Increasing Computational Efficiency with the EFEA Method

This guest contribution on Innovation Intelligence is written by Nickolas Vlahopoulos, CTO of Michigan Engineering Services (MES). EFEA software by MES is a solver that performs analysis for mid- to high-frequency and acoustic simulations for complex structural-acoustic systems. EFEA is available through the Altair Partner Alliance.

The Energy Finite Element Analysis (EFEA) has been developed and utilized for simulating the vibro-acoustic behavior of complex systems in the mid to high frequency range where conventional finite element computations are no longer efficient or even feasible. The EFEA software was originally developed by MES in 2006 under the Small Business Innovative Research (SBIR) program of the US Navy. Since then it has been applied in aircraft and automotive applications.

A summary of EFEA models from different Industries is presented below.

The Figure below shows the difference in the discretization between a conventional Finite Element Analysis (FEA) model for a vehicle and an EFEA model for the same vehicle.

FEA methods solve differential equations for which the fundamental solutions vary harmonically with space, thus, the wavelength becomes smaller as the frequency increases, requiring a prohibitively large number of elements and computational resources. In the EFEA method, the governing differential equations are formulated for an energy variable that has been spatially averaged over a wavelength and time averaged over a period. Differential equations are derived for all wave bearing domains within a system. Each differential equation represents a power balance over a control volume. The corresponding fundamental solutions vary exponentially with space, thus requiring only a small number of elements to capture numerically the smooth spatial variation. This feature allows large, complex systems to be analyzed with a small number of elements and in a short enough time that can influence the design cycle. The figure below presents the fundamental solutions and typical numerical discretizations for FEA and EFEA.

Joint matrices are required between the finite elements at locations where discontinuities in the primary EFEA variables exist. These discontinuities can originate from the geometry, from a change in material properties, from multiple components being connected together, or from different media interfacing with each other. The EFEA elements at the discontinuities are physically disconnected so that adjacent elements have duplicate nodes at the joints.   In this manner it is possible for the EFEA primary variables to acquire different values across the discontinuity in the numerical model, as dictated by the physics. The joint matrices provide the connection mechanism and describe the power transfer between the disconnected finite elements. The figure below presents how elements and joint matrices are combined for generating a numerical model.

In automotive applications the EFEA is suitable for conducting airborne computations. The exterior acoustic field created from noise sources such as engine, transmission, tires, etc., comprises the excitation that creates the airborne noise in the interior cabin of a vehicle. It is of interest to use simulation for evaluating the transfer function (i.e. noise reduction) between the external acoustic sources and the interior noise level. Such capability will allow identifying the effectiveness of different noise mitigation strategies for increasing the noise reduction for the least possible weight increase. Panel contribution information is very useful in such an effort, because it allows mapping over the surface of the structural-acoustic interface the acoustic power flow in the interior acoustic space.

The physical characteristics of the vehicle are used for constructing the EFEA model (figure below). Specifically, the structural components of the vehicle, the asphalt coating and the constraint layer damping which are applied on certain panels, the mass barrier type of materials, the acoustic treatment, the acoustic absorption associated with the seats, and all internal air cavities (main compartment, console, side doors, etc.) comprise the EFEA model. In this example an EFEA vehicle model with approximately 41,000 elements is used for analysis in the frequency range 200Hz – 8,000Hz.

EFEA structural (left); and acoustic (right) vehicle models

As representative, the acoustic loading on the exterior of the vehicle from the engine source is presented at a particular frequency in the figure below. The exterior acoustic loading is higher closer to the source and reduces on panels which are shielded from the source. In this figure the front part of the vehicle is removed in order for the acoustic loading to be visible in the dash panel area where the loading is high.

The interior noise level can be computed. For this example the difference between simulation and experiment is presented below for the noise at the driver’s ear location. The frequency averaged absolute value of the difference over the frequency range of 200Hz – 8,000Hz is 1.6dB, which represents very good agreement. For an analysis similar to the one discussed here, the computations over the entire frequency range are completed within a couple of hours on a desktop workstation.

Further, a panel contribution analysis identifies the main panels that transmit the acoustic power in the interior of the vehicle. The figure below on the left presents a plot over the acoustic part of the EFEA model, of the acoustic power entering the acoustic domain from its interface with the structural elements. This type of information can be used to identify the most important panels and the relative amount of power entering the acoustic domain from each panel. The ranking of the panels is presented on the right side of the figure below.

Now that the panels transmitting the most acoustic power in the interior of the vehicle have been identified, alternative designs can be evaluated for noise reduction. The results offered by EFEA can be visualized by any post-processor, thus the method fits perfectly in any design process for developing efficient noise-mitigation strategies. EFEA has many applications and has been applied and validated in naval, automotive and aircraft industries. To learn more about EFEA and Michigan Engineering Services (MES) click here.

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