## Modal superposition in vibro-acoustics

Introduction Last time, we introduced the fundamentals of vibroacoustics, providing a detailed explanation of fluid-structure interaction (FSI). We demonstrated how the final system is represented as a combination of individual subsystem matrices, augmented by various coupling terms. A significant challenge arises when the size of such a system expands, leading to excessively high computational times […]

## Introduction to Vibroacoustic Simulation

Introduction Vibroacoustics is an interdisciplinary domain that deals with the interaction between mechanical vibrations and acoustic waves. As computational methods gain importance in predicting and controlling noise and vibration, computational vibroacoustics has become a cornerstone for engineers and researchers. In this article we are going to understand how the coupling between the equations is handled.

## Acoustic simulation of a Muffler

Introduction Mufflers play a crucial role in reducing the noise generated by internal combustion engines and other machinery. The study of acoustic simulation in mufflers offers valuable insights into their performance and effectiveness. In this article, we will show how open-source software, in 2023, allows to simulate any “real-world” system. How mufflers work The effect

## Locally-Conformal Perfectly Matched Layer implementation in FEniCSx

Introduction Locally conformal perfectly matched layers (LC-PML) are an essential technique in computational acoustics and wave propagation simulations in general. They are designed to efficiently absorb outgoing waves and prevent unwanted reflections at the boundaries of computational domains. In this article, we will explore the implementation of LC-PML in FEniCSx, and discuss its advantages and

## Automotive cabin: application of Acoustic Modal Analysis

Introduction After a lot of mathematics and python coding, you could wonder if there are limitation to the capabilities of what has been developed in the previous articles. Starting from the finite element formulation applied on the Helmholtz equation, the full working code for Direct Frequency Response, Modal Analysis and Modal Superposition have been described. Such

## Modal Superposition in Acoustic Cavities

Introduction The last time a modal analysis has been performed on a parallepipedic cavity and all the modal shapes have been computed up to the desired frequency. The coincidence between (some) of the eigenfrequencies and the peaks in the sound pressure spectrum has been highlighted. While modal analysis itself is a good tool to investigate

## Introduction to Acoustic Modal Analysis

Introduction In previous articles, starting from the Helmholtz equation, the corresponding weak form and the related algebraic system of equation have been shown, then the system has been directly solved. Such an approach is usually called, in commercial softwares, “Direct Frequency Response Analysis” or something similar. If someone of you is familiar with Nastran, it corresponds to

## Sound propagation in 3D cavities

Introduction Hello everyone! In the last articles the way a FEniCSx code has to be written in order to perform an acoustic simulation has been explored. The 2D case was intended to be simple while keeping the simulation set up as close to a real case as possible. From now the focus will be on acoustic simulation and

## Acoustic boundary conditions: implementation in FEniCSx

Introduction In the last (and first) article we talked about the Helmholtz equation and its implementation in FEniCSx for the solution of a point source propagating in a square 2D room. In that case no boundary conditions were specified, making the walls automatically rigid (that is, the natural boundary condition for the acoustic Helmholtz equaition).

## 2D Helmholtz equation with FEniCSx: point source in a square room

Introduction This is the first article of a long series. My goal is to explain the process of performing a full aero-vibro-acoustic simulation on a real system, of industrial interest. This is what I currently do in my daily job, in which I use commercial software (coming from Siemens, ANSYS, MSC). Since these softwares don’t

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