Vibroacoustic Fluid-Structure Interaction with FEM 1. Governing Equations for 3-D Structure-Fluid Interaction 2. FEM for free vibrations (symmetry considerations) 3. FEM for forced vibrations (modal superposition) Review: 1-D Structure-Fluid Interaction 3-D HAW-M+P-CompA-Ihlenburg Acoustic Fluid-Structure Interaction x l Structural (normal) velocities Fluid pressure • Velocity-pressure equilibrium in normal direction 1
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Vibroacoustic Fluid-Structure Interaction with FEM
1. Governing Equations for 3-D Structure-Fluid Interaction
2. FEM for free vibrations (symmetry considerations)
3. FEM for forced vibrations (modal superposition)
In continuum mechanics, one distinguishes between tractions (acting at the faces of control volumes) and volume forces (acting on all interior particles of a volume). Examples of volume forces are gravitational forces or forces of inertia.
Condition 2: Kinematic compatibility (equal normal displacements)
S ⋅v n
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Dynamic coupling contition
Consider a solid boundary in contact with an ideal fluid.Define a local coordinate system with normal and two tangential direction vectors. Then the external stress vector in local coordinates is
The normal displacements of solid and (ideal) fluid are equal. Since friction is neglected, no condition can be imposed on the tangential projections of the displacement vectors.
The fluid displacement vector can be replaced by the pressure value using the Euler
Observation: the coupling matrices of the finite element model are obtained from element integrals of the product „fluid shape function * solid shape function“. Since these products are commutative, the governing equations can be scaled ( = multiplied by a constant factor) in such a way that the overall coupled system of equations is symmetric .
• The mesh size in fluid and solid can differ• The boundaries do not need to have exactly the same contours (search algorithm for non-matching boundaries)• The node numbers in fluid and solid must be different
• Parameters for the coupling procedure: ACMODL parameter in the bulk data section.
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15:46:35 Application of Loads and Boundary Conditions to the finite element model started.15:46:35 Application of Loads and Boundary Conditions to the finite element model successfully completed.15:46:35 Solution of the system equations for normal modes started.15:46:39 Solution of the system equations for normal modes successfully completed.15:46:39 Solution of the system equations for normal modes started.15:46:39 Solution of the system equations for normal modes successfully completed.15:46:39 Solution of the system equations for frequency response started.15:46:40 Solution of the system equations for frequency response successfully completed.15:46:40 Frequency response analysis completed.