”
Explain how the equation 11 is generated? If S matrix is added to the relation because of the stresses, then traditional matrix is not changed?
Thank You for the comment. The procedure for performing a modal analysis of prestressed composite shells in finite element program ANSYS is concerned by the effect of initial stress on the dynamic response of composite structure. The follow sentences were added in the text.
Nonlinear static analysis is performed to obtain the change in geometry and the arising stresses in the model. Then, the additional stiffness matrix is calculated from the stresses, and the final equation for calculating natural frequencies and modes of vibrations of the prestressed structure takes the following form:
,
(11)
where is the stiffness matrix taking to account the change in geometry, is the so-called geometric stiffness matrix obtained on the basis of the prestress tensor and the nonlinear part of the strain tensor [37].
Why the final load in Fig 9 is 4817N? which criteria is used to define this load?
The step of loading of the samples was determined by the weight of the metal parts used as weights. These parts had approximately the same weight of 33.7 ± 2.5 kg. Since the upper load limit was 5000 N, the maximum load of the 14 parts was 4817 N.
How did you do the verification process of the numerical model?
A few words about verification process were added in the text.
“Before numerical calculations, the mesh convergence analysis was carried out to obtain results with acceptable accuracy. The mesh convergence study was carried out for the element sizes of 5x5, 10x10, 15x15, and 20x20 mm on a composite cylinder shell without rigid plywood flanges [38]. Free–free boundary conditions were used for calculation of first 22 natural frequencies in composite cylinder. The mode shapes at the element size of 5x5 and 10x10 mm were similar which testifies the good correlation of the results obtained. During calculation mode shapes changed beginning with the element size of 15x15 mm and 20x20 mm after 9th and 3rd mode shapes, respectively. Thus, the finite element model with element size of 10x10 mm was chosen for ensuring the high accuracy of future research and decreasing the time of calculation.”
In eq.3 frequency on temperature, is dependence of the modal parameter on the static load linear?
Eq.3 describes modal frequency dependence on temperature based on assumption that this dependence may be linear as the numerical simulation showed (fig.5). As further experimental study indicates the modal frequencies of most of modes have behavior close to linear (fig.7).
How did you define nonlinear properties of the composite in Ansys software? The how are the interactions defined?
The properties of composite material in ANSYS software defined as Linear-Elastic-Orthotropic. Geometric nonlinearity of the model is taken into account during calculation.
The date of reference No:7 is not specified. The style and the format of references should be revised.
Thank You for the comment. I checked style format of reference No7.
Author Response File: 
Author Response.pdf
Round 2
Reviewer 2 Report
Dear The Editor
I think the paper can be accepted in the present form.
Best Regards
