A novel hybrid FS‐FEM/SEA for the analysis of vibro‐acoustic problems

Abstract

SUMMARYPredicting the frequency response of a complex vibro-acoustic system becomes extremely difficult in the mid-frequency regime. In this work, a novel hybrid face-based smoothed finite element method/ statistical energy analysis (FS-FEM/SEA) method is proposed, aiming to further improve the accuracy of 'mid-frequency' predictions. According to this approach, the whole vibro-acoustic system is divided into a combination of a plate subsystem with statistical behaviour and an acoustic cavity subsystem with deterministic behaviour. The plate subsystem is treated using the recently developed FS-FEM, and the cavity subsystem is dealt with using the SEA. These two different types of subsystems can be coupled and interacted through the so-called diffuse field reciprocity relation. The ensemble average response of the system is calculated, and the uncertainty is confined and treated in the SEA subsystems. The use of FS-FEM 'softens' the well-known 'overly stiff' behaviour in the standard FEM and reduces the inherent numerical dispersion error. The proposed FS-FEM/SEA approach is verified and its features are examined by various numerical examples.

Acoustic radiation from a sphere pulsating near an impedance plane using a boundary integral equation method

“…The vibration and acoustic responses agree well with those by the coupled FEM–BEM approach. Furthermore, Wu et al [36] introduced a novel hybrid face-based smoothed finite element method/statistical energy analysis (FS-FEM/SEA) method to study mid-frequency vibro-acoustic problems. In their approach, structure was treated using FS-FEM, while acoustic problem was solved using the SEA.…”

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

“…A solution to this problem, the smoothed finite element method (S‐FEM) based on generalized smoothed Galerkin (GS‐Galerkin) weak form, was proposed by Liu et al 26‐29 The strain smoothing technique 30 is used to convert the element‐based calculations of standard FEM into different smoothing domain calculations. According to the way to construct smooth domains in element, smoothed finite elements are classified into node‐based smoothed FEM (NS‐FEM), 31‐38 Cell‐based smoothed FEM (CS‐FEM), 39‐43 edge‐based smoothed FEM (ES‐FEM), 44‐49 and face‐based smoothed FEM (FS‐FEM), 50‐53 etc. A large number of numerical experiments show that ES‐FEM and FS‐FEM have excellent h‐convergence characteristics, accuracy and temporal and spatial stability, which can greatly improve the performance of tetrahedral elements 53 .…”

Virtual decoupling of vibroacoustical systems

“…Second, compared with the structural dynamics, the vibroacoustical system behavior has more challenging characteristics: 1) The value of acoustical response is several orders of magnitude larger than the structural response, implying that the system response is quite sensitive to the noise; 2) The coupling between the acoustic and structural parts as well as the damping terms [16,17] of the system are more complex and more difficult to be correctly represented; 3) Hard-to-control factors (e.g. sealing effectiveness and microphone sensitivity) lead the vibroacoustical experiment operationally more complex than the traditional structural experiments, introducing more noise in the measurement [18]. These difficulties hinder the properness enforcement method from providing precise results, especially in complex cases such as strong coupling or closed modes in given frequency range.…”