4. Results of modeling A

4.1. Natural frequencies

MODE	Reference
\(1\)	2,18815E+00
\(2\)	5,30484E+00

4.2. Global response on a full modal basis

Modes 1 and 2 are taken into account. The inertial (primary) and static (secondary) components of the response are directly accumulated at the level of the supports.

• calculation no. 1

COMB_MODE =” SRSS “

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

• support response \(j\mathrm{=}2\) (node \(\mathit{NO4}\)): \({R}_{2}=\sqrt{{\mathrm{Rm}}_{2}^{2}+{\text{Re}}_{2}^{2}}\) with \({\mathit{Rm}}_{2}\mathrm{=}\sqrt{{\mathit{Rm}}_{12}^{2}+{\mathit{Rm}}_{22}^{2}}\)

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

absolute displacements: DEPL

NOEUD	Reference
\(\mathit{NO1}\)	4,00000E-02
\(\mathit{NO2}\)	5,43820E-02
\(\mathit{NO3}\)	5,75544E-02
\(\mathit{NO4}\)	6,00000E-02

nodal reactions: REAC_NODA

NOEUD	Reference
\(\mathit{NO1}\)	5,36769E+01
\(\mathit{NO4}\)	7,44120E+01

4.3. Overall response on an incomplete modal basis without static correction

Only mode 1 is taken into account. The inertial (primary) and static (secondary) components of the response are directly accumulated at the level of the supports.

• calculation no 2

COMB_MODE =” SRSS “

• support response \(j\mathrm{=}1\) (node \(\mathit{NO1}\)): \({R}_{1}=\sqrt{{\mathrm{Rm}}_{1}^{2}+{\text{Re}}_{1}^{2}}\) with \({\mathrm{Rm}}_{1}={\mathrm{Rm}}_{11}\)

• support response \(j\mathrm{=}2\) (node \(\mathit{NO4}\)): \({R}_{2}=\sqrt{{\mathrm{Rm}}_{2}^{2}+{\text{Re}}_{2}^{2}}\) with \({\mathrm{Rm}}_{2}={\mathrm{Rm}}_{12}\)

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

absolute displacements: DEPL

NOEUD	Reference
\(\mathit{NO1}\)	4,00000E-02
\(\mathit{NO2}\)	5,43794E-02
\(\mathit{NO3}\)	5,73536E-02
\(\mathit{NO4}\)	6,00000E-02

nodal reactions: REAC_NODA

NOEUD	Reference
\(\mathit{NO1}\)	5,36743E+01
\(\mathit{NO4}\)	5,68312E+01

4.4. Overall response on an incomplete modal basis with static correction

Only mode 1 is involved in calculating the response. The static contribution of the neglected mode 2 is taken into account.

• calculation no 3

COMB_MODE =” SRSS “

• support response \(j\mathrm{=}1\) (node \(\mathit{NO1}\)): \({R}_{1}=\sqrt{{\mathrm{Rm}}_{1}^{2}+{\mathrm{Rc}}_{1}^{2}+{\text{Re}}_{1}^{2}}\) with \({\mathrm{Rm}}_{1}={\mathrm{Rm}}_{11}\)

• support response \(j\mathrm{=}2\) (node \(\mathit{NO4}\)): \({R}_{2}=\sqrt{{\mathrm{Rm}}_{2}^{2}+{\mathrm{Rc}}_{2}^{2}+{\text{Re}}_{2}^{2}}\) with \({\mathrm{Rm}}_{2}={\mathrm{Rm}}_{12}\)

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

absolute displacements: DEPL

NOEUD	Reference	Tolerance
\(\mathit{NO1}\)	4,00000E-02	0.001
\(\mathit{NO2}\)	0.054389658	0.001
\(\mathit{NO3}\)	0.058152653	0.001
\(\mathit{NO4}\)	6,00000E-02	0.001

nodal reactions: REAC_NODA

NOEUD	Reference	Tolerance
\(\mathit{NO1}\)	53.6846755	0.001
\(\mathit{NO4}\)	111.6190600	0.001

4.5. Partition of the primary and secondary components of the response

The inertial (primary) and static (secondary) components are treated separately.

• calculation no 4

• primary response on a full modal basis (modes 1 and 2)

COMB_MODE =” SRSS “

1. response from support \(j\mathrm{=}1\) (node \(\mathit{NO1}\)): \({\mathrm{RI}}_{1}=\sqrt{{\mathrm{Rm}}_{11}^{2}+{\mathrm{Rm}}_{21}^{2}}\) (accumulation on modes)

• support response \(j\mathrm{=}2\) (node \(\mathit{NO4}\)): \({\mathrm{RI}}_{2}=\sqrt{{\mathrm{Rm}}_{12}^{2}+{\mathrm{Rm}}_{22}^{2}}\)

• primary answer: \(\mathrm{RI}=\sqrt{{\mathrm{RI}}_{1}^{2}+{\mathrm{RI}}_{2}^{2}}\)

relative displacements: DEPL

NOEUD	Reference
NO1	0.00000E+00
NO2	4,12562E-02
NO3	6,60152E-03
NO4	0.00000E+00

nodal reactions: REAC_NODA

NOEUD	Reference
NO1	4,12562E+01
NO4	6,60152E+01

• secondary response

1. secondary answer: \(\mathrm{RII}=\sqrt{{\text{Re}}_{1}^{2}+{\text{Re}}_{2}^{2}}\)

training trips: DEPL

NOEUD	Reference
NO1	4,00000E-02
NO2	3,54306E-02
NO3	5,71746E-02
NO4	6,00000E-02

nodal reactions: REAC_NODA

NOEUD	Reference
NO1	3,43386E+01
NO4	3,43386E+01