Development of a Vibroacoustic Stochastic Finite Element Prediction Tool for a CLT Floor

Round  1

Reviewer 1 Report

Page 3

2.2. Measurement procedure

“…. to capture the vibration of the CLT panel and an impact roving hammer (Brüel&Kjær Impact hammer Type 8208 serial No. 51994) was used as excitation. The accelerometers and the impact hammer were connected to Brüel&Kjær front-end LAN-XI Type 3050”.

The acoustic measurements are important for understanding the vibrations of the wood. The authors should better describe in this paragraph specifying how the hammer is used and how the pulse is given with the same intensity.

Page 4 – row 148

“In general, it is a challenge task to create appropriate constraints to describe the boundary conditions”.

The choice of constraints is important in modeling. An incorrect choice leads to unreal results. The authors should better describe this choice. The choice of the constraints as it was performed? Has a sensitivity analysis been performed?

“Figure 10. Magnitude of the complex mobility in the vertical direction of point 11, 13, 17, 24. Simulated  FRFs in red, measured FRFs in blue.”

Over 150 Hz there is difference between  Simulated  FRFs in red, measured FRFs in blue, Why?

For the other points, what happens? Do the authors report only the best results?

With the use of software the user can get the results he wants.

Authors should perform a critical analysis of the numerical modeling performed. Maybe with sensitivity analysis of the input parameters from which it is possible to analyze how the parameters in the study are exiting the calculation model.

Author Response

Point 1:

Page 3

2.2. Measurement procedure

“…. to capture the vibration of the CLT panel and an impact roving hammer (Brüel&Kjær Impact hammer Type 8208 serial No. 51994) was used as excitation. The accelerometers and the impact hammer were connected to Brüel&Kjær front-end LAN-XI Type 3050”.

The acoustic measurements are important for understanding the vibrations of the wood. The authors should better describe in this paragraph specifying how the hammer is used and how the pulse is given with the same intensity

Response 1:

2.2.1. Measurement setup

EMA was performed on the CLT slab to characterize the dynamic properties of the CLT slab. The CLT panel was set free at two opposite long sides and simply supported (SFSF boundary condition) with two steel I-beams at two shorter edges (shown in Figure 1 (b)) in order to simplify the boundary conditions. A predefined mesh was drawn on the CLT surface to determine the excitation positions and the measurement positions. In that way, the CLT was divided into five parts in long direction and three parts in short direction, giving a total number of 16 excitation points (the nodes on the short edges were not excited). The size of mesh was decided based upon the highest frequency of interest, i.e. 200 Hz, to avoid the hammer exciting on the nodes of the eigen-modes.

Single input multiple output system (SIMO) can provide redundant data to better identify the eigen-frequencies and the local modes of complex structures basing on different frequency response function (FRF) matrices [1, 2], meanwhile, these different FRFs can be used as references to validate the FE model by comparing different simulated FRFs with different measured FRFs. Concerning the complexity and the inhomogeneity of CLT, SIMO system was employed to characterize the dynamic properties of CLT panel via different FRF matrices at different measurement positions. Five uni-axial accelerometers (Brüel&Kjær Accelerometer Type 4507 001) were attached on the different nodes (red dots in Figure 2) with the help of Faber-Castell Tack-It Multipurpose Adhesive. An impact roving hammer (Brüel&Kjær Impact hammer Type 8208 serial No. 51994) was used as excitation.

 Depending on the impulse shape and the force spectrum of the impact hammer shown in Figure 3, the medium hard hammer tip was selected for this measurement to ensure most of input energy localizing within the frequency range of interest (up to 200 Hz). Roving hammer approach was employed. The accelerometers were kept fixing on the selected positions and the hammer were roved over the predefined mesh grid except the points on boundaries. The accelerometers and the impact hammer were connected to Brüel&Kjær multi-channel front-end LAN-XI Type 3050. Then, the acceleration signals and the impact force signals were recorded by using the software Brüel&Kjær PULSE Labshop. There were 3 averages for each excitation position. The resolution of the FRF was 0.625 Hz.                                            

Figure 2. Mesh on the CLT panel. Five accelerometers (red dots) were placed at points 10, 11, 13, 17 and 24), whereas the hammer was moved around all nodes, except on the short edges.

Figure 3. (a) Impulse shapes of the hammers showing the shape as a function of used impact tip; (b) Force spectra of the hammers showing the frequency response as a function of used impact tip [3].

Point 2:

Page 4 – row 148

“In general, it is a challenge task to create appropriate constraints to describe the boundary conditions”.

The choice of constraints is important in modeling. An incorrect choice leads to unreal results. The authors should better describe this choice. The choice of the constraints as it was performed? Has a sensitivity analysis been performed?

Response 2:

3.3. Preliminary sensitivity analysis

Wood as a kind of orthotropic material has nine different variables (three Young’s moduli, three shear moduli and three Poisson’s ratios) to be calibrated. In order to decrease the complexity of calibration, an sensitivity analysis should be performed to investigate the effect of different elastic constants on simulated eigen-frequencies before stochastic process is introduced to the FE model. In this section, Young’s moduli in different directions were increased or decreased 25% comparing to the Young’s moduli given by Table 1. Shear moduli in different directions were increased or decreased 15% comparing to the shear moduli given by Table 1. The Poisson ratios, , ,  were set to be 0.25, 0.25 and 0.35, whereas the intial values were 0.3, 0.3, 0.4. The reference eigen-frequencies employed in NRFDs were calculated according to the elastic constants reported in Table 1. The measured eigen-frequencies were not selected as reference since the objective of sensitivity analysis aims at investigating how different elastic constants affect the eigen-frequencies of a FE model.

Figure 7. NRFDs of Young’s moduli.

Figure 8. NRFDs of shear moduli.

Figure 9. NRFDs of Poisson’s ratios.

From the NRFDs shown in Figure 7 and 8, it can be seen that the influence of Young’s moduli and shear moduli on eigen-frequencies cannot be ignored in general. Among all the elastic constants, Young’s modulus in longitudinal direction has the most important influence on eigen-frequency changes. Whereas, Young’s modulus in vertical direction barely changes the eigen-frequencies so that the variation of Young’s modulus in vertical direction wasn’t reported in Figure 7. When looking at Figure 9, we could find that all the NRFDs are lower than 0.5%, indicating that the influences of Poisson’s ratios on eigen-frequencies are negligible. From this sensitivity analysis, it can be concluded that the Young’s moduli and shear moduli have more significant influence on eigen-frequency calculations than Poisson’s ratios. As a result, the calibration of material properties can be reduced to five variables. 

However, from this sensitivity analysis, it was also noticed that the first four simulated eigen-frequencies are always higher than the first four measured eigen-frequencies even decreasing different elastic constants. This may be caused by the over stiffened boundary condition. Since the tested CLT is only placed on top two steel I beams. It is difficult to have a perfect simply supported boundary conditions in reality. So, restricting all the displacements at the boundaries of FE model can create over stiffened boundary conditions, resulting in over-estimated eigen-frequencies. Consequently, the displacement in vertical direction at one boundary of FE model is released to try to mimic the real boundary conditions. 

Point 3:

“Figure 10. Magnitude of the complex mobility in the vertical direction of point 11, 13, 17, 24. Simulated FRFs in red, measured FRFs in blue.”

Over 150 Hz there is difference between Simulated FRFs in red, measured FRFs in blue, Why?

For the other points, what happens? Do the authors report only the best results?

Response 3:

Row 540

The same results can also be seen in the mobility of different excitation points of the lowest NRFD values (c.f. Figure 18). The simulated FRFs at these 4 different excitation points correlate better with the measured ones, while there are extra peaks and eigen-frequency shifts in the simulated FRFs in the frequency range from 110 Hz to 170 Hz. We suspect that these discrepancies higher than 100 Hz result from the over-simplified homogenous laminated FE model which ignores the geometrical details containing in the real CLT panel. Or the boundary condition set-up in model couldn’t describe the real measurement boundary conditions.  

Row 160

Since the measurement system is SIMO system. Different FRFs (measurement point 11/excitation point 11, measurement point 13/excitation point 13, measurement point 17/excitation point 17, measurement point 24/excitation point 24) can also be saved as references to calibrate the FE model.

Row 206

Different from the conventional calibration procedure, stochastic process calibration begins with comparing eigen-frequencies (NRFDs) between the simulated FRFs and measured FRFs. So, several FRFs of different positions are needed to make sure the calibrated model validating at different positions which can increase the credibility of model. But the FRFs calibration can only ensure consistency of simulated and measured eigen-frequency but not the mode order. The simulated eigen-frequency may be same as measured eigen-frequency, but they could have different mode shapes. So, both two indictors are needed to ensure the simulated eigen-frequencies correlated with the measured ones, meanwhile, to keep the simulated mode order corresponding to the measured one.

Point 4:

With the use of software the user can get the results he wants.

Authors should perform a critical analysis of the numerical modeling performed. Maybe with sensitivity analysis of the input parameters from which it is possible to analyze how the parameters in the study are exiting the calculation model.

Response 4:

3.3. Preliminary sensitivity analysis

Wood as a kind of orthotropic material has nine different variables (three Young’s moduli, three shear moduli and three Poisson’s ratios) to be calibrated. In order to decrease the complexity of calibration, an sensitivity analysis should be performed to investigate the effect of different elastic constants on simulated eigen-frequencies before stochastic process is introduced to the FE model. In this section, Young’s moduli in different directions were increased or decreased 25% comparing to the Young’s moduli given by Table 1. Shear moduli in different directions were increased or decreased 15% comparing to the shear moduli given by Table 1. The Poisson ratios, , ,  were set to be 0.25, 0.25 and 0.35, whereas the intial values were 0.3, 0.3, 0.4. The reference eigen-frequencies employed in NRFDs were calculated according to the elastic constants reported in Table 1. The measured eigen-frequencies were not selected as reference since the objective of sensitivity analysis aims at investigating how different elastic constants affect the eigen-frequencies of a FE model.

Figure 7. NRFDs of Young’s moduli.

Figure 8. NRFDs of shear moduli.

Figure 9. NRFDs of Poisson’s ratios.

From the NRFDs shown in Figure 7 and 8, it can been seen that the infulence of Young’s moduli and shear moduli on eigen-frequencies can not be ignored in general. Among all the elastic constants, Young’s modulus in longitidunal direction has the most important infulence on eigen-frequency changes. Whereas, Young’s modulus in vertical direction barely changes the eigen-frequencies so that the variation of Young’s modulus in vertical direction wasn’t reported in Figure 7. When taking a look at Figure 9, we could find that all the NRFDs are lower than 0.5%, indicating that the influences of Poisson’s ratios on eigen-frequencies are negligable. From this sensitivity analysis, it can be concluded that the Young’s moduli and shear moduli have more significant influence on eigen-frequency calculations than Poisson’s ratios. As a result, the calibration of material properties can be reduced to five variables. 

However, from this sensitivity analysis, it was also noticed that the first four simulated eigen-frequencies are always higher than the first four measured eigen-frequencies even decreasing different elastic constants. This may be caused by the over stiffened boundary condition. Since the tested CLT is only placed on top two steel I beams. It is difficult to have a perfect simply supported boundary conditions in reality. So, restricting all the displacements at the boundaries of FE model can create over stiffened boundary conditions, resulting in over estimated eigen-frequencies. Consequently, the displacement in vertical direction at one boundary of FE model is realsed to try to micmic the real boundary conditions. 

1.             Martini A., Troncossi M., and Vincenzi N., Structural and Elastodynamic Analysis of Rotary Transfer Machines by Finite Element Model. Vol. 11. 2017.

2.             Manzato S., et al., Wind turbine model validation by full-scale vibration test. Vol. 5. 2010.

3.             Kjær, B., Product data ‐ Heavy Duty Impact Hammers ‐ Type 8207, 8208 and 8210. 2012.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper deals with the vibration response of Cross-Laminated Timber panels for wooden buildings. A method to reliably estimate the modal parameters of the panel notwithstanding the variability of its mechanical properties is proposed. The method is validated through experimental modal analysis of a simple CLT panel. The following remarks should be addressed.

MAIN REMARKS

1.       Section 2.2. Roving hammer approach is adopted for performing the EMA. However, 5 accelerometers are also installed. This setup results in a highly redundant dataset. Redundant datasets may be useful when analyzing complex structures, e.g. in order to possibly better identify local modes, but proper techniques are required (e.g. PolyMAX algorithm and stabilization diagram, see [a,b], listed below). The Authors should justify the use of such a redundant dataset. Moreover, additional information on how the collected dataset is processed should be provided. Indeed, the EMA is expected to provide a single set of natural frequencies and mode shapes. However, it appears from Fig. 7 that 4 different sets of experimental natural frequencies are obtained and compared with the simulated ones. The Authors should provide clarifications on these aspects, and the mentioned papers may be included in the References as examples.

a.       Martini, A.; Troncossi, M.; Vincenzi, N. Structural and elastodynamic analysis of rotary transfer machines by Finite Element model. Journal of the Serbian Society for Computational Mechanics, 2017, 11(2), 1-16, doi:10.24874/jsscm.2017.11.02.01

b.      Manzato, S.; Peeters,B.; Osgood, R.; Luczak, M. Wind turbine model validation by full-scale vibration test. Proceedings of the European Wind Energy Conference (EWEC) 2010, 20-23 April 2010, Warsaw, Poland.

2.       Section 3. Additional details and clarifications concerning the FE model should be provided.

·       It is stated that the model consists of 5 “partitions”. Does it mean that each layer of the panel is modelled with a different mesh of bricks? If so, which constraints are imposed between two adjacent layers? Bonded contacts?

·       In case a unique mesh is adopted for each layer, how are the discontinuities between adjacent lumber boards modelled?

·       Why are the boundary conditions of the panel modelled with two different constraints? The Authors should justify why the vertical displacement on one side of the panel is not constrained (line 153).

3.       At the end of Section 6.2 the Authors state that the boundary conditions adopted in the experimental test may introduce undesired effects, hence possibly representing an issue for the reliability of the experiment. Possible alternatives are indicated for future tests (free-free or fixed to the ground). However, it may be noticed that in real applications the actual constraints may significantly differ from the considered ones and that the response of the panel may be affected also by the behavior of the supporting structure. Hence, it may be worth considering the possibility of designing an experiment to test the behavior in real mounting conditions.  In case the actual boundary conditions could not exactly matched in the experiments, some indicators and procedures to predict the behavior in real conditions may be developed (e.g. see [c]). The authors may provide some considerations on these aspects, and the mentioned paper may be added to the references.

c.       Martini, A.; Troncossi, M. Upgrade of an automated line for plastic cap manufacture based on experimental vibration analysis. Case Studies in Mechanical Systems and Signal Processing, 2016, 3, 28-33, doi:10.1016/j.csmssp.2016.03.002

MINOR COMMENTS

4.       Introduction, line 39. What do the Author mean with the expression “diversity”? Non-homogeneous properties? Different wood types?

5.       Section 2.1, line 96. It is stated that the panel dimensions are 2x1.5 m^2. However, according to Fig. 2, the panel is 4 m long. Please, check.

6.       Section 2.2. How the accelerometers are mounted on the panel? Petroleum wax? Cyanoacrylate adhesives? Please, provide additional details on the sensor setup.

7.       Section 3.2, line 167. Please, clarify the statement.

8.       Section 6.1, Figure 5. For a better readability, it should be better to plot the experimental (blue) line on top of the simulation results (otherwise, the blue curve is almost completely covered by the red lines).

9.       Section 6.1, line 403. Is the term “pics” wrongly used instead of “peaks”?

10.   Section 6.2. It may be advisable to include a description of all the identified mode shapes (e.g. “1^st flexural/bending”, “1^st torsional” etc.) or the corresponding figures.

11.   The appendix only contains a Figure. It would be advisable to omit the appendix and, instead, move Fig. A (the flowchart) at the beginning of Section 4, in order to better introduce the Stochastic process.

Author Response

Point 1:

Section 2.2. Roving hammer approach is adopted for performing the EMA. However, 5 accelerometers are also installed. This setup results in a highly redundant dataset. Redundant datasets may be useful when analyzing complex structures, e.g. in order to possibly better identify local modes, but proper techniques are required (e.g. PolyMAX algorithm and stabilization diagram, see [a,b], listed below). The Authors should justify the use of such a redundant dataset. Moreover, additional information on how the collected dataset is processed should be provided. Indeed, the EMA is expected to provide a single set of natural frequencies and mode shapes. However, it appears from Fig. 7 that 4 different sets of experimental natural frequencies are obtained and compared with the simulated ones. The Authors should provide clarifications on these aspects, and the mentioned papers may be included in the References as examples.

a.       Martini, A.; Troncossi, M.; Vincenzi, N. Structural and elastodynamic analysis of rotary transfer machines by Finite Element model. Journal of the Serbian Society for Computational Mechanics, 2017, 11(2), 1-16, doi:10.24874/jsscm.2017.11.02.01

b.      Manzato, S.; Peeters,B.; Osgood, R.; Luczak, M. Wind turbine model validation by full-scale vibration test. Proceedings of the European Wind Energy Conference (EWEC) 2010, 20-23 April 2010, Warsaw, Poland.

Response 1:

2.2. Measurement procedure 

2.2.1. Measurement setup

EMA was performed on the CLT slab to characterize the dynamic properties of the CLT slab. The CLT panel was set free at two opposite long sides and simply supported (SFSF boundary condition) with two steel I-beams at two shorter edges (shown in Figure 1 (b)) in order to simplify the boundary conditions. A predefined mesh was drawn on the CLT surface to determine the excitation positions and the measurement positions. In that way, the CLT was divided into five parts in long direction and three parts in short direction, giving a total number of 16 excitation points (the nodes on the short edges were not excited). The size of mesh was decided based upon the highest frequency of interest, i.e. 200 Hz, to avoid the hammer exciting on the nodes of the eigen-modes.

Single input multiple output system (SIMO) can provide redundant data to better identify the eigen-frequencies and the local modes of complex structures basing on different frequency response function (FRF) matrices [1, 2], meanwhile, these different FRFs can be used as references to validate the FE model by comparing different simulated FRFs with different measured FRFs. Concerning the complexity and the inhomogeneity of CLT, SIMO system was employed to characterize the dynamic properties of CLT panel via different FRF matrices at different measurement positions. Five uni-axial accelerometers (Brüel&Kjær Accelerometer Type 4507 001) were attached on the different nodes (red dots in Figure 2) with the help of Faber-Castell Tack-It Multipurpose Adhesive. An impact roving hammer (Brüel&Kjær Impact hammer Type 8208 serial No. 51994) was used as excitation.

 Depending on the impulse shape and the force spectrum of the impact hammer shown in Figure 3, the medium hard hammer tip was selected for this measurement to ensure most of input energy localizing within the frequency range of interest (up to 200 Hz). Roving hammer approach was employed. The accelerometers were kept fixing on the selected positions and the hammer were roved over the predefined mesh grid except the points on boundaries. The accelerometers and the impact hammer were connected to Brüel&Kjær multi-channel front-end LAN-XI Type 3050. Then, the acceleration signals and the impact force signals were recorded by using the software Brüel&Kjær PULSE Labshop. There were 3 averages for each excitation position. The resolution of the FRF was 0.625 Hz.                                            

Figure 2. Mesh on the CLT panel. Five accelerometers (red dots) were placed at points 10, 11, 13, 17 and 24), whereas the hammer was moved around all nodes, except on the short edges.

Figure 3. (a) Impulse shapes of the hammers showing the shape as a function of used impact tip; (b) Force spectra of the hammers showing the frequency response as a function of used impact tip [3].

2.2.2. Modal parameters extraction

The eigen-frequencies, the mode shapes as well as the damping ratios were extracted by applying rational fraction polynomial - Z algorithm in Brüel&Kjær PULSE Connect. The frequency band of FRFs was divided into several parts, meaning that identification of poles was restricted in a narrow frequency band each time in order to easily select the stable poles (eigen-frequencies) from the FRFs in each divided frequency range. An example of the stabilization diagram is shown in Figure 4.

Figure 4. Stabilization diagram with rational fraction polynomial - Z algorithm.

Iteration times of rational fraction polynomial - Z algorithm was 40. The synthesized FRF is shown in Figure 5. The corresponding eigen-frequencies and the corresponding damping ratios are shown in Table 2.

Figure 5. Synthesized FRF, measured FRF and relative errors between the synthesized FRF and the measured FRF.

Since the measurement system is SIMO system. Different FRFs (measurement point 11/excitation point 11, measurement point 13/excitation point 13, measurement point 17/excitation point 17, measurement point 24/excitation point 24) can also be saved as references to calibrate the FE model.

Row 206

Different from the conventional calibration procedure, stochastic process calibration begins with comparing eigen-frequencies (NRFDs) between the simulated FRFs and measured FRFs. So, several FRFs of different positions are needed to make sure the calibrated model validating at different positions which can increase the credibility of model. But the FRFs calibration can only ensure consistency of simulated and measured eigen-frequency but not the mode order. The simulated eigen-frequency may be same as measured eigen-frequency, but they could have different mode shapes. So, both two indictors are needed to ensure the simulated eigen-frequencies correlated with the measured ones, meanwhile, to keep the simulated mode order corresponding to the measured one.

Point 2:

Section 3. Additional details and clarifications concerning the FE model should be provided.

·       It is stated that the model consists of 5 “partitions”. Does it mean that each layer of the panel is modelled with a different mesh of bricks? If so, which constraints are imposed between two adjacent layers? Bonded contacts?

·       In case a unique mesh is adopted for each layer, how are the discontinuities between adjacent lumber boards modelled?

·       Why are the boundary conditions of the panel modelled with two different constraints? The Authors should justify why the vertical displacement on one side of the panel is not constrained (line 153).

Response 2:

3.1. Model description

A numerical model of the CLT slab was created in the commercial FE software Abaqus [4]. Five different layers were modelled by assigning different oriented material properties in different layers of model. So, there is no relative displacement between different layers in this model, meaning that the CLT model is a complete one model and each layer is fully tied together. The same material was assigned to each layer, except that the in-plan material orientation assignments were 90 degrees oriented from the adjacent layer to mimic the cross-laminate layers of CLT panel. The material properties of CLT were gathered from the literature [5, 6], reported in Table 1. The meshes of 20-node quadratic brick, reduced integration (C3D20R) quadratic type were assigned to the entire model. Since the shape of each layer is a simple rectangular so that there is no discontinuity between different layers. Details of mesh are shown in Figure 6. The mesh size was 0.1 to ensure the accuracy of the highest frequency interest. The eigen-frequencies and the eigen-modes were calculated by the linear perturbation frequency step. The frequency response function (FRF) of the CLT was obtained by the Steady-state dynamics, Modal step. The damping extracted from the measurement was included in the model by means of the direct modal damping (c.f. Table 2). In this framework, the FRFs of CLT were first calculated to quantify the uncertainties of material properties. Then the best FRF justified by different criterions was selected to extract the material properties of this under investigated CLT.

Figure 6. Meshes of FE CLT model.

Row 244

However, from this sensitivity analysis, it was also noticed that the first four simulated eigen-frequencies are always higher than the first four measured eigen-frequencies even decreasing different elastic constants. This may be caused by the over stiffened boundary condition. Since the tested CLT is only placed on top two steel I beams. It is difficult to have a perfect simply supported boundary conditions in reality. So, restricting all the displacements at the boundaries of FE model can create over stiffened boundary conditions, resulting in over estimated eigen-frequencies. Consequently, the displacement in vertical direction at one boundary of FE model is realsed to try to micmic the real boundary conditions. 

Point 3:

 At the end of Section 6.2 the Authors state that the boundary conditions adopted in the experimental test may introduce undesired effects, hence possibly representing an issue for the reliability of the experiment. Possible alternatives are indicated for future tests (free-free or fixed to the ground). However, it may be noticed that in real applications the actual constraints may significantly differ from the considered ones and that the response of the panel may be affected also by the behavior of the supporting structure. Hence, it may be worth considering the possibility of designing an experiment to test the behavior in real mounting conditions.  In case the actual boundary conditions could not exactly matched in the experiments, some indicators and procedures to predict the behavior in real conditions may be developed (e.g. see [c]). The authors may provide some considerations on these aspects, and the mentioned paper may be added to the references.

c.       Martini, A.; Troncossi, M. Upgrade of an automated line for plastic cap manufacture based on experimental vibration analysis. Case Studies in Mechanical Systems and Signal Processing, 2016, 3, 28-33, doi:10.1016/j.csmssp.2016.03.002

Response 3:

Row 571

Furthermore, as one of the objectives of this stochastic approach is to calibrate the material properties of target structure. It would be better to decrease the influence of other influence factors, such as boundary conditions. So, it is suggested to hang up the under investigated structure (free-free boundary condition) or fix the structure boundary to the ground (perfect simply supported condition) to eliminate the influence of boundary conditions as far as possible. In the work reported here, due to lack of support materials, the CLT panel just laid on top of the I-steel beam and it wasn’t screwed into the ground. Consequently, when the CLT is excited, the deformation of I-steel beam can affect the vibration of CLT slab. Furthermore, the laboratory boundary conditions are always different from the in-situ boundary conditions [7]. Thus, it would be necessary to investigate the dynamic response of CLT in a real building. To achieve that, the FRFs could be firstly measured from a CLT bare floor in real mounting conditions. Then the same CLT bare floor could be set in the simplified laboratory conditions to compare the relative differences between different FRFs under different boundary conditions.

Point 4:

Introduction, line 39. What do the Author mean with the expression “diversity”? Non-homogeneous properties? Different wood types?

Response 4:

Row 38

Furthermore, wood as a natural material is hard to predict its dynamic behavior due to its inhomogeneity.

Point 5:

Section 2.1, line 96. It is stated that the panel dimensions are 2x1.5 m^2. However, according to Fig. 2, the panel is 4 m long. Please, check.

Response 5:

Row 96

The test structure was a 4×1.5 m² 5-ply 175 mm thick CLT panel made of Canadian black spruce of machine stress rated grade 1950f-1.7E in parallel layers and visual grade No.3 in perpendicular layers with density of 520 kg/m³.

Point 6:

Section 2.2. How the accelerometers are mounted on the panel? Petroleum wax? Cyanoacrylate adhesives? Please, provide additional details on the sensor setup.

Response 6:

Row 127

Five uni-axial accelerometers (Brüel&Kjær Accelerometer Type 4507 001) were attached on the different nodes (red dots in Figure 2) with the help of Faber-Castell Tack-It Multipurpose Adhesive.

Point 7:

Section 3.2, line 167. Please, clarify the statement.

Response 7:

Row 206

Different from the conventional calibration procedure, stochastic process calibration begins with comparing eigen-frequencies (NRFDs) between the simulated FRFs and measured FRFs. So, several FRFs of different positions are needed to make sure the calibrated model validating at different positions which can increase the credibility of model. But the FRFs calibration can only ensure consistency of simulated and measured eigen-frequency but not the mode order. The simulated eigen-frequency may be same as measured eigen-frequency, but they could have different mode shapes. So, both two indictors are needed to ensure the simulated eigen-frequencies correlated with the measured ones, meanwhile, to keep the simulated mode order corresponding to the measured one.

Point 8:

Section 6.1, Figure 5. For a better readability, it should be better to plot the experimental (blue) line on top of the simulation results (otherwise, the blue curve is almost completely covered by the red lines).

Response 8:

Figure 13. Measured (blue) and simulated (red) FRFs at point 11, 13, 17, 24.

Point 9:

Section 6.1, line 403. Is the term “pics” wrongly used instead of “peaks”?

Response 9:

All the “pics” are changed into “peaks”.

Point 10:

Section 6.2. It may be advisable to include a description of all the identified mode shapes (e.g. “1st flexural/bending”, “1st torsional” etc.) or the corresponding figures.

Response 10:

Figure 17. Measured and simulated modes.

Point 11:

The appendix only contains a Figure. It would be advisable to omit the appendix and, instead, move Fig. A (the flowchart) at the beginning of Section 4, in order to better introduce the Stochastic process.

Response 11:

The flow chart is added at the beginning of section 4.

Uncertainties of material properties are always assumed to follow the Gaussian distribution because of its simplicity and the lack of relevant experimental data, even though most material property distributions are no-Gaussian in nature [26, 27]. The theory introduced here is about the probabilistic modeling of random elasticity tensor in orthotropic symmetric level within the framework of maximum entropy principle under the constraint of the available information [18, 19, 28]. The established random elasticity tensor is considered as the inputs in FE model to quantify the uncertainties induced by the CLT material properties and to seek the best combination of CLT material properties to calibrate the CLT model. 

In this section, elastic tensor is firstly decomposed in terms of random coefficients and tensor basis so that the fluctuation of different elastic constants can be characterized by the probability distribution functions (PDF). Next, construction of PDFs of different elastic constants in high-dimension [16] is shortly introduced. Lagrange multipliers associated with the explicit PDFs of random variables in high dimensions is estimated with help of Itô differential equation. The established PDFs is sampled by Metropolis-Hastings algorithm to obtain the random data to construct random elasticity matrix [18, 19] in order to derive the corresponding random combinations of elasticity constants to quantify the uncertainties of material properties and to calibrate the CLT model. A flow chart of application of stochastic procedure is shown in Figure 12.

Figure 12. Flow chart of application of stochastic process.

1.             Martini A., Troncossi M., and Vincenzi N., Structural and Elastodynamic Analysis of Rotary Transfer Machines by Finite Element Model. Vol. 11. 2017.

2.             Manzato S., et al., Wind turbine model validation by full-scale vibration test. Vol. 5. 2010.

3.             Kjær, B., Product data ‐ Heavy Duty Impact Hammers ‐ Type 8207, 8208 and 8210. 2012.

4.             Dassault, ABAQUS/CAE. 2017, Simulia.

5.             Zhou J.H., et al., Elastic properties of full-size mass timber panels: Characterization using modal testing and comparison with model predictions. Composites Part B: Engineering, 2017. 112: p. 203-212.

6.             Ussher E., et al., Prediction of motion responses of cross-laminated-timber slabs. Structures. 11: p. 49-61.

7.             Martini A. and Troncossi M., Upgrade of an automated line for plastic cap manufacture based on experimental vibration analysis. Case Studies in Mechanical Systems and Signal Processing, 2016. 3: p. 28-33.

Author Response File: Author Response.pdf

Round  2

Reviewer 1 Report

accept in present form

Reviewer 2 Report

The review comments have been addressed satisfactorily.

Please, check the completeness of the added references: apparently, in some of them the journal/conference name is missing. It may be advisable including the DOI, if available.