Rossi et al 2019a - Revision history

Cinmemj: Cinmemj moved page Draft Samper 231103336 to Rossi et al 2019a

2019-01-09T13:25:11Z

Cinmemj moved page Draft Samper 231103336 to Rossi et al 2019a

Cinmemj at 13:16, 9 January 2019

2019-01-09T13:16:27Z

Cinmemj at 13:15, 9 January 2019

2019-01-09T13:15:26Z

Cinmemj at 13:13, 9 January 2019

2019-01-09T13:13:48Z

Cinmemj at 13:12, 9 January 2019

2019-01-09T13:12:28Z

Cinmemj at 13:11, 9 January 2019

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Cinmemj at 13:09, 9 January 2019

2019-01-09T13:09:16Z

Cinmemj at 13:08, 9 January 2019

2019-01-09T13:08:21Z

Cinmemj at 13:06, 9 January 2019

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Cinmemj at 13:01, 9 January 2019

2019-01-09T13:01:01Z

← Older revision		Revision as of 13:16, 9 January 2019
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−	The identification of the parameters can be performed by non linear fitting techniques. The nonlinear fitting routines provided in scipy a scientific library included in ~~python (see~~ www.python.org) were used in the computations. The convergence of the fitting process was ensured by taking as initial value for the fitting process an estimate for all the relevant parameters.	+	The identification of the parameters can be performed by non linear fitting techniques. The nonlinear fitting routines provided in scipy a scientific library included in [http://www.python.org python] were used in the computations. The convergence of the fitting process was ensured by taking as initial value for the fitting process an estimate for all the relevant parameters.

@@ Line 1,936: / Line 1,936: @@
 which is the desired result.
-===A.3 Free heave===
+===Free heave===
 The identification of the remaining four derivatives follows a similar path. Once the non linear fitting of the lift equation is performed, two of the aeroelastic parameters can be identified as

@@ Line 1,804: / Line 1,804: @@
 ===Free vibration method===
-The second procedure for the determination of the aeroelastic coefficients is based on the analysis of the displacement history of the sectional model mounted on a set of springs of known stiffness. This testing procedure is more challenging for the interaction as it involves a completely coupled analysis, which introduces a further error source. An excellent example of application to bridges can be found in <span id='citeF-19'></span><span id='citeF-22'></span>[[#cite-19|19]]], [[#cite-22|22]]]. In these works however the free vibration procedure is used to assess directly the flutter speed by evaluating the energy variation.
+The second procedure for the determination of the aeroelastic coefficients is based on the analysis of the displacement history of the sectional model mounted on a set of springs of known stiffness. This testing procedure is more challenging for the interaction as it involves a completely coupled analysis, which introduces a further error source. An excellent example of application to bridges can be found in <span id='citeF-19'></span><span id='citeF-22'></span>[[#cite-19|[19]]], [[#cite-22|[22]]]. In these works however the free vibration procedure is used to assess directly the flutter speed by evaluating the energy variation.
 The original identification procedure as proposed by Scanlan <span id='citeF-17'></span>[[#cite-17|[17]]], is based on a three step analysis in which the cross section mounted on springs is first restrained in heave, then in rotation and finally left completely free. This was needed as the available setup allowed to record exclusively the displacement history but not the restrain forces. The approach described in the following is slightly different and it involves only two sets of simulations by making use of both displacement histories and forces records.

@@ Line 1,804: / Line 1,804: @@
 ===Free vibration method===
-The second procedure for the determination of the aeroelastic coefficients is based on the analysis of the displacement history of the sectional model mounted on a set of springs of known stiffness. This testing procedure is more challenging for the interaction as it involves a completely coupled analysis, which introduces a further error source. An excellent example of application to bridges can be found in <span id='citeF-19'></span><span id='citeF-22'></span>[[#cite-19|19]], [[#cite-22|22]]. In these works however the free vibration procedure is used to assess directly the flutter speed by evaluating the energy variation.
+The second procedure for the determination of the aeroelastic coefficients is based on the analysis of the displacement history of the sectional model mounted on a set of springs of known stiffness. This testing procedure is more challenging for the interaction as it involves a completely coupled analysis, which introduces a further error source. An excellent example of application to bridges can be found in <span id='citeF-19'></span><span id='citeF-22'></span>[[#cite-19|19]]], [[#cite-22|22]]]. In these works however the free vibration procedure is used to assess directly the flutter speed by evaluating the energy variation.
 The original identification procedure as proposed by Scanlan <span id='citeF-17'></span>[[#cite-17|[17]]], is based on a three step analysis in which the cross section mounted on springs is first restrained in heave, then in rotation and finally left completely free. This was needed as the available setup allowed to record exclusively the displacement history but not the restrain forces. The approach described in the following is slightly different and it involves only two sets of simulations by making use of both displacement histories and forces records.

@@ Line 1,802: / Line 1,802: @@
 which represents a heaving motion, it is possible to identify the remaining four derivatives. Table ([[#table-A1|A1]]) summarizes  the relevant formulae for computing the aeroelastic derivatives.
-===A.2 Free vibration method===
+===Free vibration method===
-The second procedure for the determination of the aeroelastic coefficients is based on the analysis of the displacement history of the sectional model mounted on a set of springs of known stiffness. This testing procedure is more challenging for the interaction as it involves a completely coupled analysis, which introduces a further error source. An excellent example of application to bridges can be found in <math display="inline"><span id='citeF-19'></span><span id='citeF-22'></span>[[#cite-19|[19,22]]]</math>. In these works however the free vibration procedure is used to assess directly the flutter speed by evaluating the energy variation.
+The second procedure for the determination of the aeroelastic coefficients is based on the analysis of the displacement history of the sectional model mounted on a set of springs of known stiffness. This testing procedure is more challenging for the interaction as it involves a completely coupled analysis, which introduces a further error source. An excellent example of application to bridges can be found in <span id='citeF-19'></span><span id='citeF-22'></span>[[#cite-19|19]], [[#cite-22|22]]. In these works however the free vibration procedure is used to assess directly the flutter speed by evaluating the energy variation.
 The original identification procedure as proposed by Scanlan <span id='citeF-17'></span>[[#cite-17|[17]]], is based on a three step analysis in which the cross section mounted on springs is first restrained in heave, then in rotation and finally left completely free. This was needed as the available setup allowed to record exclusively the displacement history but not the restrain forces. The approach described in the following is slightly different and it involves only two sets of simulations by making use of both displacement histories and forces records.

← Older revision	Revision as of 13:25, 9 January 2019
(No difference)

@@ Line 1,790: / Line 1,790: @@
 |-
 | style="text-align: center;" | <math>             H_4 = {\frac{{             B^{heave}_{lift}}}{\rho \,{B}^{2}{w}^{2}{ y_0}}} \, ;             \, H_1 = {\frac{{             C^{heave}_{lift}}}{\rho \,{B}^{2}{w}^{2}{ y_0}}}         </math>
+|-
 | style="text-align: center;" | <math>             A_4 = {\frac{{             B^{heave}_{mom}}}{\rho \,{B}^{3}{w}^{2}{ y_0}}} \, ;             \, A_1 = {\frac{{             C^{heave}_{mom}}}{\rho \,{B}^{3}{w}^{2}{ y_0}}}         </math>
 |-
@@ Line 1,796: / Line 1,796: @@
 |-
 | style="text-align: center;" | <math>             H_3 = {\frac{{             B^{pitch}_{lift}}}{\rho \,{B}^{3}{w}^{2}{ \alpha _0}}}             \, ; \, H_2 = {\frac{{             C^{pitch}_{lift}}}{\rho \,{B}^{3}{w}^{2}{ \alpha _0}}}         </math>
+|-
 | style="text-align: center;" | <math>             A_3 = {\frac{{             B^{pitch}_{mom}}}{\rho \,{B}^{4}{w}^{2}{ \alpha _0}}}             \, ; \, A_2 = {\frac{{             C^{pitch}_{mom}}}{\rho \,{B}^{4}{w}^{2}{ \alpha _0}}}         </math>
 |}

@@ Line 1,787: / Line 1,787: @@
 |+ style="font-size: 75%;" |<span id='table-A1'></span>'''Table. A1''' Relations for computing the aeroelastic derivatives:     the upper index indicates the prescribed sectional motion, the     lower index     the equation used in fitting the load history
 |-
+|style="text-align: center;" |Prescribed heave:
-* Prescribed heave:
-−
-{| class="formulaSCP" style="width: 100%; text-align: left;"
-|-
-−
-{| style="text-align: left; margin:auto;width: 100%;"
 |-
 | style="text-align: center;" | <math>             H_4 = {\frac{{             B^{heave}_{lift}}}{\rho \,{B}^{2}{w}^{2}{ y_0}}} \, ;             \, H_1 = {\frac{{             C^{heave}_{lift}}}{\rho \,{B}^{2}{w}^{2}{ y_0}}}         </math>
 |-
 | style="text-align: center;" | <math>             A_4 = {\frac{{             B^{heave}_{mom}}}{\rho \,{B}^{3}{w}^{2}{ y_0}}} \, ;             \, A_1 = {\frac{{             C^{heave}_{mom}}}{\rho \,{B}^{3}{w}^{2}{ y_0}}}         </math>
 |-
+|style="text-align: center;" |Prescribed rotation:
-{| style="text-align: left; margin:auto;width: 100%;"
 |-
 | style="text-align: center;" | <math>             H_3 = {\frac{{             B^{pitch}_{lift}}}{\rho \,{B}^{3}{w}^{2}{ \alpha _0}}}             \, ; \, H_2 = {\frac{{             C^{pitch}_{lift}}}{\rho \,{B}^{3}{w}^{2}{ \alpha _0}}}         </math>
 |-
 | style="text-align: center;" | <math>             A_3 = {\frac{{             B^{pitch}_{mom}}}{\rho \,{B}^{4}{w}^{2}{ \alpha _0}}}             \, ; \, A_2 = {\frac{{             C^{pitch}_{mom}}}{\rho \,{B}^{4}{w}^{2}{ \alpha _0}}}         </math>
 |}

@@ Line 1,784: / Line 1,784: @@
-{|  class="floating_tableSCP" style="text-align: left; margin: 1em auto;border-top: 2px solid;border-bottom: 2px solid;min-width:50%;"
+{|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;"
-|+ style="font-size: 75%;" |<span id='table-3'></span>'''Table. 3''' Relations for computing the aeroelastic derivatives:     the upper index indicates the prescribed sectional motion, the     lower index     the equation used in fitting the load history
+|+ style="font-size: 75%;" |<span id='table-A1'></span>'''Table. A1''' Relations for computing the aeroelastic derivatives:     the upper index indicates the prescribed sectional motion, the     lower index     the equation used in fitting the load history
 |-
+|
@@ Line 1,828: / Line 1,828: @@
 |}
-which represents a heaving motion, it is possible to identify the remaining four derivatives. Table ([[#table-3|3]]) summarizes  the relevant formulae for computing the aeroelastic derivatives.
+which represents a heaving motion, it is possible to identify the remaining four derivatives. Table ([[#table-A1|A1]]) summarizes  the relevant formulae for computing the aeroelastic derivatives.
 ===A.2 Free vibration method===