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6.10 Acoustic and shock analysis
• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1
6.10.1 ACOUSTIC, SHOCK, AND COUPLED ACOUSTIC-STRUCTURAL ANALYSIS
Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
References
• “Acoustic medium,” Section 26.3.1
• “Acoustic and shock loads,” Section 34.4.6
• “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1
• “ALE adaptive meshing: overview,” Section 12.2.1
• “Steady-state transport analysis,” Section 6.4.1
• *ACOUSTIC FLOW VELOCITY
• *ACOUSTIC WAVE FORMULATION
• *ADAPTIVE MESH
• *BEAM FLUID INERTIA
• *CONWEP CHARGE PROPERTY
• *IMPEDANCE
• *IMPEDANCE PROPERTY
• *INCIDENT WAVE
• *INCIDENT WAVE INTERACTION
• *INITIAL CONDITIONS
• *SIMPEDANCE
• *TIE
• “Defining an acoustic pressure boundary condition,” Section 16.10.19 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
• “Creating the submodel boundary condition,” Section 38.4 of the Abaqus/CAE User’s Guide
Overview
Analyses performed using acoustic elements, an acoustic medium, and a dynamic procedure can simulate a variety of engineering phenomena including low-amplitude wave phenomena involving fluids such as air and water and “shock” analysis involving higher amplitude waves in fluids interacting with structures. An acoustic analysis:
• is used to model sound propagation, emission, and radiation problems;
• can include incident wave loading to model effects such as underwater explosion (UNDEX) on structures interacting with fluids, airborne blast loading on structures, or sound waves impinging on a structure;
• in Abaqus/Explicit can include fluid undergoing cavitation when the absolute pressure drops to a limit value;
• is performed using one of the dynamic analysis procedures (“Dynamic analysis procedures: overview,” Section 6.3.1);
• can be used to model an acoustic medium alone, as in the study of the natural frequencies of vibration of a cavity containing an acoustic fluid;
• can be used to model a coupled acoustic-structural system, as in the study of the noise level in a vehicle;
• can be used to model the sound transmitted through a coupled acoustic-structural system;
• requires the use of acoustic elements and, for coupled acoustic-structural analysis, a surface-based interaction using a tie constraint or, in Abaqus/Standard, acoustic interface elements;
• can be used to obtain the scattered wave solution directly under incident wave loading when the mechanical behavior of the fluid is linear;
• can be used to obtain a total wave solution (sum of the incident and the scattered waves) by selecting the total wave formulation, particularly when nonlinear fluid behavior such as cavitation is present in the acoustic medium;
• can be used to model problems where the acoustic medium interacts with a structure subjected to large static deformation;
• in Abaqus/Standard can be used with symmetric model generation (“Symmetric model generation,” Section 10.4.1) and symmetric results transfer (“Transferring results from a symmetric mesh or a partial three-dimensional mesh to a full three-dimensional mesh,” Section 10.4.2);
• in Abaqus/Standard can be used with steady-state transport (“Steady-state transport analysis,” Section 6.4.1) and an acoustic flow velocity (“*ACOUSTIC FLOW VELOCITY,” Section 1.2 of the Abaqus Keywords Reference Guide) to model acoustic perturbations of a moving fluid;
• in Abaqus/Standard can include a coupled structural-acoustic substructure that was previously defined (“Defining substructures,” Section 10.1.2);
• can be used to model both interior problems, where a structure surrounds one or more acoustic cavities, and exterior problems, where a structure is located in a fluid medium extending to infinity; and
• is applicable to any vibration or dynamic problem in a medium where the effects of shear stress are negligible.
A shock analysis:
• is used to model blast effects on structures;
• often requires double precision to avoid roundoff error when Abaqus/Explicit is used;
• may include acoustic elements to model the effects of fluid inertia and compressibility;
• may include virtual mass effects to model the effect of an incompressible fluid interacting with a pipe structure;
• is performed using one of the dynamic analysis procedures (“Dynamic analysis procedures: overview,” Section 6.3.1);
• can be used to model both interior problems, where a structure surrounds one or more fluid cavities, and exterior problems, where a structure is located in a fluid medium extending to infinity; and
• in Abaqus/Explicit can include air blast loading on structures using the CONWEP model.
Procedures available for acoustic analysis
Acoustic elements model the propagation of acoustic waves and are active only in dynamic analysis procedures. They are most commonly used in the following procedures:
• Direct solution, steady-state, harmonic analysis. See “Direct-solution steady-state dynamic analysis,” Section 6.3.4.
• Frequency analysis. See “Natural frequency extraction,” Section 6.3.5.
• Subspace-based steady-state dynamic analysis. See “Subspace-based steady-state dynamic analysis,” Section 6.3.9.
• Explicit dynamic analysis. See “Explicit dynamic analysis,” Section 6.3.3.
Acoustic analysis can also be performed using:
• Direct time integration analysis. See “Implicit dynamic analysis using direct integration,” Section 6.3.2.
• Complex frequency analysis. See “Natural frequency extraction,” Section 6.3.5.
• Mode-based transient dynamic analysis. See “Transient modal dynamic analysis,” Section 6.3.7.
• Mode-based steady-state dynamic analysis. See “Mode-based steady-state dynamic analysis,” Section 6.3.8.
• Dynamic fully coupled temperature-displacement analysis. See “Fully coupled thermal-stress analysis,” Section 6.5.3.
In general, analysis with acoustic elements should be thought of as small-displacement linear perturbation analysis, in which the strain in the acoustic elements is strictly (or overwhelmingly) volumetric and small. In many applications the base state for the linear perturbation is simply ignored: for solid structures interacting with air or water, the initial stress (if any) in the air or water has negligible physical effect on the acoustic waves. Most engineering acoustic analyses, transient or steady state, are of this type.
An important exception is when the acoustic perturbation occurs in a gas or liquid with high-speed underlying flow. If the magnitude of the flow velocity is significant compared to the speed of sound in the fluid (i.e., the Mach number is much greater than zero), the propagation of waves is facilitated in the direction of flow and impeded in the direction against the flow. This phenomenon is the source of the well-known “Doppler effect.” In Abaqus/Standard underlying flow effects are prescribed for nodes making up acoustic elements by specifying an acoustic flow velocity.
Acoustic elements can be used in a static analysis, but all acoustic effects will be ignored. A typical example is the air cavity in a tire/wheel assembly. In such a simulation the tire is subjected to inflation, rim mounting, and footprint loads prior to the coupled acoustic-structural analysis in which the acoustic response of the air cavity is determined. See “Defining ALE adaptive mesh domains in
Abaqus/Standard,” Section 12.2.6, and “ALE adaptive meshing and remapping in Abaqus/Standard,” Section 12.2.7, for more information.
Acoustic elements also can be used in a substructure generation procedure to generate coupled structural-acoustic substructures. Only structural degrees of freedom can be retained. The retained eigenmodes must be selected when an acoustic-structural substructure is generated. In a static analysis involving a substructure containing acoustic elements, the results will differ from the results obtained in an equivalent static analysis without substructures. The reason is that the acoustic-structural coupling is taken into account in the substructure (leading to hydrostatic contributions of the acoustic fluid), while the coupling is ignored in a static analysis without substructures. More details on coupled structural-acoustic substructures can be found in “Defining substructures,” Section 10.1.2.
A volumetric drag coefficient, , can be defined to simulate fluid velocity-dependent pressure amplitude losses. These occur, for example, when the acoustic medium flows through a porous matrix that causes some resistance (see “Acoustic medium,” Section 26.3.1), such as a sound-deadening material like fiberglass insulation. For direct time integration dynamic analysis we assume there are no significant spatial discontinuities in the quantity \gamma / \rho _ { f } , where \rho _ { f } is the density of the fluid (acoustic medium), and that the volumetric drag is small at acoustic-structural boundaries. These assumptions, which can limit the applicability of the analysis, are discussed further in “Coupled acoustic-structural medium analysis,” Section 2.9.1 of the Abaqus Theory Guide.
The direct-solution steady-state dynamic harmonic response procedure is advantageous for acoustic-structural sound propagation problems, because the gradient of \gamma / \rho _ { f } need not be small and because acoustic-structural coupling and damping are not restricted in this formulation. If there is no damping or if damping can be neglected, factoring a real-only matrix can reduce computational time significantly; see “Direct-solution steady-state dynamic analysis,” Section 6.3.4, for details.
Some fluid-solid interaction analyses involve long-duration dynamic effects that more closely resemble structural dynamic analysis than wave propagation; that is, the important dynamics of the structure occur at a time scale that is long compared to the compressional wave speed of the solid medium and the acoustic wave speed of the fluid. Equivalently, in such cases, disturbances of interest in the structure propagate very slowly in comparison to waves in the fluid and compressional waves in the structure. In such instances, modeling of the structure using beams is common. When these structural elements interact with a surrounding fluid, the important fluid effect is due to motions associated with incompressible flow (see “Loading due to an incident dilatational wave field,” Section 6.3.1 of the Abaqus Theory Guide). These motions result in a perceived inertia added to the structural beam; therefore, this case is usually referred to as the “virtual mass approximation.” For this case Abaqus allows you to modify the inertia properties of beam and pipe elements, as described below. Loads on the structure associated with incident waves in the fluid can be accommodated under this approximation as well.
Natural frequency extraction
Abaqus can compute both real and complex eigensolutions for purely acoustic or structural-acoustic systems, with or without damping. Exterior acoustic problems may also be solved.
Selecting an eigensolver
In a coupled acoustic-structural model, real-valued coupled modes are extracted by default using the Lanczos eigenfrequency extraction procedure. Coupling may be suppressed in the frequency extraction step; in this case the structural elements behave as though the interface with the acoustic elements were free (as though this surface were “in vacuo”), and the acoustic elements behave as though the boundary with the structural elements were rigid. Extracting the coupled acoustic-structural modes is also available for the AMS eigensolver.
Structural-acoustic coupling is ignored if the subspace iteration eigensolver is used.
When applying the AMS eigensolver to a coupled structural-acoustic model, Abaqus by default projects and stores the acoustic coupling matrix during the natural frequency extraction, for later use in coupled forced response analyses. The structural and acoustic regions are not actually coupled during the eigenanalysis; Abaqus solves the two regions separately but computes and stores the projected coupling operator for use in subsequent steady-state dynamic steps. Only structural-acoustic coupling defined using tied contact is supported. You can suppress this coupling if desired. Damping due to acoustic volumetric drag is also projected by default during an eigenanalysis and is restored by default in subsequent steady-state dynamic steps. Projecting and storing the acoustic coupling matrix during the natural frequency extraction is also available for the Lanczos eigensolver based on the SIM architecture.
Damping and inertia effects in an acoustic natural frequency extraction
Since damping is not taken into account in real-valued modal extraction, the volumetric drag effect is not considered, except for its small contribution to any nonreflecting boundaries (see “Coupled acousticstructural medium analysis,” Section 2.9.1 of the Abaqus Theory Guide). The damping contributions due to any impedance boundary conditions (element-based or surface-based) or acoustic infinite elements are not included in an eigenfrequency extraction step, but the contributions to the acoustic element mass and stiffness matrices are included. Similarly, the (symmetrized) stiffness and mass contributions of acoustic infinite elements are included in an eigenfrequency extraction step, but the damping effects are neglected.
Modal analysis of damped and radiating acoustic systems can be performed in Abaqus as well. Using the complex eigenvalue extraction procedure, the damping contributions of acoustic infinite elements, nonreflecting impedance conditions, and general impedance layers are restored to the element operators.
If an underlying flow field is defined for the acoustic region by specifying an acoustic flow velocity, the natural frequencies and modes are affected. However, in real-valued frequency extraction only the acoustic element mass and stiffness matrices contribute to the solution. Since the formulation for acoustics in the presence of a flow field requires a complex part in the element operator (damping matrix), the real-valued procedure can include the effects of flow only to a limited degree. The complex frequency procedure in Abaqus/Standard includes the damping matrix contribution and is, therefore, required when modes of a system with moving fluid are sought. The complex frequency procedure can be used only following the Lanczos real-valued frequency procedure.
Virtual mass effects defined for beams by adding inertia (“Additional inertia due to immersion in fluid” in “Beam section behavior,” Section 29.3.5) are included in modal analysis: their effect is simply to add inertia to a beam element.
Interpreting the extracted modes in a coupled structural-acoustic natural frequency analysis
While all the modes extracted in a coupled Lanczos structural-acoustic natural frequency analysis include the effects of fluid-solid interaction, some of them may have predominantly structural contributions while others may have predominantly acoustic contributions. Coupled structural-acoustic eigenmodes can be categorized as follows:
• Most generally, an individual mode may exhibit participation in both the fluid and the solid media; this is referred to as a “coupled mode.”
• Second, there are the “structural resonance” modes. These are modes corresponding to the eigenmodes of the structure without the presence of the acoustic fluid. The presence of the acoustic fluid has a relatively small effect on these eigenfrequencies and the mode shapes.
• Third, there are the “acoustic cavity resonance” modes. These are nonzero eigenfrequency coupled modes that have a significant contribution in the resulting dynamics of the acoustic pressure in mode-based dynamic procedures.
• Fourth, if insufficient boundary conditions are specified on the structural part of a model, the frequency extraction procedure will extract rigid body modes. These modes have zero eigenfrequencies (sometimes they appear as either small positive or even negative eigenvalues). However, if sufficient structural degrees of freedom are constrained, these rigid body modes disappear.
• Finally, there are the singular acoustic modes, which have zero eigenfrequencies and constant acoustic pressure; they are mathematically analogous to structural rigid body modes. The structural part of the singular acoustic modes corresponds to the quasi-static structural response to constant pressure in unconstrained acoustic regions. These eigenmodes are predominantly acoustic and are important in representing the (low-frequency) acoustic response in mode-based analysis in the presence of acoustic loads, in the same way that rigid body modes are important in the representation of structural motion. As is true for the structural rigid body modes, if a sufficient number of constrained acoustic degrees of freedom is specified (one degree of freedom 8 per acoustic region is enough), the singular acoustic modes will disappear. In models with only one unconstrained acoustic region (the most common case) only one singular acoustic mode will be computed. In general there are as many singular acoustic modes as there are independent unconstrained acoustic regions. If these modes are present, they are always reported first by the Lanczos eigensolver; and a note at the bottom of the eigenfrequency table in the data file provides information about the number of singular acoustic modes.
The generalized masses and effective masses can help distinguish between the various types of modes and can be used to assess which modes are important for subsequent mode-based analyses. In addition, the acoustic contribution to the generalized masses is reported as a fraction for each eigenmode. The closer the value of this fraction is to unity, the more pronounced is the acoustic component of this eigenmode. An acoustic effective mass is also computed for each eigenmode. This scalar quantity is scaled such that when all eigenmodes in a model are extracted, the sum of all acoustic effective masses is equal to 1.0 (minus the contributions from nodes with restrained acoustic degrees of freedom). The acoustic effective mass can be compared between different modes: the higher the acoustic effective
mass, the more important (typically) the mode is for accurate representation of the acoustic pressure. For example, the fluid cavity acoustic resonance modes will have larger acoustic effective masses compared to the other modes.
Modal superposition procedures
In Abaqus acoustic domains are handled quite similarly to solid and structural domains. Real-valued eigenmodes, resulting from a previous real-valued eigenfrequency extraction procedure with or without coupling effects included, are used as a basis for modal solutions. The mode-based steady-state dynamic procedure is the most computationally efficient alternative to compute the steady-state response of structural-acoustic systems. Structural-acoustic coupling and damping effects in these analyses depend on the type of modal procedure and the eigensolver that was used to compute the eigenfrequencies.
Structural-acoustic coupling in modal analyses using the Lanczos eigensolver without the SIM architecture
If coupled modes are computed using the Lanczos eigensolver, both the mode-based and subspace projection steady-state dynamic procedures will include structural-acoustic coupled effects. If uncoupled Lanczos modes are computed, coupling can be restored only by using subspace projection. It is sufficient to project at a single frequency (constant subspace) to resolve the acoustic coupling for all frequencies.
Acoustic medium damping in modal analyses using the Lanczos eigensolver without the SIM architecture
In subspace-based steady-state dynamic analysis, acoustic medium damping and structural material damping are considered, and the structural-acoustic interaction, infinite element, and impedance boundary terms are also included.
Acoustic medium damping is not considered in the procedures that base the response prediction directly on the system’s eigenmodes, such as transient modal dynamic analysis or the mode-based steadystate dynamic procedure. These methods should, therefore, be used with caution for problems with impedance boundary conditions. Modal damping can be used in these procedures (“Material damping,” Section 26.1.1) to model material damping and volumetric drag effects; however, modal damping usually cannot be used to model the fluid-solid coupling or the impedance boundary effects accurately.
Structural-acoustic coupling and damping in modal analyses using the subspace iteration eigensolver
The subspace iteration eigensolver neglects the effects of structural-acoustic coupling; therefore, coupling effects are not included in subsequent modal procedures.
As with analyses using the Lanczos eigensolver, acoustic medium damping and structural material damping are considered in subsequent subspace-based steady-state dynamic procedures, but these damping effects are not considered in subsequent transient modal or mode-based steady-state dynamic procedures.
Structural-acoustic coupling and damping in modal analyses using the AMS eigensolver or the Lanczos eigensolver based on the SIM architecture
The structural-acoustic modes, extracted using the AMS eigensolver or the Lanczos eigensolver, can be used in modal analyses using the SIM architecture. When uncoupled modes are computed using the AMS eigensolver or the Lanczos eigensolver based on the SIM architecture with projection of the structuralacoustic coupling specified, the coupling and acoustic damping operators are projected and stored during the natural frequency extraction. Subsequent coupled forced response analyses using modal steady-state dynamics automatically restore the effects of structural-acoustic coupling and damping by automatically using these projected matrices; if the matrices were not projected, the steady-state dynamic step would not include these effects. A mode-based steady-state dynamic step cannot use unsymmetric damping, such as from acoustic flow velocity or infinite element effects. To take these effects into account, a subspace-based steady-state dynamic analysis should be used.
Defining translational or rotational underlying flow velocity in Abaqus/Standard
As described above, acoustic analysis in Abaqus/Standard can be performed as a linear perturbation of a high-speed flow field. The flow velocity field affects the propagation of acoustic waves in the medium through the effect of the flow velocity on the speed of the wave propagation. Waves travel faster along the direction of the local flow vector and are correspondingly impeded in the direction against the flow direction. It is sufficient for you to define the velocity field in the affected acoustic region; the accelerations do not play a role in the formulation.
You specify the flow in the acoustic finite element region as history data within a dynamic linear perturbation step. The flow field can be described either by direct input of the velocity components or by defining rotating motion associated with a reference frame. In the former case, each node in the acoustic region where flow occurs is assigned a Cartesian velocity defined by specifying the components of the velocity vector, . In the latter case, the rotational velocity for the nodes in the acoustic region is defined by specifying the magnitude of an angular rotation velocity, , and the position and orientation of the axis of rotation in the current configuration. The position and orientation of the axis are applied at the beginning of the step and remain fixed during the step.
The specified underlying flow is active only for acoustic finite elements; other elements with acoustic degrees of freedom, such as acoustic infinite and interface elements, are unaffected by the specified flow velocity. The effect of underlying flow on the acoustic finite elements depends also on the procedure used: the effects are present only in frequency-domain dynamic procedures and natural frequency extraction. For complex-valued procedures, such as complex frequency extraction and steady-state dynamics, the presence of underlying flow affects the acoustic finite element stiffness matrices and adds a significant contribution to the element damping matrix. For real-valued procedures, such as eigenfrequency extraction and steady-state dynamics analysis in which a real-only system matrix is factored, the presence of underlying flow affects only the acoustic finite element stiffness matrices; the damping matrix is ignored. Consequently, the effect of flow on the acoustic field is fully realized only in complex-valued procedures.
For rotating systems, solid and acoustic materials are treated differently in Abaqus. Flow of solid material through a mesh may induce significant deformation and is handled by using steady-state