# Acoustics: Bringing lightweight construction and NVH into harmony

You can hear quality. Most people associate the quality of devices, machines or vehicles with their acoustics. How does the engine sound when accelerating? Especially when it comes to engine noise, acoustics or acoustic feedback is desirable or even perceived as a quality feature. Vibro-acoustic properties of vehicles have gained in significance in recent years and play a central role in the customer’s purchasing decision.

Typically, however, noise and vibration phenomena inside the vehicle are perceived as disturbing.

In this context, it is becoming increasingly important to evaluate and influence vibroacoustic behavior at an early stage of vehicle development.

At the same time, a clear trend towards high-strength steel and lightweight construction can be observed in the automotive industry. The aim of lightweight design concepts is to reduce the energy consumption of vehicles and thus ensure that the exhaust emission regulations prescribed by the EU are complied with. However, the use of lighter materials also has a considerable influence on the vibro-acoustic behaviour of the vehicle, as the resulting vibrations are less reduced by the lighter structure. A central question is therefore how lightweight construction can be reconciled with NVH (noise, vibration, harshness).

##### How can vibroacoustic behaviour be predicted? Possibilities and limits.

**FEM, BEM & SEA**

To determine this usually requires very complex acoustic models.

Numerical methods such as the Finite Element Method (FEM) or the Boundary Element Method (BEM) are widely used to predict vibroacoustic behavior at low to medium frequencies or in the time domain.

For higher frequencies as well as for large and complex technical systems, the wavelength is short compared to the overall system under consideration. The density of the eigenmodes also increases considerably. In order to be used effectively, FEM requires a high number of finite elements in this case, which increases the calculation costs.

Lower costs can be achieved by using the BEM. 3D structures are reduced to 2D surface models and thus simplified. A big shortcoming, however, is the reduced scope of possible numerical solutions due to the strong simplification. In addition, both FEM and BEM can react extremely sensitively to parameter deviations. Therefore, statistical methods such as Statistical Energy Analysis (SEA) are mainly used for simulations in the high frequency range.

For SEA, a system is divided into several coupled subsystems and the acoustic behavior of each individual subsystem is described by a defined number of equations. Although the number of equations to be solved in the SEA is comparatively small, the corresponding models cannot be derived directly from the CAD data and modelling requires a high level of application-specific expertise. In addition, the SEA does not provide any information on spatial energy distribution and therefore effects such as damping or structural excitation cannot be described locally.

**EFEM – Calculation based on energy density**

As an alternative approach, the Energy Flow Analysis (EFA) was developed, which describes the energy distribution with regard to the average area energy density. The central energy balance of the EFA was subsequently transformed into a partial differential equation in which a similarity of the propagation of acoustic energy to heat conduction is exploited. On this basis, the energy density can now be calculated using existing FEM methods – the EFA becomes the Energy-Based Finite Element Method (EFEM).

While conventional FEM is based on displacements, EFEM is based on time- and location-averaged energy densities. Thus, calculations can also be performed in the higher frequency range with a relatively high accuracy. Due to the low discretization effort it is possible to simulate even large and complex structures such as complete vehicles or ships and still consider local effects.

In contrast to the SEA, it is not necessary with the EFEM to limit the attenuation between the subsystems and the coupling strength when defining the subsystems. This makes it possible to perform detailed analyses, for example for the precise definition of external loads, the consideration of arbitrarily distributed attenuation or the analysis of frequency-dependent and spatially distributed results.

The underlying energy equations are set up on an element basis analogous to FEM. Since these elements or subsystems are significantly smaller than in the SEA, they allow a finer modelling as well as a more detailed prediction of the energy flows and distributions within the structure to be investigated. Due to the energy-based approach, however, a much coarser discretization is possible compared to conventional FEM/BEM, so that larger structures can also be investigated in the high-frequency range. Various application examples with promising results show the great potential of EFEM for the analysis of large structures.

EFEM reaches its limits when calculating very small components. Basically, the shortest distance of the considered component should be at least 2.47 times the wavelength in order to achieve a reliable result. If smaller components are treated as part of a larger structure, a model deviating from the EFEM standard must be used.

##### Would you like to learn more about EFEM or other options for calculating technical systems?

In the fields of vibration engineering, flow, electromagnetics and especially acoustics we work together with our partner Novicos. With the development of multiphysical concepts and models for vibration reduction, through extensive measurements and the creation of computer-aided simulations of complex processes, we support our customers in a wide variety of industries.

We are also happy to arrange a non-binding consultation appointment or a telephone consultation.

Phone: +49 (0)7321 9343-0

E-mail: info@merkle-partner.de

Of course you can also have a look at our website:

www.merkle-partner.de

PS: We would like to thank Novicos for their content contribution to this newsletter.