For Acoustics and Vibrations Analysis
Bringing Acoustics and Vibrations Analysis to a New Level
The Acoustics Module is designed specifically for those who work with devices that produce, measure, and utilize acoustic waves. Application areas include speakers, microphones, hearing aids, and sonar devices, to name a few. Noise control can be addressed in muffler design, sound barriers, and building acoustic applications.
Gain Insight Into Your Existing and New Products
Straightforward user interfaces provide tools for modeling acoustic pressure wave propagation in air, water, and other fluids. Dedicated modeling tools for thermoacoustics enable highly accurate simulation of miniaturized speakers and microphones in handheld devices. You can also model vibrations and elastic waves in solids, piezoelectric materials, and poroelastic structures. Multiphysics interfaces for acoustic-solid, acoustic-shell, and piezo-acoustics bring your acoustic simulations to a new level of predictive power.
By using realistic simulations in 1D, 2D, or 3D, you can optimize existing products and design new products more quickly. Simulations also help designers, researchers, and engineers gain insight into problems that are difficult to handle experimentally. By testing a design before manufacturing it, companies save both time and money.
- The sound pressure level distribution in a muffler system.
- A 3D far-field polar plot of loudspeaker sensitivity at 3,000 Hz.
- The tonpilz (sound mushroom) piezo transducer is a transducer for relatively low-frequency, high-power sound emission. The transducer consists of piezoceramic rings stacked between massive ends, and pre-stressed by a central bolt. The tail and head mass lower the resonance frequency of the device.
- Poroelastic waves and acoustics in a conceptual particulate-filter system. Diesel particulate filters (DPFs), are designed to remove/filter soot (diesel particles) from the exhaust of diesel engine vehicles. Although the main function of a particulate filter is to filter the exhaust flow, it also has acoustic damping properties that relate to the muffler system.
- This is a model of the Brüel and Kjær 4134 condenser microphone. The geometry and material parameters are those of the actual microphone. The modeled sensitivity level is compared to measurements performed on an actual microphone and shows good agreement. The membrane deformation, pressure, velocity, and electric field are also determined. Model provided courtesy Brüel & Kjær Sound & Vibration Measurement, Nærum, Denmark.
- The visualization shows isosurfaces of the acoustic pressure in a car interior. LiveLink™ for Inventor® allows users to access COMSOL functionality directly from within the Inventor® user interface including that of the Acoustics Module.
For Modeling a Variety of Different Acoustics Applications
The Acoustics Module consists of a set of physics interfaces – user interfaces with associated modeling and simulation tools – that enable you to simulate the propagation of sound in fluids and solids. Within the Acoustics Module, these are organized into pressure acoustics, acoustic-structure interaction, aeroacoustics, and thermoacoustics.
Acoustic simulations with the physics interfaces for pressure acoustics can easily model classic problems such as scattering, diffraction, emission, radiation, and the transmission of sound. These problems are relevant to muffler design; loudspeaker construction; sound insulation for absorbers and diffusers; the evaluation of directional acoustic patterns, like directivity; noise radiation problems; and much more. The physics interfaces for acoustic-structure interaction can model problems involving structure elastic waves and fluid-borne sound and their interaction. For example, acoustic-structure interaction is used in detailed muffler design, ultrasound piezo-actuators, sonar technology, and noise and vibration analysis of machinery in the automotive industry. Using the COMSOL Multiphysics capabilities enables you to analyze and design electroacoustic transducers, including loudspeakers, sensors, microphones, and receivers.
The physics interfaces for aeroacoustics are used to model the one-way interaction between an external flow and an acoustic field, that is, fluid-borne noise. Applications range from jet-engine noise analysis to wind sensor simulation. The physics interfaces for thermoacoustics can accurately model systems where small geometrical dimensions are present, which is relevant to the cell phone and hearing aid industries, MEMS applications, and for all of you working with transducer design.
Completely integrated in the COMSOL environment, the Acoustics Module can be combined with other modules for a wider range of multiphysics simulations. Such is the case for the physics interfaces for acoustic-shell interaction and thermoacoustic-shell interaction, which are available when combining the Acoustics Module with the Structural Mechanics Module. Similarly, the physics interfaces for pipe acoustics are available when combining the Acoustics Module with the Pipe Flow Module. There are many application areas where these physics interfaces are used – from modeling simple pressure waves in air, to examining complex interactions between elastic waves and pressure waves in porous materials.
Simulations Including Acoustic Losses
The Acoustics Module is shipped with an extensive Model Library with many examples of applications ranging from modeling sound insulation lining, loudspeakers, microphones, and mufflers. Many of these examples show how to simulate acoustic losses. The loss models of the Acoustics Module range from empirical equivalent-fluid models for fibrous materials, solving Biot's theory in the Poroelastic Waves interface, to a fully-fledged thermal and viscous loss model using the Thermoacoustics interface.
The Acoustics Module adheres to the same workflow as any other add-on module in the COMSOL Product Suite. All modeling steps are accessed from the COMSOL Desktop® and include defining the geometry, selecting materials, selecting a suitable physics interface, defining boundary and initial conditions, automatically creating the finite element mesh, solving, and visualizing the results. Acoustics Module simulations can be coupled with any other COMSOL product in just about any way imaginable by a suite of preset couplings, such as with the Structural Mechanics Module for acoustic-shell interaction, or by user-defined couplings. The Optimization Module can be combined with the Acoustics Module for optimizing geometric dimensions, acoustic transmission, and more.
Connecting the Acoustics Module with CAD, MATLAB®, and Excel®
For repetitive modeling tasks, LiveLink™ for MATLAB® makes it possible to drive COMSOL simulations with MATLAB® scripts or functions. Any operation available in the COMSOL Desktop® can alternatively be accessed through MATLAB commands. You can also blend COMSOL commands in the MATLAB environment with your existing MATLAB code. For acoustic simulations driven from spreadsheets, LiveLink™ for Excel® offers a convenient alternative to modeling from the COMSOL Desktop® with synchronization of spreadsheet data with parameters defined in the COMSOL environment. The CAD Import Module and the LiveLink™ products for leading CAD systems makes it easy to perform acoustic simulations using CAD models. The LiveLink™ products make it possible to keep the parametric CAD Model intact in its native environment but still control the geometric dimensions from within COMSOL Multiphysics. Linking your acoustics models to CAD products allows you to simultaneously perform parametric sweeps over several model parameters
Flexible and Robust Acoustics Modeling
The equations of the Acoustics Module are solved using the finite element method with higher-order element discretization in combination with state-of-the-art solvers. The different formulations cover both frequency- and time-domain simulations. Your results are presented in the graphics window through preset plots of acoustic and displacement fields, sound pressure levels, stresses and strains, or as expressions of physical quantities that you can define freely, as well as derived tabulated quantities.
Easy-to-use Physics Interfaces for Acoustics Analysis
The Pressure Acoustics physics interfaces describes and solves the sound field through a scalar acoustic pressure field. The acoustic pressure field represents the acoustic variations (or excess pressure) with respect to the ambient stationary pressure. The ambient pressure is, in the absence of flow, simply the static absolute pressure. The physics interfaces enable solving both in the frequency domain, where the Helmholtz equation is solved, and as a transient system, where the classical wave equation is solved. A special physics interface for boundary mode acoustics is used to study propagating modes in waveguides and ducts, and is based on the fact that only a finite set of shapes, or modes, can propagate over longer distances.
A large variety of boundary conditions are available and include hard walls and impedance conditions, radiation, symmetry, and periodic conditions for modeling open boundaries as well as conditions for applying sources. The interfaces also have several equivalent-fluid models, which mimic the behavior of sound propagation in more complex media like porous materials, fibrous materials, as well as viscous and thermally conducting fluids. Perfectly matched layers (PMLs) are also available to truncate the computational domain by absorbing outgoing acoustic waves, thereby mimicking an infinitely extended domain. Finally, a far-field feature can be used to determine the pressure outside the computational domain. Dedicated results and analysis capabilities are available for visualizing the far-field with polar plots in 2D and 3D.
From one side of the fluid-solid boundary, the Acoustic-Structure Interaction interfaces treat the fluid pressure that acts on the solid domain and, from the other, the structural acceleration acts on the fluid domain. The interfaces cover acoustic-solid, acoustic-shell, and acoustic-piezoelectric interactions – all within the frequency and time domains and in 3D, 2D, and 2D axisymmetric geometry models. The interfaces involving structural shells are available when combining the Acoustics Module with the Structural Mechanics Module, where you are also able to access more advanced structural modeling capabilities. The Acoustic-Piezoelectric Interaction interface not only simulates the acoustic-structure interaction with great accuracy, but also supports solving and modeling the electric field in the piezoelectric material. When combined with the AC/DC Module or MEMS Module, you can also combine piezoelectric simulations with SPICE circuits. This capability is also excellent when, for example, using lumped models to describe certain parts of a transducer while using the full finite element description for the rest. The models are fully coupled.
The Pipe Acoustics interfaces (available together with the Pipe Flow Module) are used for 1D modeling of the propagation of sound waves in flexible pipe systems. The equations are formulated in a general way to include the effects of the pipe wall compliance with the possibility of a stationary background flow. The Elastic Waves interface is a full structural-dynamics formulation that includes all the effects of shear waves and pressure waves. The Poroelastic Waves interface precisely models the propagation of sound in a porous material, including the two-way coupling between deformation of the solid matrix and the pressure waves in the saturating fluid, using Biot's theory.
Ideally, computational aeroacoustic (CAA) simulations would involve solving the fully compressible Navier-Stokes equations in the time domain. The acoustic pressure waves would then form a subset of the fluid solution. This approach is often impractical for real-world applications due to the required computational accuracy necessary, the computational time, and the memory resources. Instead, for solving many practical engineering problems, a decoupled two-step approach is used: first solve for the background mean fluid flow, then the acoustic perturbations of the flow. This very important one-way interaction of a background fluid flow with an acoustic field is also known as fluid-borne noise/sound.
The primary tool in the Acoustics Module for fluid-borne sound is the Linearized Euler physics interfaces. These are used to compute the acoustic variations to pressure, velocity, and density for a given background mean-flow. They solve for the linearized Euler equations, including the energy equation, with the assumptions that the background flow is an ideal gas (or is well-approximated by an ideal gas) and that there are no thermal or viscous losses. The Linearized Euler physics interfaces are available for time domain, frequency domain, and eigenfrequency studies. Application examples for areoacoustics with the Linearized Euler equations include analyzing the propagation of noise from jet engines, modeling the attenuation properties of mufflers in the presence of non-isothermal flow, and the study of gas flow meters. These are all situations where a gas background flow influences the propagation of acoustic waves in the fluid.
For simplified one-way interactions, formulations based on a fluid-potential, the Linearized Potential Flow physics interfaces, are also available in both the frequency and transient domains. The Compressible Potential Flow interface is used to model the background mean flow of an inviscid, compressible fluid that has no vorticity as it is irrotational by nature. The Boundary Mode Aeroacoustics interface is used to study boundary mode acoustic problems in a background flow field, typically used to specify sources at inlets.
The Acoustics Module provides state-of-the-art modeling capabilities for thermoacoustics (also known as viscothermal or thermoviscous acoustics), which is critical for accurate simulation of acoustics in geometries with small dimensions. Close to walls, viscosity and thermal conduction become important as a viscous and thermal boundary layer are created, resulting in significant losses. This makes it necessary to include thermal conduction effects and viscous losses explicitly in the governing equations. The physics interfaces for thermoacoustics are used for solving the full set of linearized compressible flow equations, that is, the linearized Navier-Stokes, continuity, and energy equations all together. Because a detailed description is needed to model thermoacoustics, all the physics interfaces simultaneously solve for the acoustic pressure, the particle velocity vector, and the acoustic temperature variation.
In the Thermoacoustics physics interface, the governing equations are implemented as a time-harmonic formulation and solved in the frequency domain. Both mechanical and thermal boundary conditions are available. Coupling the thermoacoustic domain to a pressure acoustic domain is also straightforward with a predefined boundary condition. A Thermoacoustic-Solid Interaction interface is available, and makes it easy to solve for coupled vibro-acoustics. You can, for example, use it to model small electroacoustic transducers or damping in MEMS devices. Predefined boundary conditions exist between solid and fluid domains. The Thermoacoustic-Shell Interaction interface is used for modeling the interaction between shells and acoustics in small dimensions. This is used to analyze the damped vibrations of shells in hearing aids and prevent feedback problems.
Wind Turbine Noise Reduction
Xi Engineering Consultants Ltd, Edinburgh, UK
Xi Engineering Consultants Ltd specializes in complex vibration issues, like those caused by wind turbines. The meshing of teeth within the gearbox of a wind turbine can cause great vibrations which are perceived as excessive noise. This presents a problem as there are strict regulatory standards throughout Europe and North America limiting ...
Metamaterials Make Physics Seem Like Magic
David Smith & Yaroslav Urzhumov Duke University Pratt School of Engineering Durham, NC Jeff Wilson NASA Glen Research Center, Cleveland, OH Fabio Alves and Gamani Karunasiri Naval Postgraduate ...
Metamaterials are manufactured, structured materials that they can interact and manipulate wave phenomena such that objects surrounded by metamaterials are shielded from these waves. In the case of light, metamaterials make these objects ‘invisible’. Researchers throughout the world are applying these materials to many different ...
Optimizing Ultrasound Piezo-disk Transducers
Lorenzo Spicci & Marco Cati R&D Department Esaote S.P.A. Florence, Italy
Esaote S.p.A. produces medical diagnostic systems, including the manufacturing and sales of ultrasound imaging systems. Lorenzo Spicci and Marco Cati are researching ways to improve ultrasound probes to maximize their performance, knowing a smaller, more effective machine could make this technology more accessible. They used COMSOL Multiphysics ...
Muffler with Perforates
Reflective mufflers are best suited for the low frequency range where only plane waves can propagate in the system, while dissipative mufflers with fibers are efficient in the mid-to-high frequency range. Dissipative mufflers based on flow losses, on the other hand, work also at low frequencies. A typical automotive exhaust system is a hybrid ...
The modeling of aircraft-engine noise is a central problem in the field of computational aeroacoustics. The acoustic field in a model of an axially symmetric aero-engine duct, generated by a noise source at the boundary, is computed and visualized. Results are presented for situations with as well as without a compressible irrotational ...
The sound level from a car depends to a great extent of the quality of the muffler. Over the years, researchers in the car industry have struggled to produce mufflers that are efficient from both an acoustic and an environmental perspective. This model describes the pressure wave propagation in a muffler for an internal combustion ...
Focused Ultrasound Induced Heating in Tissue Phantom
This model example shows how to model tissue heating induced by focused ultrasound. First, the stationary acoustic field in the water and the tissue are modeled to obtain the acoustic intensity distribution in the tissue. The absorbed acoustic energy is then calculated and used as the heat source for a Bioheat Transfer physics in the tissue ...
SAW Gas Sensor
A surface acoustic wave (SAW) is an acoustic wave propagating along the surface of a solid material. Its amplitude decays rapidly, often exponentially, through the depth of the material. SAWs are utilized in many kinds of electronic components, including filters, oscillators, and sensors. SAW devices typically apply electrodes to a ...
Test Bench Car Interior
Sound is generated by a point source located in the wall of this test bench car interior. The sound pressure level response at a point of measurement is investigated for a range of frequencies and four different mesh resolutions. The model is first solved with the default direct solvers. Finally, it is shown how to set up an iterative solver which ...
Acoustic Transmission Loss through Periodic Elastic Structures
In this model, two fluids are separated by a solid elastic structure. An acoustic pressure wave impacts the structure resulting in a reflected wave and a wave transmitted with a loss through the structure. This model investigates the transmission loss through the structure. The effects of incident angle, frequency, and dampings are studied. ...
Probe Tube Microphone, Transient Model
It is often not possible to insert a normal microphone directly into the sound field being measured. The microphone may be too big to fit inside the measured system, such as for in-the-ear measurements for hearing aid fitting. The size of the microphone may also be too large compared to the wavelength, so that it disturbs the acoustic field. In ...