People pursue engineering for various reasons – an interest in math and precision, creating things of significance or something else entirely – but one common thread they all share is an ambition to shape society for the better.
FE and BE models may not always be viable solutions in mid-frequency range, which has resulted in various new methods being developed to fill this void.
Finite Element Method (FEM)
The Finite Element Method (FEM) is a computational technique used in engineering and mathematical modeling that relies on computer software to solve differential equations that arise during engineering projects or mathematical models. Once the results of such complex issues have been obtained, they are then assembled into larger systems of equations representing them; FEM solutions often arise during structural analyses, while high-speed supercomputers may be necessary in performing calculations with this approach.
FEM models are created by creating small units of geometry called elements and assigning each an element-specific material property set that reflects its behavior; in acoustics applications these properties may also be used to calculate vibration and noise produced by the system.
These elements are combined into an extensive system of equations to represent the problem at the structural-acoustic interface, and their solutions approximated via calculus of variations – an extremely powerful technique used to predict vehicle response.
FEM models can be enhanced for special cases of interest by employing advanced techniques, such as discontinuity handling. This is achieved by expanding element shape functions with Heaviside step functions and adding extra degrees of freedom to account for discontinuities and jumps – this enables FEM models to handle more complex problems than would otherwise be possible with traditional Bubnov-Galerkin methods.
Crystal Plasticity Finite Element Method (CPFEM) is another advanced technique, using finite elements (FE) to simulate deformations in anisotropic materials. This tool has been utilized extensively when studying fracture mechanics of metals and other materials.
Engineering Vibroacoustic Analysis: Methods and Applications also details newer techniques, such as hybrid FE/SEA, TPA hybridization, EFEA analysis and wave-based structural modeling. Each chapter covers modeling, computational and application considerations of each method as well as procedures for noise and vibration control treatments and optimizing structures to reduce vibroacoustic emissions – an indispensable resource for those interested in modeling structural-acoustic systems analysis.
Statistical Energy Analysis (SEA)
SEA method is an efficient, fast method that applies to structural vibrations and acoustics across a broad frequency range. Based on energy conservation principles, all mechanical or acoustic excitation introduced into a system must leave through damping or radiation; when used with statistical systems with multiple input sources (point forces or sound), modal response quantities such as pressure and velocity are expressed as average of mean square response quantities at each point; these figures are then added together to find power balance across subsystems which is then expressed as power balance matrix as shown in Figure 1 (see Figure 1).
The SEA method can be applied to airborne and structure-borne systems alike. Furthermore, its applicability to high frequency regions where deterministic methods fail can make this an invaluable method. Coupled with wave-based methodologies like FEM or BEM hybrid methods are able to offer both microscopic and macroscopic insights into complex structure dynamics.
Modal Analysis (MA)
Modal analysis is an experimental technique for gathering modal data from structures. Mechanical excitation forces are applied, and response vibrations (usually accelerations) are measured. FRF data should ideally be obtained at multiple points/directions within the structure in order to accurately reflect its behavior and accurately identify modal parameters such as natural frequencies, damping coefficients and mode shapes. However, due to the nature of modal testing it may be necessary to interpolate measurements in order to create an accurate representation of a structure’s geometry. Engineering judgment should be used when deciding how many measurement points will suffice in this instance.
Engineers use modal data to assess resonant behavior of structures by identifying their natural frequencies and modes. Once known, Engineers can compare them against potential excitation frequencies that a structure could experience during operation – any natural frequencies close to an operating frequency could cause excessive vibration which poses either safety or reliability risks for that structure.
Modal analysis serves as the foundation for conducting coupled vibroacoustic simulations, which enable engineers to predict how resonating modes will influence sound pressure levels at various locations within a structure. This information is especially beneficial when designing structures to meet requirements for structural-acoustic performance such as those enforced by automotive industries or consumer electronics to ensure products operate quietly while remaining comfortable for users.
Typically, the modal approach is best utilized when structures exhibit significant nonlinear behavior or require an accurate acoustic model. Meanwhile, FEA methods tend to be better for structures that exhibit more linear behaviors and do not necessitate detailed modeling of the acoustic wave field – these models can often be simplified in order to save computational time and runtime costs.
Nonlinear Finite Element Method (NFEM)
The finite element method (FEM) is an engineering analysis tool that uses computer simulation to model complex physical problems. It solves partial differential equations that describe solids and fluids’ behavior – including heat transfer, fluid mechanics, structural elasticity and electromagnetics. FEM has proven useful for designing aircraft, cars, bridges, ships, buildings as well as scientific modeling of medical diagnoses/surgery planning as well as additive manufacturing applications.
FEM has revolutionized how we design and engineer materials, yet requires significant computational resources and time for large systems. High-performance computing can be utilized to speed up simulation process while increasing accuracy.
There are various FEM models, from linear to nonlinear. Nonlinear FEM models are often used for modal analysis and vibration, yet are less efficient than their linear counterparts due to requiring many elements and iterations – ultimately becoming more costly to operate than linear methods.
Emerging FEM techniques have emerged to address these concerns, with one approach known as the spectral element formulation approach being particularly successful at doing so. It uses convex quadrilateral elements arranged overlapping together that represent structures to predict acoustic response with less elements than conventional FEM models, making this an efficient method for rod and beam structures.
Another promising approach is the DG-FEM method, which combines features of FEM with discretizations of structural domain and fields. Furthermore, this technique can solve hyperbolic equations that are typically difficult to solve using standard FEM algorithms – making this an effective approach to modeling acoustic and elastic wave phenomena in two and three dimensional structures.
Another key benefit of DG-FEM is its ability to accurately represent acoustic waves and predict their behavior. Studies have demonstrated that DG-FEM models provide comparable or even superior acoustic eigenfrequencies than comparable FEM solutions while their analysis and matrix construction times are typically shorter, further increasing efficiency.