Structure-borne sound transmission through plate junctions and estimates of sea coupling loss factors using the finite element method

doi:10.1016/0022-460X(91)90745-6

Journal of Sound and Vibration

Volume 144, Issue 2, 22 January 1991, Pages 215-227

https://doi.org/10.1016/0022-460X(91)90745-6 Get rights and content

Abstract

The finite element method (FEM) is used to calculate the vibrational energies of plates forming L- and H-structures at discrete frequencies between 10 and 2000 Hz, where one plate is excited by a point force and the power is transmitted through the junction to the other plates. The energies can be used to characterize the transmission of structure-borne sound through that junction. The results agree very well with the results from measurements and classical theoretical methods. It is observed that the displacements predicted by FEM at individual positions and frequencies are not reliable, because both the discretized model and the discrepancies between the real and the modelled plate properties and boundary conditions shift the mode shapes and the eigenfrequencies. The average energy of a plate, derived from the squared and spatially averaged displacements in a frequency band, is easier to interpret and generally more accurate than the predicted displacements at individual positions and frequencies. The coupling loss factor of a junction can be derived from such averaged energies of the plates that form the junction. The coupling loss factor characterizes the specific type of junction that is analyzed and it can be applied in statistical energy analyses (SEA) of structures with the same type of junction.

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The average vibro-acoustic performance of a junction between two-dimensional structural elements is often quantified by its diffuse vibration reduction index, especially for building structures. Existing prediction methods either assume an infinite junction length or consider non-diffuse transmission. In this work an approach for predicting the diffuse vibration reduction index of finite junctions of arbitrary complexity is developed. First, the mean and (co)variance of the diffuse coupling loss factor of a finite junction are obtained within the hybrid deterministic-statistical energy analysis framework. Dedicated basis functions are proposed to efficiently describe the interface displacements of the diffuse subsystems. Subsequently, the relation between the mean vibration reduction index and the coupling loss factor is established. It is demonstrated that this relation involves both the mean and the variance of the coupling loss factor. Additionally, the relation between the variance of the vibration reduction index and the (co)variances of the coupling loss factors is derived. Finally, the proposed approach is both numerically validated and compared to experimental results for several finite junctions between building elements, which are modelled as plates. For the numerical validation, the results obtained with the proposed approach are compared with those of an ensemble of junctions with the same bare structure but with point masses attached at random locations on the walls and floors. The validations demonstrate that an accurate prediction of the mean and variance of the diffuse vibration reduction index is possible when the uncertainty across the random ensemble is sufficiently large. The comparison to experimental results involves T and X junctions between directly coupled plates. At low and medium frequencies, the experimental data are well captured within the 95% confidence interval of the hybrid model results. At high frequencies, the uncertainty on the hybrid results is very small; such differences with the experimental data are caused by modelling errors.
Analysis of the forced response of coupled panels using a hybrid finite element/wave and finite element method
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Citation Excerpt :
However, SEA involves a number of assumptions and approximations which may or may not be accurate, such as there being diffuse, reverberant wave fields in each subsystem, weak coupling between subsystems and so on [6]. The reliability and accuracy of SEA predictions also depend on the accuracy of estimated parameters such as modal densities and coupling loss factors [4]. Park et al. [7], for example, proposed using an “effective” coupling loss factor in an SEA model for estimating the energy transmission between semi-infinite plates and finite plates instead of using coupling loss factors of coupled infinite panels which do not take account of detailed structural modal behaviour.
This paper presents a hybrid finite element/wave and finite element method for predicting the forced response of coupled rectangular panels subjected to a time-harmonic point force. The panels are coupled by a joint having an arbitrarily-shaped cross-section. The panels are assumed to be uniform and homogenous in-plane and the through-thickness construction can be arbitrarily complicated. The method represents the response of the panels as a sum of wave modes and determines the characteristics of each wavemode in order to calculate the structural response. Examples of coupled thin plates and cross-laminated timber panels connected by an L joint are presented to illustrate this method. For the coupled thin plates, results calculated using the method are compared with analytical expressions and show excellent agreement. The forced response of the coupled cross-laminated timber panel system is found straightforwardly at low computational cost.
Fast average prediction method based on the upper -lower limit theory for ship's mechanical noise
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The equipment loads include acoustic excitation and mechanical excitation which is characterized by acceleration, and a reliable prediction method of mechanical noise is important to control the hull vibration noise and improve the accuracy of hydroacoustic detection. To address the issue, an accurately and efficiently predicting method is proposed and verified by the hydroacoustic experiments which included the three different diesel engine working conditions. In the method, for the acceleration loads with complete information, an equivalent load model and a gradient meshing model are used to identify the generalized forces, and the mechanical noise is predicted by the identified load and acoustic BEM. For the acceleration loads with missing partly information, the interval theory and the energy superposition method are introduced to calculate the mechanical noise, and the upper-lower limit theory and the average method are proposed to determine the range of mechanical noise and average value. The effect of acoustic excitation generated by diesel engines on mechanical noise is also discussed in detail. The results of hydroacoustic experiments show that the identified forces and mechanical noise can be obtained by the present method, with an error nearby 1 dB, under the accelerations with complete information. For the average acceleration, the range of mechanical noise is obtained and the average sound power is used to represent the ship's mechanical noise, with an error of less than 3 dB. The experimental results also reveal that the effect of acoustic cavity resonance should be included in low frequencies.
Estimation of the coupling loss factors of structural junctions with in-plane waves by means of the inverse statistical energy analysis problem
2021, Journal of Sound and Vibration
Citation Excerpt :
In general, the CLF must be obtained by means of direct measurements or complex simulation models that can account for the detail of the connection. For the case of structural junctions, the most common techniques are: wave-based models [5–9], direct measurement in an in-situ or laboratory experiment (Experimental SEA, ESEA [10–16]), estimation of the CLF from numerical simulations based on the Finite Element Method (FEM, Virtual SEA) or equivalent techniques [17–19]. In addition to the simulation models for junctions some formulas are available, see for example [6,20,21].
The Coupling Loss Factors (CLF) to describe the vibration transmission at junctions in the context of Statistical Energy Analysis (SEA) are determined. Out-of-plane energy (bending waves) and in-plane energy (treating transverse shear waves and quasi longitudinal waves as a single subsystem) as well as their interactions are considered. The CLF values are obtained from the inverse SEA problem where the energies and input powers are computed numerically by means of a Spectral Finite Element model. A set of L, T and X-junctions with variable dimensions and material properties typical from heavy building structures is considered. The Transmission Loss (TL) of the junctions is computed from the CLF values. Afterwards the TL results are approximated by means least squares leading to simplified expressions for each transmission path. The TL SEA results are compared with the TL predicted by means of a semi-infinite wave-based model.
A dual modal formulation for multiple flexural subsystems connected at a junction in energy-based models
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Statistical energy methods in vibroacoustics, like the statistical energy analysis (SEA) or the statistical modal energy distribution analysis (SmEdA), rely on specific modal coupling assumptions (MCAs) between subsystem modes. These methods assume that the behavior of subsystem mode amplitudes mimic that of oscillators, that the modes within a subsystem are uncoupled, and that the coupling between two different subsystems only takes place through the interaction of resonant modes. In the case of more than two subsystems being connected at a junction, however, it becomes difficult to establish a modal interaction scheme for them. In SEA, the problem is avoided by resorting to the travelling wave approach instead of the modal one. Nevertheless, there is a need for other energy-based methods, like SmEdA, to deal with such a situation. In this work it is proposed to extend the displacement-stress dual formulation, originally intended for two subsystems, to the case of multiple flexural waveguides connected at a junction. Numerical results are presented for a test case consisting of a floor coupled to two walls at right angle. The fulfillment of the MCAs by the dual modal formulation is examined in terms of the impedance mismatch between the floor and the walls.
A hybrid boundary element-statistical energy analysis for the mid-frequency vibration of vibro-acoustic systems
2018, Computers and Structures
Based on the concept of hybrid Finite Element (FE) analysis and Statistical Energy Analysis (SEA), a new hybrid method is developed for the mid-frequency vibration of vibro-acoustic systems. The Boundary Element (BE) method is used to describe the motion of a deterministic acoustic cavity. By enforcing the continuity conditions of displacement and velocity at the coupling interface, the dynamic coupling between the deterministic acoustic cavity and the statistical structure described by SEA is established. Then, a hybrid BE-SEA method for the mid-frequency vibration of vibro-acoustic systems is proposed. Post-processing provides formulations for calculating the sound pressure at points inside the acoustic cavity. Due to the nature of the BE method for acoustics, the proposed method not only has few degrees of freedom, but also automatically satisfies the Sommerfeld radiation condition at infinity for exterior acoustics problems. A numerical example compares results from the proposed hybrid BE-SEA method with those from the hybrid FE-SEA method and Monte Carlo simulation. The comparison illustrates that the proposed method gives good predictions for the mid-frequency behavior of vibro-acoustic systems and has the fewest degrees of freedom.

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References (21)

Energy transmission in finite coupled plates, part I: theory

Journal of Sound and Vibration

Energy transmission in finite coupled plates, part II: application to an L-shaped structure

Journal of Sound and Vibration

Statistical energy analysis of strongly coupled systems

Journal of Sound and Vibration

Analytical solution for the power exchange between strongly coupled plates under random excitation: a test of statistical energy analysis concepts

Journal of Sound and Vibration

Coupling loss factors for statistical energy analysis of sound transmission at rectangular structural slab joints, part I

Journal of Sound and Vibration

The use of power flow methods for the assessment of sound transmission in building structures

Journal of Sound and Vibration

Sound transmission and mode coupling at junctions of thin plates, part I: representation of the problem

Journal of Sound and Vibration

Sound transmission and mode coupling at junctions of thin plates, part II: parametric survey

Journal of Sound and Vibration

In situ determination of loss and coupling loss factors by the power injection method

Journal of Sound and Vibration

On the measurement of the coupling loss factor of structural connections

Journal of Sound and Vibration

Cited by (76)

A hybrid deterministic-diffuse approach to the analysis of vibration transmission across finite junctions

Analysis of the forced response of coupled panels using a hybrid finite element/wave and finite element method

Fast average prediction method based on the upper -lower limit theory for ship's mechanical noise

Estimation of the coupling loss factors of structural junctions with in-plane waves by means of the inverse statistical energy analysis problem

A dual modal formulation for multiple flexural subsystems connected at a junction in energy-based models

A hybrid boundary element-statistical energy analysis for the mid-frequency vibration of vibro-acoustic systems