# Analyze Acoustics and Vibrations with the Acoustics Module

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## Software for Modeling Acoustic Behavior of Products and Designs

Products and designs involving acoustic phenomena can be modeled to study and predict factors like sound quality and noise reduction performance. The Acoustics Module is an add-on to the COMSOL Multiphysics^{®} software that provides tools for modeling acoustics and vibrations for applications such as speakers, mobile devices, microphones, mufflers, sensors, sonar, and flow meters. You can use the specialized features to visualize acoustic fields and build virtual prototypes of devices or components.

For more detailed studies, acoustics can be coupled with other physical effects, including structural mechanics, piezoelectricity, and fluid flow. The COMSOL^{®} software contains multiphysics couplings to enable you to evaluate the performance of a product or design in an environment that is as close as possible to the real world.

The Acoustics Module also includes many specialized formulations and material models that can be used for dedicated application areas, like thermoviscous acoustics used in miniature transducers and mobile devices or Biot's equations for modeling poroelastic waves. The multiphysics environment is extended further with several dedicated numerical methods, including the finite element method (FEM), boundary element method (BEM), ray tracing, and discontinuous Galerkin finite element method (dG-FEM).

## What You Can Model with the Acoustics Module

When you expand the COMSOL Multiphysics^{®} platform with the Acoustics Module, you have access to features for specialized acoustics and vibration analysis in addition to the core functionality of the COMSOL^{®} software.

**The Acoustics Module includes tools for modeling:**

- Absorbers
- Acoustic cloaking
- Acoustic radiation
- Acoustic streaming

- Microphones
- Mobile devices
- Modal behavior of rooms
- Mufflers

- Bioacoustic applications
- Bulk acoustic waves (BAW)
- Concert hall acoustics
- Convected acoustics
- Combustion instabilities
- Coriolis flow meters
- Car cabin acoustics
- Diffusers
- Electroacoustic transducers
- Flow meters
- Fluid-borne noise
- Fluid-structure interaction (FSI) in the frequency domain
- Hearing aids
- Impulse response
- Jet noise
- Loudspeakers
- MEMS acoustics sensors
- MEMS microphones

- Musical instruments
- Noise and vibration of machinery
- Noise-reducing materials and insulation
- Nondestructive testing (NDT)
- Oil and gas exploration
- Piezoacoustic transducers
- Reactive and absorptive mufflers
- Room and building acoustics
- Transducers
- Sensors and receivers
- Sonar devices
- Surface acoustic waves (SAWs)
- Sound insulation
- Vibroacoustics
- Woofers and subwoofers
- Ultrasound
- Ultrasonic flow meters
- Ultrasound transducers
- Underwater acoustics

**Multiphysics Couplings**

#### Included in the Acoustics Module:

- Acoustic-structure interaction
- Acoustic-structure interaction in piezoelectric materials
- Acoustic-poroelastic waves interaction
- Poroelastic-structure interaction
- Coupling acoustic FEM and BEM domains
- Acoustic-thermoviscous acoustic interaction
- Thermoviscous acoustic-structure interaction
- Aeroacoustic-structure interaction

#### Accessible with additional modules:

- Acoustic-shell interaction
- Thermoviscous acoustic-shell interaction
- Sound propagation in pipe systems
- Electrical behavior of transducers via lumped models
- Electrical behavior of magnets, coils, and soft iron materials in transducers
- Background mean flow in aeroacoustics
- Poroelastic waves-shell interaction

To model pressure acoustics effects, such as the scattering, diffraction, emission, radiation, and transmission of sound, you can use the pressure acoustics interfaces. Problems are modeled in the frequency domain via the Helmholtz equation or in the time domain via the classical scalar wave equation.

There are many options to account for boundaries in acoustics models. For instance, you can add a boundary condition for a wall or an impedance condition for a porous layer. You can use ports to excite or absorb acoustic waves at the inlet and outlet of waveguides using multimode expansion. Sources like prescribed acceleration, velocity, displacement, or pressure can be applied on exterior or interior boundaries. Further, you are able to use radiation or Floquet periodic boundary conditions to model open or periodic boundaries.

You can also compute and visualize the exterior field in a model with open boundaries including everything from the near field to the far field. The radiation pattern or spatial response can be visualized with polar plots or a directivity plot.

#### Pressure acoustics interfaces:

*Pressure Acoustics, Frequency Domain*- Solve problems described by the Helmholtz equation and include many engineering relations for boundary conditions and fluid models
- Use an eigenfrequency analysis to find acoustic modes and shapes

*Pressure Acoustics, Transient*- Study the transient propagation of acoustic waves using arbitrary time-dependent input signals
- Include nonlinear effects using the Westervelt model

*Boundary Mode Acoustics*- Identify and study propagating and nonpropagating modes in waveguides and ducts

*Pressure Acoustics, Boundary Element*- Use the boundary element method to efficiently solve radiation and scattering problems
- Couple seamlessly to FEM-based physics like elastic structures and piezoelectric materials

*Pressure Acoustics, Time Explicit*- Use the dG method to model the transient propagation of sound in room acoustics or model large scattering problems with computational efficiency

#### Application areas:

- Mufflers
- Loudspeakers
- Noise radiation from machines
- Car cabin acoustics
- Modal behavior in room acoustics
- Absorbers and diffusers
- Scattering problems

Using the Acoustics Module, you can simulate the interaction between acoustics and structural mechanics within a product or design. Predefined interfaces enable you to study vibroacoustics and automatically couple fluid and structural domains. The *Solid Mechanics* interface uses a full structural dynamics formulation that accounts for the effects of shear waves and pressure waves in solids and analyzes elastic waves. A dedicated *Poroelastic Waves* interface is used to model the coupled propagation of elastic and pressure waves in porous materials solving Biot's equations.

Multiphysics couplings can easily couple porous domains, solid domains, piezoelectric materials, and fluid domains to model the behavior of real-life devices. Structures can be prestressed and their harmonic behavior can be analyzed while fully coupled to acoustics.

#### Application areas:

- Muffler interactions with structural vibrations
- Loudspeaker components
- Cabinets
- Drivers

- Machinery
- Vibroacoustics
- Headphones
- Sound insulation and transmission in building materials

- Piezotransducers
- Ultrasound transducers
- Linear arrays
- Sonar transducers
- Sonar arrays

- Detailed modeling of porous materials with poroelastic waves (Biot)
- Feedback problems

The geometrical acoustics capabilities of the COMSOL^{®} software can be used to evaluate high-frequency systems where the acoustic wavelength is smaller than the characteristic geometric features. There are two interfaces for computing geometric acoustics available with the Acoustics Module: *Ray Acoustics* and *Acoustic Diffusion Equation*.

With the *Ray Acoustics* interface, you can compute the trajectories, phase, and intensity of acoustic rays. Additionally, you can calculate impulse responses and energy decay curves with a specialized *Receiver* data set and other postprocessing tools. The rays can propagate in graded media, which is necessary in underwater acoustics applications. For simulating ray acoustics in both air and water, specialized atmosphere and ocean attenuation material models are available that are important for wave propagation over large distances and at high frequencies.

With the *Acoustic Diffusion Equation* interface, you can determine the sound pressure level distribution in coupled rooms and the reverberation times at different locations. The acoustics are modeled in a simplified way using a diffusion equation for the acoustic energy density. This interface is well suited for quick analyses inside buildings and other large structures.

#### Application areas:

- Room acoustics
- Concert hall acoustics
- Underwater acoustics
- Car cabin acoustics
- Outdoor sound propagation
- Atmospheric acoustics

You can efficiently solve computational aeroacoustics (CAA) problems with a decoupled two-step approach in the Acoustics Module. First, you find the background mean flow using tools from the CFD Module or a user-defined flow profile; then, you solve the acoustic propagation problem. This is also sometimes referred to as convected acoustics or flow-borne noise simulations.

Predefined interfaces can compute acoustic variations in pressure, density, velocity, and temperature in the presence of any stationary isothermal or nonisothermal background mean flow.

There are stabilized finite element formulations for:

- Linearized Navier-Stokes
- Linearized Euler
- Linearized potential flow

The formulations readily account for the fluid-borne sound, convection, damping, reflection, and diffraction of acoustic waves by the flow. There is also functionality for FSI analyses in the frequency domain with predefined couplings to elastic structures.

#### Application areas:

- Jet engine noise
- Mufflers including background flow
- Flow meters
- Coriolis flow meters
- Analysis of liners and perforates in the presence of flow
- Combustion instabilities

For an accurate analysis of acoustic propagation in geometries with small dimensions, you need to account for losses associated with viscosity and thermal conduction; particularly, the losses in the viscous and thermal boundary layers. These effects are solved in full and automatically included within the equations solved by the thermoviscous acoustics interfaces.

These interfaces are well suited for vibroacoustics modeling in miniature electroacoustic transducers like microphones, mobile devices, hearing aids, and MEMS devices. For detailed transducer modeling, you can use the built-in multiphysics couplings between structures and thermoviscous acoustic domains.

The interface accounts for additional effects, including the full transitional behavior from adiabatic to isothermal at very low frequencies. There is also a dedicated interface for computing and identifying propagating and nonpropagating modes in narrow waveguides and ducts.

#### Application areas:

- Mobile devices
- Miniature transducers
- MEMS
- Hearing aids
- Microphones
- Perforates and perforated plates

The *Ultrasound* interfaces are used to compute the transient propagation of acoustic waves over large distances, relative to the wavelengths. Acoustic disturbances with frequencies that are not audible for humans are classified as ultrasound. This implies that ultrasonic waves have a short wavelength.

The *Convected Wave Equation, Time Explicit* interface is used to solve large transient linear acoustic problems containing many wavelengths in a stationary background flow. It is suited for time-dependent simulations with arbitrary time-dependent sources and fields.

The interface is based on the dG method and uses a time-explicit solver, which is a very memory-lean method.

#### Application areas:

- Ultrasound flow meters
- Ultrasound sensors with time of flight
- Transient propagation of sound signals in the presence of flow

## Features and Functionality Included with the Acoustics Module

### Intuitive Modeling Workflow

The COMSOL^{®} software provides a consistent and easy-to-follow workflow, whether you are working only with COMSOL Multiphysics^{®} and the Acoustics Module or combining additional products from the product suite. The modeling steps are straightforward and include:

- Defining the geometry
- Selecting materials
- Selecting a suitable physics interface
- Defining the boundaries and initial conditions
- Automatically creating the finite element mesh
- Solving the physics
- Visualizing the results

### Interfacing Capabilities for Other Software Platforms

Whether you want to use spreadsheet data in your model or import a complex CAD geometry, there is an interfacing product for your needs. You can interface the COMSOL Multiphysics^{®} software with a number of third-party tools, such as MATLAB^{®} software, Microsoft^{®} Excel^{®} spreadsheet software, Inventor^{®} software, and more via the LiveLink™ products.

### Numerical Methods and Studies

The solvers and methods used to complete analyses in the COMSOL^{®} software are both flexible and efficient. Problems encountered in acoustics span many decades of frequencies. The computational complexity can be highly dependent on the acoustic formulation. As a consequence, no single method or numerical technique is suitable for all acoustic problems.

The Acoustics Module includes four different computational methods: FEM, BEM, ray tracing, and dG-FEM, as described below. Different study types complement the different numerical formulations in order to allow for all necessary analysis types. This includes, but is not restricted to, frequency domain, eigenfrequency and eigenmodes, and transient studies. Dedicated iterative methods make it possible to model large multiphysics and multimethod problems involving many million degrees of freedom.

#### The Acoustics Module includes formulations based on:

- FEM
- The most common and versatile method that includes higher-order element discretization
- Frequency-domain and time-domain-implicit formulations

- BEM
- Integral formulation of the governing equations only requiring surface meshes
- Offers full multiphysics capabilities for seamlessly coupling to structures (solids, shells, membranes) and FEM acoustic domains

- dG-FEM
- Time-explicit dG method
- Memory-efficient technique for transient simulations of large models including many million degrees of freedom

- Ray methods
- Model high-frequency acoustics, such as for underwater and room acoustics simulations

#### The Acoustics Module includes the following studies:

- Frequency domain
- Compute acoustic response and behavior over a frequency range

- Transient
- Calculate time of flight
- Simulate transient build-up time
- Analyze broadband acoustic signals
- Simulate nonlinear behavior

- Eigenfrequency
- Compute modes and resonance frequencies of closed spaces and structures
- Extract Q and loss factor

- Mode analysis
- Compute and identify propagating and nonpropagating modes in waveguides and ducts

### Acoustic Losses

It is simple to include acoustic losses in a model. This enables you to model, for example, porous and fibrous materials by solving Biot's theory via the *Poroelastic Waves* interface. Alternatively, porous domains can be modeled with an equivalent fluid approach using the *Poroacoustics* material model in pressure acoustics. Poroacoustics include, for example, the Delany-Bazley, Miki, and Johnson-Champoux-Allard models. Losses and attenuation can also be included as user-defined expressions, analytical models, or data based on measurements.

Detailed models including thermal and viscous losses can be set up with the *Thermoviscous Acoustics* interface. This includes all effects associated with the acoustic viscous and/or thermal boundary layers. To model their damping, you can couple to vibrating structures by simply using the built-in multiphysics couplings. In waveguides or structures of constant cross section, a simplified approach based on homogenization of the boundary layer losses can be achieved using the *Narrow Region Acoustics* material model in pressure acoustics problems.

The attenuation of acoustic signals as they travel through a moving fluid including high flow gradients, temperature gradients, or turbulence can be modeled in detail with the *Linearized Navier-Stokes* interfaces. The background flow can be calculated using the capabilities of the CFD Module.

### Electroacoustics Capabilities

When modeling transducers of all sorts, the capabilities included in the Acoustics Module are readily combined with functionality from the AC/DC Module or the MEMS Module to create fully coupled multiphysics FEM models. This includes detailed modeling of magnets and voice coils in loudspeaker drivers or the electrostatic forces in condenser microphones. In electro-mechanical-acoustic transducer systems, it is easy to use lumped circuit models to simplify the electric and mechanical components. Both approaches are solved with a fully two-way coupling. In miniature transducer systems, like mobile devices, condenser microphones, and hearing aid receivers, the important damping due to the thermoviscous boundary layer losses is included in detail using the *Thermoviscous Acoustics* interfaces and the multiphysics couplings to other physics like vibrating structures.

Applications include, but are not limited to:

- Fully coupled loudspeaker modeling
- Loudspeaker drivers
- Coupling lumped circuit models to FEM domains
- Use of the AC/DC Module to optimize magnetic components
- Microphones
- MEMS microphones
- Hearing aids
- Mobile devices

### Open Domains and Radiation Problems

In the study of acoustics, it is common to simulate open problems where acoustic waves should be able to radiate without any reflections. This includes modeling the spatial sensitivity of transducers or scattering problems in sonar applications. Modeling nonreflecting boundaries is achieved using different techniques and features. Impedance conditions and radiation conditions exist for simple problems. For complex radiation patterns or advanced physics, it can be advantageous to use a so-called sponge layer.

The Acoustics Module includes several formulations for this purpose:

- Perfectly matched layers (PMLs), which can be applied in all frequency-domain models
- PMLs formulated for the time domain, which exist for the
*Pressure Acoustics, Transient*interface - So-called absorbing layers (ALs), which exist for all interfaces based on the dG-FEM formulation and for the
*Linearized Euler*interface

Using the multiphysics capabilities for modeling with the hybrid FEM-BEM approach, open problems are efficiently treated with BEM and the *Pressure Acoustics, Boundary Element* interface.

### Equation-Based Modeling: Modify the Governing Equations or Set Up User-Defined Multiphysics Couplings

For full control over simulations, you can use equation-based modeling to modify the governing equations and boundary conditions directly within the software, further customizing models for your own analyses. For example, you can model physics that are not predefined in the Acoustics Module or set up new multiphysics couplings. This includes modifying material models to model nonlinear effects by adding or modifying constitutive relations. Coupling physics in a nonstandard way is also possible. Examples of this include coupling acoustics and CFD to model acoustic streaming or the nonlinear effects of vortex shedding generated by acoustic waves.

As an added benefit, by using an equation-based modeling approach and eliminating the need for fundamental coding, you can greatly increase the flexibility in what you can model and reduce the time it would take to set up simulations.

## Simulation Apps: Simplified Modeling Workflow

Think of the time and energy you would be able to devote to new projects if you did not have to run repetitious simulation tests for other people on your team. With the Application Builder, built into COMSOL Multiphysics^{®}, you can build simulation apps that further simplify the simulation workflow by enabling you to restrict the inputs and control the outputs of your model so that your colleagues can run their own analyses.

With apps, you can easily change a design parameter, such as acoustic impedance, and test it as many times as you need without having to rerun the entire simulation. You can use apps to run your own tests more quickly or distribute apps to other members of your team to run their own tests, further freeing up your time and resources for other projects.

The process is simple:

- Transform your complex acoustics model into a simple user interface (an app)
- Customize the app to your needs by selecting inputs and outputs for the app users
- Use the COMSOL Server™ product to catalogue apps and make them accessible to other team members
- Enable your team to run their own design analyses without further assistance

You can expand the capabilities of simulation throughout your team, organization, classroom, or customer base by building and using simulation apps.

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