Natural frequency analysis is one of the most useful applications in FEA. It is commonly used in relation to modal analysis in structural mechanics. Acoustics simulation based on natural frequency analysis for complex geometries can provide engineers with essential information about the free vibration of an object or the acoustic behavior of a structure.
What is Acoustics Simulation?
The mathematical basis of modal analysis in acoustics is eigensystem algorithms, which allows the physical interpretation of the corresponding mode shapes offered by eigenvalues (characteristic values) associated as scalars with an eigenvector (characteristic vector of a square matrix). In many structural analyses, the only desired modes are the lowest natural frequencies.
In a simplified definition, the modal analysis can be described through a comparison with frequency analysis, where a complex signal is resolved into a set of simple waves with individual frequencies and amplitude parameters. In a modal analysis, however, a complex deflection pattern (usually from a vibrating structure) is resolved into a set of simple mode shapes with individual frequencies and damping parameters .
For many reasons, vibration analysis of mechanical structures is a very important subject within modal analysis because eigenvalues are closely related to the natural frequencies (eigenfrequencies) of vibration and eigenvectors to the shapes of vibration modes.
The most important applications of modal analyses are related to computer simulations. In mechanical engineering simulation, a good approximation model of the natural frequency behavior is a critical element of the best performance analysis of any prototype project related to a component, product ensemble, or mechanical structure. Different simulation scenarios allow the vibration response of the structure to be modeled when multiple excitation forces are applied.
Iterative simulation could provide engineers with alternative answers related to model behavior after every physical modification of modal parameters (such as geometry, mass dampers, materials, or stiffness). The predicted response, when converted into noise, strain, or fatigue effects, could be compared with established standards and design criteria, which leads to the implementation of further improvements to reach the desired model.
Using simulation to get a better understanding of natural vibration modes and have the ability to consistently predict possible failure modes are essential for an effective product manufacturing workflow. It significantly reduces the costs associated with physical model testing, improves the quality of the product and reduces the product’s overall time to the market.
Acoustics Analysis with SimScale
The SimScale 3D simulation platform is a web-based environment providing powerful end-to-end simulation solutions for a whole set of engineering analyses, like structural mechanics, fluid dynamics, thermodynamics analyses. Structural mechanics simulations performed with SimScale are based on a comprehensive set of static and dynamic analysis capabilities for investigating phenomena related to structural mechanics, including acoustic simulations based on acoustic eigenfrequency analysis.
The finite element-based solver integrated by SimScale give engineers the possibility to use multiple natural frequency analysis for complex geometries. The visual images of eigenmodes and eigenfrequencies provide optimum models related to the acoustic behavior of a structure.
Acoustics Simulation in the Automotive Industry
The automotive industry depends on modal and frequency analysis to determine the influence of acoustics and vibration on their structures.
One example to consider is the acoustic simulation of a car cabin. This simulation illustrates the acoustic eigenfrequencies of a car cabin and the corresponding bounding box. It can be downloaded as a public template from the SimScale Public Projects Library.
If you are interested in this project, make a copy and follow the complete step-by-step tutorial for car cabin acoustic natural frequencies found in the SimScale documentation.
To discover all the simulation features provided by SimScale, download the document below.
- Ole Døssing– “Structural Testing, Part II: Modal Analysis and Simulation”, Brüel Kjær, 1988.