Predicting vibration transmission across junctions using diffuse field reciprocity

2021 ◽  
Vol 263 (6) ◽  
pp. 722-733
Author(s):  
Wannes Stalmans ◽  
Cédric Van hoorickx ◽  
Edwin Reynders
Keyword(s):  
Dynamic Stiffness ◽  
Element Model ◽  
Complex Problem ◽  
Sound Insulation ◽  
Engineering System ◽  
Elastic Plates ◽  
Perfectly Matched Layers ◽  
Vibration Transmission ◽  
Stiffness Matrices ◽  
Field Dynamic

Predicting the sound insulation of an engineering system is a complex problem since not only the direct path through a separating element but also the flanking transmission paths can largely influence the sound insulation of the system. When conventionally analyzing flanking transmission, a diffuse field is assumed in the walls and floors, which are modelled as plates. The junction connecting the walls and floors is assumed to be of infinite extent and the transmission of vibration across the junction is calculated by integrating over all possible angles of incidence. Due to the limitations of the conventional approach, a new approach based on diffuse field reciprocity is proposed. The diffuse field reciprocity relationship relates the vibration transmission to the direct field of a diffuse subsystem to the direct field dynamic stiffness of the subsystem, i.e., the dynamic stiffness of the equivalent infinite subsystem as observed at the junction. The direct field dynamic stiffness matrices of thin, isotropic, elastic plates can be analytically derived. For more complex walls or floors a possible approach is to calculate the direct field dynamic stiffness using finite elements and perfectly matched layers. The perfectly matched layer surrounding the finite element model absorbs the wave propagating outwards from the bounded domain, thus simulating an infinite subsystem.

Power balance analysis of nonperiodic structural components from a model converted from FEM to SEA.

2021 ◽  
Vol 263 (2) ◽  
pp. 4672-4682
Author(s):  
Mathias Hinz ◽  
Júlio Apolinário Cordioli ◽  
Luca Alimonti ◽  
Bryce Gardner
Keyword(s):  
Power Flow ◽  
Matrix Theory ◽  
Dynamic Stiffness ◽  
Power Balance ◽  
Fem Model ◽  
Monte Carlo Techniques ◽  
Stiffness Matrices ◽  
Balance Analysis ◽  
Field Dynamic ◽  
Complex Construction

Using Statistical Energy Analysis (SEA) to characterize the power flow within a vibroacoustic system is a challenging task when the subsystems have irregular shape and complex construction. Retrieving analytical solutions for the ordinary SEA parameters is nearly impractical without restricting simplifications and periodicity is usually not exploitable due to the lack of repetition patterns. A promising option to perform the power balance for such cases is to filter part of the information contained in a Finite Element Method (FEM) model of the system, in order to convert it into a SEA model. In this paper, the Lorentzian Frequency Average and the Nonparametric Random Matrix Theory are applied to randomize the dynamic stiffness matrix of the FEM components from a system of industrial application. The obtained direct field dynamic stiffness matrices are employed along the diffuse field reciprocity relationship as a general framework to determine the energetic content of each component. The results obtained with this procedure are evaluated against the ones from classical SEA and Monte Carlo techniques.

scholarly journals Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1703
Author(s):  
Michael Coja ◽  
Leif Kari
Keyword(s):  
Natural Rubber ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Complex Problem ◽  
Wide Frequency Range ◽  
Vibration Isolators ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Frequency Magnitude ◽  
Good Agreement

A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag–Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.

Non-Linear Analysis and Modeling of the Structure with Bolted Joints

2015 ◽  
Vol 656-657 ◽  
pp. 694-699
Author(s):  
Xin Liao ◽  
Jian Run Zhang ◽  
Dong Lu
Keyword(s):  
Dynamic Stiffness ◽  
Element Model ◽  
Outer Radius ◽  
Bolted Joints ◽  
Structure Model ◽  
Test Results ◽  
Bolted Joint ◽  
Joint Structure ◽  
Non Linear ◽  
Simulation Results

In this study, a non-linear finite element model for a simplified single-bolted joint structure model is built. Static analysis on the structure under different shear force and pretension effect is done, and the non-linear contact behavior is analyzed. Through comparing datum, it is found that interface area of each bolted joint region can be described an annular region around bolt hole, whose outer radius has increased by 85% compared with radius of bolt hole. Also, the frequency responses of the multi-bolted joint structure under sinusoidal excitation are investigated. Simulation results show that the resonance regions basically remain unchanged in different pretension effect and the largest amplitude will increase with the increasing preloads. Finally, the vibration experiments are conducted. Interface nonlinear affect dynamic stiffness considerably. The test results illustrate that dynamic behaviors of bolted joint agree with the simulation results and the proposed non-linear contact model was reasonable.

scholarly journals Characteristic Constraint Modes for Component Mode Synthesis

1999 ◽  
Author(s):  
Matthew P. Castanier ◽  
Yung-Chang Tan ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Cantilever Plate ◽  
Vibration Transmission ◽  
Stiffness Matrices ◽  
Physical Insight ◽  
Insight Into

Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.

Manufacturing Error Detection in Plate and Cylindrical Composite Structures

2020 ◽  
Author(s):  
Cihan Talebi ◽  
Bülent Acar ◽  
Gökhan O. Özgen
Keyword(s):  
Error Detection ◽  
Composite Structure ◽  
Composite Structures ◽  
Dynamic Properties ◽  
Dynamic Stiffness ◽  
Element Model ◽  
Mode Shapes ◽  
Fiber System ◽  
Error Identification ◽  
Manufacturing Error

Abstract Due to their superior weight to strength ratio of composites to common metallic structures, composite technology is widely used in aerospace industry. Assessment of damage in composites has gained interest after a large number of accidents caused by unanticipated damages in the composite structures. Many different structural health monitoring applications were developed over the years due to the fact that composite materials may inherit damage from within, not always visible from surface. The most common types of errors encountered in the industry are due to misaligned fibers, a mix-up in ply order, and delaminations: all presenting changes in the vibro-acoustical performance of the composite structure. This paper discusses the change in the dynamic properties of a composite structure contains a manufacturing error such as a ply lay-up error, and a ply angle error. Both plate and cylindrical structure types were considered for the stated error types. Effect of symmetric errors, unsymmetrical and unbalanced errors, and mid-plane errors were considered in the case of ply orientations, and dynamic stiffness matrix was used to identify the error. Identification of the structure’s layup properties and manufacturing error identification is employed. From the measured modal properties of the structure, a back-tracking strategy was used to generate the ply lay-up of the composite structure. Prepreg plates of a single carbon fiber system and filament wound hybrid cylinders consisting of glass and carbon fibers were manufactured for testing. Modal tests on plates and cylindrical composite structures were performed and compared with the analysis. A good match between the finite element model and experiment was shown in natural frequencies and mode shapes.

Application of a FRF Based Model Updating Technique for the Validation of Finite Element Models of Components of the Automotive Industry

1995 ◽  
Author(s):  
Stefan Lammens ◽  
Marc Brughmans ◽  
Jan Leuridan ◽  
Ward Heylen ◽  
Paul Sas
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Automotive Industry ◽  
Stiffness Matrix ◽  
Model Updating ◽  
Dynamic Stiffness ◽  
Element Model ◽  
Model Parameters ◽  
Finite Element Models ◽  
Analytical Dynamic

Abstract This paper presents two applications of the RADSER model updating technique (Lammens et al. (1995) and Larsson (1992)). The RADSER technique updates finite element model parameters by solution of a linearised set of equations that optimise the Reduced Analytical Dynamic Stiffness matrix based on Experimental Receptances. The first application deals with the identification of the dynamic characteristics of rubber mounts. The second application validates a coarse finite element model of a subframe of a Volvo 480.

Sound insulation of timber hollow box floors: Collection of laboratory measurement data and trend analysis

2020 ◽  
pp. 1351010X2096615
Author(s):  
Anders Homb ◽  
Simone Conta ◽  
Christoph Geyer ◽  
Niko Kumer
Keyword(s):  
Unit Area ◽  
Dynamic Stiffness ◽  
Measurement Data ◽  
Sound Insulation ◽  
Frequency Dependent ◽  
Long Span ◽  
Wide Range ◽  
Application Data ◽  
Cavity Filling ◽  
Single Number

The industrialisation of timber buildings has improved strongly in recent years. When long span is required, timber hollow-box floor elements are increasingly used due to their structural performance. The aim of this paper is to assess the acoustic performance of timber hollow-box floors, determine the governing parameters and identify the corresponding trends. We collected results from laboratory measurements covering both airborne and impact sound insulation from four different laboratories covering a wide range of application. Data include the bare floor constructions and their combination with different floating floors including both lightweight solutions and hybrid solution. We performed the analysis focusing on following parameters: element stiffness, element mass per unit area, dynamic stiffness of the resilient layer, cavity filling and floating floor material. We present the collected data both frequency-dependent and as single number quantities. General trends and features are identified in the frequency-dependent diagrams. A further detailed analysis is based on the single number quantities. It includes a general relationship between element mass per unit area and given requirements for R’W + C50-5000 and L’n,w + CI,50-2500. Furthermore, diagrams are presented illustrating the dependence of impact sound insulation numbers on the cavity filling, the dynamic stiffness of the resilient layer and the type of material used for the floating floor. The additional mass in the cavity improves both airborne and impact sound insulation by minimum 10 dB. This, combined with a floating floor, allows the fulfilment of a wide range of requirements.

Research on Sound Insulation Performance of Poroelastic Material in Complex Structure

2018 ◽  
Vol 911 ◽  
pp. 56-60
Author(s):  
Jun Zhang ◽  
Yi Hang Yu ◽  
Wen Zhong Zhao
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Transmission Loss ◽  
Complex Structure ◽  
Element Model ◽  
Acoustic Vibration ◽  
Acoustic Power ◽  
Sound Insulation ◽  
Poroelastic Materials ◽  
Flow Resistivity

A finite element model of the double-wall acoustic insulation structure with a air layer and an acoustic absorbent layer made of the poroelastic materials is set up, the responses of this acoustic-vibration system are calculated by using of the direct finite element method when having a diffuse incident acoustic field acting on the incident surface, the radiant acoustic power from the another surface are achieved, then the Transmission Loss(TL) are formulated using the incident acoustic power and the radiant acoustic power. The effects of the thicknesses, elastic modulus, flow resistivity and viscous lengths of the poroelastic materials on TL are analyzed. The results show that the thicknesses and elastic modulus have a significant effects on TL, TL are enhanced with the thicknesses increasing of the poroelastic materials layers, a 4.9dB addition of TL is achieved when thickness is added from 2cm to 3cm; TL are enhanced with the reduction of the elastic modulus in considered frequency range, and TL are reduced with the declining of viscous lengths and with the addition of the flow resistivity when the frequencies are higher than 600Hz.

A New Finding on the Dynamic Stiffness Matrices of Asymmetric and Axisymmetric Shafts

2001 ◽  
Author(s):  
Francesco A. Raffa ◽  
Furio Vatta
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Rotational Inertia ◽  
Dynamic Stiffness Matrix ◽  
Rayleigh Beam ◽  
Principal Moments Of Inertia ◽  
Stiffness Matrices ◽  
New Finding

Abstract In this paper the dynamic stiffness method is developed to analyze a rotating asymmetric shaft, i.e. a shaft whose transverse section is characterized by dissimilar principal moments of inertia. The shaft is modeled according to the Rayleigh beam theory including the effects of both translational and rotational inertia, and gyroscopic moments. The mathematical description is carried out in a reference system rotating at the shaft speed and is based on the exact solution of the governing differential equations of motion. The exact expressions of the shaft displacements are utilized for deriving the 8 × 8 complex dynamic stiffness matrix of the shaft. A new relationship is obtained which links the dynamic stiffness matrix of the asymmetric shaft to the 4 × 4 real dynamic stiffness matrix of the axisymmetric shaft.

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