3. Modeling A#

3.1. Characteristics of modeling#

The system is modelled by:

  • 3 discrete elements K_T_D_L,

  • 2 discrete M_T_D_N elements.

3.2. Characteristics of the mesh#

The mesh consists of 3 SEG2 meshes.

3.3. Tested sizes and results#

3.3.1. Natural frequencies#

MODE

Reference

Tolerance \((\text{\%})\)

\(1\)

\(1.000E+00\)

\(0.1\)

\(2\)

\(2.236E+00\)

\(0.1\)

3.3.2. Static training modes#

Fashion \(\mathrm{1 }\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(0.4E+00\)

\(0.1\)

\(\mathrm{NO3}\)

\(0.6E+00\)

\(0.1\)

Fashion \(\mathrm{2 }\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(0.4E+00\)

\(0.1\)

\(\mathrm{NO3}\)

\(0.6E+00\)

\(0.1\)

3.3.3. Static modes for static correction#

Fashion \(\mathrm{1 }\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.317E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.216E-02\)

\(0.1\)

Fashion \(\mathrm{2 }\): absolute movements \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.216E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.317E-02\)

\(0.1\)

3.3.4. Global response on a complete modal basis (uncorrelated multi-support calculation)#

The \(1\) and \(2\) modes are taken into account.

  • calculation \(n°1\)

COMB_MODE =” SRSS “

For each active degree of freedom \(2\) and \(\mathrm{3 }\):

  • response from support \(j=1\) (node \(\mathrm{NO1}\)): \({R}_{1}=\sqrt{{\mathrm{Rm}}_{11}^{2}+{\mathrm{Rm}}_{21}^{2}}\) (cumulative on modes \(1\) and \(2\))

  • response from support \(j=2\) (node \(\mathrm{NO4}\)): \({R}_{2}=\sqrt{{\mathrm{Rm}}_{12}^{2}+{\mathrm{Rm}}_{22}^{2}}\) (cumulative on modes \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative support)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(5.65E-03\)

\(0.1\)

\(\mathrm{NO3}\)

\(5.65E-03\)

\(0.1\)

  • calculation \(n°2\)

COMB_MODE =” ABS “

  • response from support \(j=1\) (node \(\mathrm{NO1}\)): \({R}_{1}=∣{\mathrm{Rm}}_{11}∣+∣{\mathrm{Rm}}_{21}∣\) (cumulative on modes \(1\) and \(2\))

  • response from support \(j=2\) (node \(\mathrm{NO4}\)): \({R}_{2}=∣{\mathrm{Rm}}_{12}∣+∣{\mathrm{Rm}}_{22}∣\) (cumulative on modes \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative support)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(6.476E-03\)

\(0.1\)

\(\mathrm{NO3}\)

\(6.476E-03\)

\(0.1\)

  • calculation \(n°3\)

COMB_MODE =” DPC “

  • response from support \(j=1\) (node \(\mathrm{NO1}\)): \({R}_{1}=\sqrt{{\mathit{Rm}}_{11}^{2}+{\mathit{Rm}}_{21}^{2}}\) (cumulative on modes \(1\) and \(2\))

  • response from support \(j=2\) (node \(\mathrm{NO4}\)): \({R}_{2}=\sqrt{{\mathrm{Rm}}_{12}^{2}+{\mathrm{Rm}}_{22}^{2}}\) (cumulative on modes \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative support)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(5.65E-03\)

\(0.1\)

\(\mathrm{NO3}\)

\(5.65E-03\)

\(0.1\)

  • calculation \(n°4\)

COMB_MODE =” CQC “

modal depreciation = \(0.05\)

  • response from support \(j=1\) (node \(\mathrm{NO1}\)): \({R}_{1}=\sqrt{{\rho }_{12}{\mathrm{Rm}}_{11}{\mathrm{Rm}}_{21}}\) (cumulative on modes \(1\) and \(2\))

  • response from support \(j=2\) (node \(\mathrm{NO4}\)): \({R}_{2}=\sqrt{{\rho }_{12}{\mathrm{Rm}}_{12}{\mathrm{Rm}}_{22}}\) (cumulative on modes \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative support)

absolute displacements: \(\mathit{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathit{NO2}\)

\(5.65E-03\)

\(0.1\)

\(\mathit{NO3}\)

\(5.65157E-03\)

\(0.1\)

  • calculation \(n°5\)

COMB_MODE =” DSC “

modal depreciation = \(0.05\)

duration: 15 s

  • response from support \(j=1\) (node \(\mathrm{NO1}\)): \({R}_{1}=\sqrt{{\rho }_{12}{\mathrm{Rm}}_{11}{\mathrm{Rm}}_{21}}\) (cumulative on modes \(1\) and \(2\))

  • response from support \(j=2\) (node \(\mathrm{NO4}\)): \({R}_{2}=\sqrt{{\rho }_{12}{\mathrm{Rm}}_{12}{\mathrm{Rm}}_{22}}\) (cumulative on modes \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative support)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(5.649E-03\)

\(0.1\)

\(\mathrm{NO3}\)

\(5.6521E-03\)

\(0.1\)

Global response on a complete modal basis (single-support calculation with \({\mathit{SRO}}_{\mathit{NO}1}\)) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~

The \(1\) and \(2\) modes are taken into account.

  • calculation \(n°1\)

COMB_MODE =” SRSS “

For each active \(\mathrm{ddl}\) \(2\) and \(\mathrm{3 }\):

  • \(\mathrm{1 }\) mode response: \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\)

  • \(\mathrm{2 }\) mode response: \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\)

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(1.01321E-02\)

\(0.1\)

\(\mathrm{NO3}\)

\(1.01321E-02\)

\(0.1\)

  • calculation \(n°2\)

COMB_MODE =” ABS “

  • \(\mathrm{1 }\) mode response: \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\)

  • \(\mathrm{2 }\) mode response: \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) r

  • global response: \(R=∣{R}_{1}∣+∣{R}_{2}∣\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(0.01013\)

\(0.1\)

\(\mathrm{NO3}\)

\(0.01013\)

\(0.1\)

  • calculation \(n°3\)

COMB_MODE =” DPC “

  • \(\mathrm{1 }\) mode response: \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\)

  • \(\mathrm{2 }\) mode response: \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\)

  • global response: \(R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}\) (cumulative mode)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathrm{NO2}\)

\(0.01013\)

\(0.1\)

\(\mathrm{NO3}\)

\(0.01013\)

\(0.1\)

  • calculation \(n°4\)

COMB_MODE =” CQC “

modal depreciation = \(0.05\)

  • \(\mathrm{1 }\) mode response: \({R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}\)

  • \(\mathrm{2 }\) mode response: \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\)

  • global response: \(R=\sqrt{{\rho }_{12}{R}_{1}{R}_{2}}\) (cumulative mode)

absolute displacements: \(\mathit{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathit{NO2}\)

\(0.01013\)

\(0.1\)

\(\mathit{NO}3\)

\(0.01013\)

\(0.1\)

  • calculation \(n°5\)

COMB_MODE =” DSC “

modal depreciation = \(0.05\)

duration: 15 seconds

  • \(1\) mode response: \({R}_{1}={\mathit{Rm}}_{11}+{\mathit{Rm}}_{12}\)

  • \(2\) mode response: \({R}_{2}={\mathit{Rm}}_{21}+{\mathit{Rm}}_{22}\)

  • global response: \(R=\sqrt{{\rho }_{12}{R}_{1}{R}_{2}}\) (cumulative mode)

absolute displacements: \(\mathit{DEPL}\)

NOEUD

Reference

Tolerance \((\text{\%})\)

\(\mathit{NO}2\)

\(0.01013\)

\(0.1\)

\(\mathit{NO}3\)

\(0.01013\)

\(0.1\)

3.3.5. Overall response on an incomplete modal basis (single-support calculation with static correction)#

Modal base consisting of mode 2 only.

  • calculation \(n°1\)

COMB_MODE =” ABS “

For each active degree of freedom \(2\) and \(3\):

  • response from mode \(i=2\) (node \(\mathrm{NO4}\)): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (cumulative support \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{2}^{2}+{U}^{2}}\) (cumulative modal response and static correction)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance

\(\mathrm{NO2}\)

0.02302302705

\(0.001\)

\(\mathrm{NO3}\)

0.02302302705

\(0.001\)

  • calculation \(n°2\)

COMB_MODE =” SRSS “

For each active degree of freedom \(2\) and \(3\):

  • response from mode \(i=2\) (node \(\mathrm{NO4}\)): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (cumulative support \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{2}^{2}+{U}^{2}}\) (cumulative modal response and static correction)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance

\(\mathrm{NO2}\)

0.02302302705

\(0.001\)

\(\mathrm{NO3}\)

0.02302302705

\(0.001\)

  • calculation \(n°3\)

COMB_MODE =” DPC “

For each active degree of freedom \(2\) and \(3\):

  • response from mode \(i=2\) (node \(\mathrm{NO4}\)): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (cumulative support \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{2}^{2}+{U}^{2}}\) (cumulative modal response and static correction)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance

\(\mathrm{NO2}\)

0.02302302705

\(0.001\)

\(\mathrm{NO3}\)

0.02302302705

\(0.001\)

  • calculation \(n°4\)

COMB_MODE =” CQC “

modal depreciation = \(0.05\)

For each active degree of freedom \(2\) and \(3\):

  • response from mode \(i=2\) (node \(\mathrm{NO4}\)): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (cumulative support \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{2}^{2}+{U}^{2}}\) (cumulative modal response and static correction)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance

\(\mathrm{NO2}\)

0.02302302705

\(0.001\)

\(\mathrm{NO3}\)

0.02302302705

\(0.001\)

  • calculation \(n°5\)

COMB_MODE =” DSC “

For each active degree of freedom \(2\) and \(3\):

  • response from mode \(i=2\) (node \(\mathrm{NO4}\)): \({R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}\) (cumulative support \(1\) and \(2\))

  • global response: \(R=\sqrt{{R}_{2}^{2}+{U}^{2}}\) (cumulative modal response and static correction)

absolute displacements: \(\mathrm{DEPL}\)

NOEUD

Reference

Tolerance

\(\mathrm{NO2}\)

0.02302302705

\(0.001\)

\(\mathrm{NO3}\)

0.02302302705

\(0.001\)