Fluid Structure Interaction - Moving Wall in Still Water

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Malcolm Barnett
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1 Fluid Structure Interaction - Moving Wall in Still Water

2 Outline 1 Problem description 2 Methodology 2.1 Modelling 2.2 Analysis 3 Finite Element Model 3.1 Project settings 3.2 Units 3.3 Geometry Definition Reservoir without wall Subtracting geometry shapes 3.4 Properties Reservoir Concrete wall Reservoir-Wall Interface 3.5 Boundary constraints Support Fixed potentials 3.6 Load 3.7 Meshing 4 Analysis 4.1 Structural analysis Eigenvalue analysis of dry wall 4.2 Fluid-Structure Interaction Analysis Eigenvalue analysis Frequency response analysis 5 Results 5.1 Results - Structural analysis Results - Eigenvalue analysis 5.2 Results - Fluid-Structure Interaction Results - Eigenvalue analysis Results - Frequency response analysis Fluid Structure Interaction - Moving Wall in Still Water 2/35

3 1 Problem description This example studies the frequency response of a vertical wall in a water reservoir through a fluid-structure interaction analysis. The dimensions and properties of the model are described in [Fig. 1]. The case study has the following characteristics: The wall is clamped at the upper end and excitated at the lower end with a periodic force F in a frequency range up to 10 Hz. The water is assumed to be incompressible (no compression effects). Due to the presence of water, both sides of the wall are loaded by a pressure which depends on the horizontal velocities. Therefore, the presence of water adds a virtual mass to the wall. The eigenvalues of the wall, moving in the water, are expected to be lower than in the case without the water. As the front and back side of the reservoir are assumed to have negligible influence on the structural behaviour, a two-dimensional analysis can be performed. Neither radiation nor surface effects are considered. Therefore, zero dynamic water pressure is assumed at the semi-infinite and surface boundaries of the reservoir. There is no flow across the bottom surface of the reservoir. Figure 1: Idealized 2D model The objectives of this example are the following: Simulate the fluid-structure interaction. Estimate the system behaviour under the applied periodic force. Examine the wall behaviour with and without the reservoir. Fluid Structure Interaction - Moving Wall in Still Water 3/35

4 2 Methodology 2.1 Modelling The following methodology was used to model this problem: A two dimensional plane strain model is used. The structural and water domains are coupled by fluid-structure interface elements, which are applied along the wet surface of the wall, [Fig. 18]. The top boundary of the wall is fixed in the two translational directions. The zero dynamic water pressure on the reservoir boundaries is modelled with fixed potentials. The wall is assigned with linear elastic concrete material. Quadrilateral elements with quadratic interpolation are assigned to the wall. Two-dimensional heat flow elements are assigned to the reservoir. 2.2 Analysis A frequency response analysis is carried out following an initial eigenvalue analysis. In detail,the following steps are considered: 1. An eigenvalue analysis of the dry wall is carried out, to gain insight into the behaviour of the wall without the water pressure. 2. Since no compression, surface or radiation effects are assumed, it is possible to perform a modal analysis. The eigenvalues of the coupled system are, first, determined. Subsequently, a modal response analysis is carried out. Fluid Structure Interaction - Moving Wall in Still Water 4/35

5 3 Finite Element Model 3.1 Project settings For the modelling session we start a new project by a two dimensional plane strain analysis. The analysis type is set to Fluid-Structure Interaction and Structural. We specify quadrilateral mesh with quadratic interpolation. Main menu File New project [Fig. 2] Figure 2: New project Fluid Structure Interaction - Moving Wall in Still Water 5/35

6 3.2 Units We select meter [m] for the unit length and Newton [N] for the force. These units are selected by default in. Geometry browser Reference system Units [Fig. 3] Property Panel [Fig. 4] Figure 3: Geometry browser - Units Figure 4: Properties panel - Units Fluid Structure Interaction - Moving Wall in Still Water 6/35

3.3 Geometry Definition 3.3.1 Reservoir without wall First, we create a rectangular polygon sheet (24x6m) to represent the reservoir excluding the discontinuity by the wall, [Fig. 5] & [Fig. 7].

Note that we specify two additional points on the wall sheet, which indicate the intersection of the water level with the wall.

7 3.3 Geometry Definition Reservoir without wall First, we create a rectangular polygon sheet (24x6m) to represent the reservoir excluding the discontinuity by the wall, [Fig. 5] & [Fig. 7]. We create a rectangular polygon sheet (0.1x6m), representing the wall [Fig. 6], [Fig. 8]. The structure lies in the middle of the reservoir, being elevated 0.5 m over its bottom surface. Note that we specify two additional points on the wall sheet, which indicate the intersection of the water level with the wall. This is done to later assign the fluid-structure interface to the wet surface of the wall. Main Menu Geometry Create Add polygon sheet [Fig. 5] [Fig. 7] Main Menu Geometry Create Add polygon sheet [Fig. 6] [Fig. 7] Figure 7: Reservoir excluding wall discontinuity Figure 8: Wall Figure 5: Geometry - Add polygon sheet: reservoir Figure 6: Geometry - Add polygon sheet: wall Fluid Structure Interaction - Moving Wall in Still Water 7/35

The Merge option is not activated since the two surfaces will be connected by fluid-structure interface elements.

8 3.3.2 Subtracting geometry shapes We subtract the wall sheet from the reservoir sheet, [Fig. 9]. We keep the wall geometry after the subtraction by activating the Keep tools option. The Merge option is not activated since the two surfaces will be connected by fluid-structure interface elements. Main Menu Geometry Modify Subtract shapes [Fig. 9] [Fig. 10] [Fig. 11] Figure 10: Wall discontinuity subtracted from reservoir Figure 9: Geometry - Subtract shapes Figure 11: Reservoir including wall discontinuity Fluid Structure Interaction - Moving Wall in Still Water 8/35

3.4 Properties 3.4.1 Reservoir The reservoir is modelled with 2D flow elements, [Fig. 13]. The water is defined as incompressible fluid, [Fig. 14].

9 3.4 Properties Reservoir The reservoir is modelled with 2D flow elements, [Fig. 13]. The water is defined as incompressible fluid, [Fig. 14]. Main Menu Geometry Analysis Property assignments [Fig. 12] Shape property assignments dialog Add new material [Fig. 13] [Fig. 14] Figure 12: Analysis - Property assignments Figure 13: Add neew material Figure 14: Edit material Fluid Structure Interaction - Moving Wall in Still Water 9/35

3.4.2 Concrete wall The wall is modelled with plane strain elements, [Fig. 15].

16], [Fig. 17]. Main Menu Geometry Analysis Property assignments [Fig.

17] Figure 15: Analysis - Property assignments Figure 16: Add new material

10 3.4.2 Concrete wall The wall is modelled with plane strain elements, [Fig. 15]. The concrete of the wall is considered as a linear elastic material, [Fig. 16], [Fig. 17]. Main Menu Geometry Analysis Property assignments [Fig. 15] Shape property assignments dialog Add new material [Fig. 16] [Fig. 17] Figure 15: Analysis - Property assignments Figure 16: Add new material Figure 17: Edit material Fluid Structure Interaction - Moving Wall in Still Water 10/35

3.4.3 Reservoir-Wall Interface Fluid-structure interface elements are applied along the submerged surface of the wall.

The normal direction of the fluid-structure interface element must point outward into the fluid domain.(!

2) In this manner, the nodes on the remaining edge of the interface are automatically connected to the coincident nodes of the reservoir edge.

11 3.4.3 Reservoir-Wall Interface Fluid-structure interface elements are applied along the submerged surface of the wall. Note that for the fluid-structure interface elements, the node sequence in the connectivity specification determines the fluid and the structural sides of the element. The normal direction of the fluid-structure interface element must point outward into the fluid domain.(!!!visualize this) Thus, the interface must be assigned to the submerged edges of the wall, and not to the reservoir edges in contact with the wall. (!!!! check this for DIANA 10.2) In this manner, the nodes on the remaining edge of the interface are automatically connected to the coincident nodes of the reservoir edge. Main Menu Geometry Analysis Interface property assignments [Fig. 18] Shape property assignments dialog Add new material [Fig. 19] [Fig. 20] Figure 19: Add new material Figure 21: Selecting interface lines on wall Figure 18: Analysis - Interface property assignments Figure 20: Edit material Figure 22: Fluid-structure interface Fluid Structure Interaction - Moving Wall in Still Water 11/35

3.5 Boundary constraints 3.5.1 Support We attach supports to the top boundary of the wall and constrain it in the in-plane directions, X and Y.

12 3.5 Boundary constraints Support We attach supports to the top boundary of the wall and constrain it in the in-plane directions, X and Y. Main Menu Geometry Analysis Attach support [Fig. 23] Figure 23: Geometry - Attach support Figure 24: View of the model: wall support Fluid Structure Interaction - Moving Wall in Still Water 12/35

13 3.5.2 Fixed potentials The outer edges and the top surface of the reservoir have zero pressure(see [Fig. 1]). Therefore, we attach Fixed Heads to the left, right and upper edges of the reservoir, [Fig. 25] & [Fig. 26]. Note that, by attaching Fixed Heads, the zero value is automatically assigned. In case of a non-zero value, we assign it by attaching Ground water boundary conditions on top of the existing Fixed Heads. Main Menu Geometry Analysis Attach ground water fixed potential [Fig. 25] [Fig. 26] Figure 25: Geometry - Attach ground water fixed potentials Figure 26: Attach ground water fixed potentials - select edges Note that in order to be visualized, the fixed heads must be first assigned to nodes (!!! check nodes). In this manner, this specific visualization is possible after the mesh generation (as later presented in [Fig. 39]). Fluid Structure Interaction - Moving Wall in Still Water 13/35

14 3.6 Load We apply the horizontal force of 100N at the bottom left corner of the wall, [Fig. 27] & [Fig. 28]. Note that at the specific location there are two vertices: one belongs to the wall and the other to the reservoir. The force must be attached only on the vertex of the wall. The frequency of the periodic force will be defined in the set-up of the Frequency Response Analysis, [ 4.2.2]. Main Menu Geometry Analysis Attach load [Fig. 27] [Fig. 28] Figure 27: Geometry - Attach load Figure 28: Attach point load Fluid Structure Interaction - Moving Wall in Still Water 14/35

75m below the wall, with 50% size transition smoothness. Main Menu Geometry Analysis Set mesh properties [Fig. 29] [Fig. 30] Set mesh properties dialog <edge selection> [Fig. 31] [Fig.

15 3.7 Meshing Mesh properties We specify the mesh of the top edges of the reservoir, left and right of the wall. We divide each edge into 8 elements.to seed the bottom edge of the reservoir we use symmetric gradation, starting from element size of 2m at the reservoir ends and reducing to element size of 0.75m below the wall, with 50% size transition smoothness. Main Menu Geometry Analysis Set mesh properties [Fig. 29] [Fig. 30] Set mesh properties dialog <edge selection> [Fig. 31] [Fig. 32] Figure 31: Selecting seeded edges - top of reservoir Figure 32: Selecting seeded edges - bottom of reservoir Figure 29: Set mesh properties - top edges of reservoir Figure 30: Set mesh properties - bottom edge of reservoir Fluid Structure Interaction - Moving Wall in Still Water 15/35

16 Similarly, the reservoir side edges are divided into 5 parts. Further, the submerged part of the wall is divided into 11 parts over its vertical height. Main Menu Geometry Analysis Set mesh properties [Fig. 33] [Fig. 34] Set mesh properties dialog <edge selection> [Fig. 35] [Fig. 36] Figure 35: Selecting seeded edges - top of reservoir Figure 33: Set mesh properties - side edges of reservoir Figure 34: Set mesh properties - submerged (vertical) edges of wall Figure 36: Selecting seeded edges - submerged (vertical) edges of wall Fluid Structure Interaction - Moving Wall in Still Water 16/35

17 The submerged part of the wall is divided into 3 parts over its width. Main Menu Geometry Analysis Set mesh properties [Fig. 37] Set mesh properties dialog <edge selection> [Fig. 38] Figure 38: Selecting seeded edges - submerged (horizontal) edge of wall Figure 37: Geometry - Set mesh properties: submerged wall Fluid Structure Interaction - Moving Wall in Still Water 17/35

18 Generate mesh We generate the mesh [Fig. 39]. The wall is modelled with structural plain strain elements, the reservoir with potential flow elements and their interface with fluid-structure interface elements. Main Menu Geometry Generate mesh [Fig. 39] Mesh browser Shrunken shading with feature edges [Fig. 39] Figure 39: Mesh view: shrunken shading; reservoir fixed heads (blue); fluid-structure interface elements (red) Fluid Structure Interaction - Moving Wall in Still Water 18/35

4 Analysis 4.1 Structural analysis 4.1.1 Eigenvalue analysis of dry wall We define an eigenvalue analysis of the dry wall. Here, the influence of the water pressure is not considered.

19 4 Analysis 4.1 Structural analysis Eigenvalue analysis of dry wall We define an eigenvalue analysis of the dry wall. Here, the influence of the water pressure is not considered. This is done by defining a Phased analysis command where we de-activate the reservoir elements. Main Menu Analysis Add analysis Analysis1 [Fig. 40] rename: Eigenvalue analysis - Wall Analysis browser Eigenvalue analysis - Wall Add analysis command Phased [Fig. 41] [Fig. 42] Analysis browser Eigenvalue analysis - Wall Add analysis command Structural eigenvalue [Fig. 41] [Fig. 42] Figure 40: Analysis menu Figure 41: Analysis commands menu Figure 42: Analysis browser Fluid Structure Interaction - Moving Wall in Still Water 19/35

(!!!!! add eigenfrequency interval; get rid of Figure 47) For the phased analysis only the wall and its fixed support are activated; the reservoir, the fixed potentials and the interface elements are

We start with determining the first four eigenvalues of the dry wall. We use the default output of the Structural eigenvalue analysis.

20 (!!!!! add eigenfrequency interval; get rid of Figure 47) For the phased analysis only the wall and its fixed support are activated; the reservoir, the fixed potentials and the interface elements are deactivated [Fig. 43]. The eigenfrequencies of this problem range from 0 to 10 Hz, which is the frequency range of the periodic force. We start with determining the first four eigenvalues of the dry wall. We use the default output of the Structural eigenvalue analysis. Analysis browser Eigenvalue analysis - Wall Phased Edit properties [Fig. 42] [Fig. 43] Analysis browser Eigenvalue analysis - Wall Structural eigenvalue Execute eigenvalue analysis Edit properties [Fig. 42] [Fig. 44] Main Menu Analysis Run analysis Figure 43: Phased analysis - Edit properties Figure 44: Eigenvalue analysis - Edit properties Fluid Structure Interaction - Moving Wall in Still Water 20/35

21 4.2 Fluid-Structure Interaction Analysis Next, we define the modal response analysis of the wall-reservoir system. We add a new analysis [Fig. 45], with the User-specified named Modal response - System. Main Menu Analysis Add analysis Analysis2 [Fig. 45] rename: Modal response - System Analysis browser Modal response - System Add analysis command Structural modal response [Fig. 46] [Fig. 47] Figure 45: Analysis menu Figure 46: Analysis commands menu Figure 47: Analysis browser Fluid Structure Interaction - Moving Wall in Still Water 21/35

4.2.1 Eigenvalue analysis The first step of the Structural Modal Response analysis is an Eigenvalue Analysis from which we derive the eigenmodes that lie within the specified frequency interval, 0-10

22 4.2.1 Eigenvalue analysis The first step of the Structural Modal Response analysis is an Eigenvalue Analysis from which we derive the eigenmodes that lie within the specified frequency interval, 0-10 Hz. These eigenvalues will be then used for the Frequency Response Analysis. The eigenfrequencies of the wet wall are expected to be lower than of the dry wall, owing to the mass added by the water pressure. Thus, to be sure to capture all the eigenfrequencies within the range of 0 to 10 Hz, we raise the number of specified eigenfrequencies to 5. Analysis browser Modal response - System Structural modal response Frequency response analysis < Toggle off > [Fig. 48] Analysis browser Modal response - System Structural modal response Eigenvalue analysis Execute eigenvalue analysis Edit properties [Fig. 48] [Fig. 49] Main Menu Analysis Run analysis Figure 48: Analysis browser Figure 49: Eigenvalue analysis - Edit properties Fluid Structure Interaction - Moving Wall in Still Water 22/35

The other two eigenvalues lie outside the periodic force frequency range and, for this reason, are neglected. We specify frequency step sizes of 0.025 Hz.

23 4.2.2 Frequency response analysis The periodic force is now applied in sequential frequency increments. To get accurate results we refine the incremental step sizes around the first three eigenvalues of the wall-reservoir system [Fig. 63]-[Fig. 65]. The other two eigenvalues lie outside the periodic force frequency range and, for this reason, are neglected. We specify frequency step sizes of Hz. Analysis browser Frequency response analysis < Toggle on > [Fig. 50] Analysis browser Modal response - System Structural modal response Frequency response analysis Execute frequency analysis Edit properties [Fig. 50] [Fig. 49] Figure 50: Analysis browser Figure 51: Eigenvalue analysis - Edit properties Fluid Structure Interaction - Moving Wall in Still Water 23/35

We select displacement, velocity and acceleration for the output of the Frequency response analysis.

[Fig. 50] [Fig. 52] Properties-OUTPUT dialog Result User selection Modify Results selection dialog DISPLA TOTAL TRANSL GLOBAL Add [Fig. 52] [Fig.

54] Repeat for next two output items: velocity (VELOCI), acceleration (ACCELE) [Fig. 53] [Fig.

24 We select displacement, velocity and acceleration for the output of the Frequency response analysis. Analysis browser Modal response - System Structural modal response Frequency response analysis Output frequency response analysis Edit properties [Fig. 50] [Fig. 52] Properties-OUTPUT dialog Result User selection Modify Results selection dialog DISPLA TOTAL TRANSL GLOBAL Add [Fig. 52] [Fig. 53] Results Selection dialog DISPLA TOTAL TRANSL GLOBAL Properties [Fig. 53] [Fig. 54] Result Item Properties dialog Amplitude/Phase angle [Fig. 54] Repeat for next two output items: velocity (VELOCI), acceleration (ACCELE) [Fig. 53] [Fig. 54] Main Menu Analysis Run analysis Figure 52: Output frequency response analysis - Edit properties Figure 53: Results selection Figure 54: Results selection Fluid Structure Interaction - Moving Wall in Still Water 24/35

25 5 Results 5.1 Results - Structural analysis Results - Eigenvalue analysis We obtain the results of the first 4 eigenvalues and vibration modes. The contour plot of the normalized deformation for Vibration mode 1 is presented in [Fig. 56]. (!!!! are the results matching with DIANA 10.2 results?) Results browser Analysis Eigenvalue analysis - Wall [Fig. 55] Results browser Case Mode 1 [Fig. 55] Results browser Output eigenvalue analysis Nodal results Total Displacements DtXYZ [Fig. 55] [Fig. 56] Figure 55: Results window, Eigenvalue analysis - Wall Figure 56: Dry wall - Vibration mode 1 Fluid Structure Interaction - Moving Wall in Still Water 25/35

26 Similarly, the contour plots of the remaining vibration modes are also obtained: [Fig. 57], [Fig. 58], [Fig. 59], [Fig. 60]. The respective eigenvalues are given on the title of each contour plot. We observe that only the first two eigenvalues lie within the required frequency range: 0 to 10 Hz. The fourth eigenvalue lies well beyond the frequency upper bound. Figure 57: Dry wall - Vibration mode 1 Figure 58: Dry wall - Vibration mode 2 Figure 59: Dry wall - Vibration mode 3 Figure 60: Dry wall - Vibration mode 4 Fluid Structure Interaction - Moving Wall in Still Water 26/35

27 5.2 Results - Fluid-Structure Interaction Results - Eigenvalue analysis The first 5 eigenvalues and vibration modes are obtained. The contour plot of the normalized deformation for Vibration mode 1 is presented in [Fig. 62]. In this figure, the first eigenvalue is displayed in the title and the dotted horizontal lines represent the deformed fluid-structure interface. By comparing the eigenvalues of the wet wall [Fig. 62] and the dry wall [Fig. 56] we observe the reduction due to fluid-structure interaction, as expected. Results browser Analysis Modal response - System [Fig. 61] Results browser Case Mode 1, Eigen value... [Fig. 61] Results browser Output eigenvalue analysis Nodal results Total Displacements DtXYZ [Fig. 61] [Fig. 62] Figure 61: Results window, Eigenvalue analysis - Wall Figure 62: Wet wall - Vibration mode 1 Fluid Structure Interaction - Moving Wall in Still Water 27/35

28 Similarly, we obtain the contour plots for the remaining vibration modes: (!!!! change cotnour plot settings to make plots more visible) [Fig. 57], [Fig. 58], [Fig. 59], [Fig. 60]. The respective eigenvalues are given on the title of each contour plot. As expected, the eigenmodes are analogous to those of the dry wall [Fig. 57]-[Fig. 60]. However,due to the added water pressure, the eigenvalues of the wall are reduced (compared to dry wall [Fig. 57] - [Fig. 60]). We also observe that, now, the first three eigenvalues lie within the required frequency range: 0 to 10 Hz. The fourth and fifth eigenvalues lie well beyond the frequency upper bound. Results browser Case Mode 1, 2,3 [Fig. 63] [Fig. 64] [Fig. 65] Figure 63: Wet wall - Vibration mode 1 Figure 64: Wet wall - Vibration mode 2 Figure 65: Wet wall - Vibration mode 3 Fluid Structure Interaction - Moving Wall in Still Water 28/35

29 5.2.2 Results - Frequency response analysis The amplitude and the phase angle of the displacement are given for the excitation frequency (Excitation 5) closer to the first eigenvalue of the system (see [Fig. 62]). Results browser Analysis Modal response - System [Fig. 66] Results browser Case Excitation 5, Frequency... [Fig. 66] Results browser Output frequency response analysis Nodal results Total Displacements DCtXA [Fig. 66] [Fig. 67] DCtXP [Fig. 66] [Fig. 68] Figure 66: Results window, Eigenvalue analysis - Wall Figure 67: Displacement amplitude - - Excitation 5 Figure 68: Displacement phase angle - - Excitation 5 Fluid Structure Interaction - Moving Wall in Still Water 29/35

30 We also check the line-diagram plots for the amplitude and the phase angle of the velocity and the acceleration [Fig. 69] - [Fig. 72]. Results browser Analysis Modal response - System [Fig. 66] Results browser Case Excitation 5 [Fig. 66] Results browser Output frequency response analysis Nodal results Total Translational Velocities VtXA [Fig. 66] [Fig. 69] VtXP [Fig. 66] [Fig. 70] Results browser Output frequency response analysis Nodal results Total Translational Velocities AtXA [Fig. 66] [Fig. 71] AtXP [Fig. 66] [Fig. 72] Figure 69: Velocity amplitude - - Excitation 5 Figure 70: Velocity phase angle - - Excitation 5 Figure 71: Acceleration amplitude - - Excitation 5 Figure 72: Acceleration amplitude - - Excitation 5 Fluid Structure Interaction - Moving Wall in Still Water 30/35

31 We draw the amplitude-frequency and the phase-frequency graphs for the displacement results. The graphs relate to three nodes along the west side of the wall, including the node where the periodic force is applied [Fig. 74]. To do so, we first select the nodes. To avoid selecting the coincident nodes of the reservoir, we must first hide the reservoir elements and the fluid-structure interface elements [Fig. 73]. Mesh browser Mesh reservoir, interf < hide > [Fig. 73] Selection nodes toolbar Select nodes [Fig. 74] Figure 73: Mesh browser - - hiding shapes Figure 74: Selecting nodes to check output results Fluid Structure Interaction - Moving Wall in Still Water 31/35

32 We select the table results of displacement amplitude and displacement phase angle for the specified node. Then, the Chart view dialog appears where the specified results are given in both chart and table format. In the same dialog we can select different result items (i.e. translational accelerations), different range of excitation frequencies and specific elements/nodes. Results browser Analysis Modal response - System [Fig. 75] Results browser Case Excitation 5 [Fig. 75] Results browser Output frequency response analysis Nodal results Displacements DCtXA Show table [Fig. 75] [Fig. 76] Chart view dialog Results selection Displacements [Fig. 75] [Fig. 77] Figure 75: Results browser Figure 76: Table of results - DCtXA: excitation 16 Figure 77: Table of results - DCtXP: excitation 16 Fluid Structure Interaction - Moving Wall in Still Water 32/35

Remaining in the Chart view dialog, we further check the result charts of amplitude-frequency and phase-frequency for: velocity [Fig. 78] & [Fig. 79], amplitude [Fig. 80] & [Fig. 81].

33 Remaining in the Chart view dialog, we further check the result charts of amplitude-frequency and phase-frequency for: velocity [Fig. 78] & [Fig. 79], amplitude [Fig. 80] & [Fig. 81].These results are checked for the specified nodes [Fig. 74]. Chart view dialog Results selection Translational Velocities - VtXA [Fig. 78] Chart view dialog Results selection Translational Velocities - VtXP [Fig. 79] Figure 78: Velocity amplitude - Excitation frequency Figure 79: Velocity phase angle - Excitation frequency Fluid Structure Interaction - Moving Wall in Still Water 33/35

In the Chart view dialog we also check the result charts of amplitude-frequency and phase-frequency for: velocity [Fig. 78] & [Fig. 79], amplitude [Fig. 80] & [Fig. 81].

34 In the Chart view dialog we also check the result charts of amplitude-frequency and phase-frequency for: velocity [Fig. 78] & [Fig. 79], amplitude [Fig. 80] & [Fig. 81].These results are checked for the specified nodes [Fig. 74]. Chart view dialog Results selection Translational Accelerations - AtXA [Fig. 80] Chart view dialog Results selection Translational Accelerations - AtXP [Fig. 81] Figure 80: Acceleration amplitude - Excitation frequency Figure 81: Acceleration phase angle - Excitation frequency Fluid Structure Interaction - Moving Wall in Still Water 34/35

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