•Stochastic model of the speed of leak noise propagation in plastic water pipes is derived.•Uncertainties in the pipe material/geometry and soil properties are modelled and their influence on the ...speed of leak noise propagation is investigated.•Properties of statistical moments are used to derive the confidence intervals for the variance of the wave speed.•The proposed approach is applied to data from in-air and buried plastic water pipes.
A good estimate of the speed of leak noise propagation is necessary to pinpoint the location of a leak using acoustic correlators. Models currently exist for this purpose, but they do not consider uncertainties in the pipe geometry and the properties of the pipe and soil. Using the fact that leak noise propagates as a predominantly fluid-borne wave, this paper develops a stochastic model of the speed of leak noise propagation in plastic water distribution pipes that can account for these uncertainties. The model provides confidence limits for the estimate of this wave speed. It is based on the mean and standard deviation of the pipe geometry as well as the pipe and soil material properties, which have strong influence on the speed at which the leak noise propagates in the pipe. Numerical examples, using parameters from water supply systems found in the field, in which the pipe is made from Medium-Density Polyethylene (MDPE) and Polyvinyl Chloride (PVC) are presented to validate the model. Monte Carlo simulations for both in-air and buried pipes are presented to check the 99.7% confidence interval. To verify that the predictions from the stochastic models give realistic results, they are compared with some measurements from different sites, in which nominal properties and tolerances for the pipe and soil properties are assumed.
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A modal impedance technique is introduced for mid frequency vibration analyses. The approach is mainly based on statistical energy analysis (SEA), however loss factors are determined by not only ...driving but also contributed by transfer mobilities. The mobilities are computed by finite element modal analysis. The technique takes geometrical complexity and boundary condition into account to handle their mid-frequency effects. It is applied to a stiffened composite plate having randomized mass, i.e., uncertain plate. For the verification, several numerical and experimental tests are performed. Internal damping of subsystems is evaluated using power injection and is then fed to finite element software to perform numerical analyses. Monte Carlo simulation is employed for the uncertainty analyses. To imitate plate mass heterogeneity, many small masses are used in both numerical and experimental analysis. It is shown that the proposed technique can reliably be used for vibration analyses of uncertain complex structures from mid to high frequency regions.
Discrete singular convolution (DSC) algorithm is an accurate dynamic analysis method for single structures. However, vibration analysis of connected structures via the DSC method is limited to step ...beams and plates. This paper extends the applicability of the DSC method in handling acoustic transmission lines composed of several duct elements with different diameter ratios. Connections of elements are handled by setting up continuity equations at geometric discontinuities. Conformity of DSC equations at these connections is carried out using Taylor series expansion. In this study, natural frequencies, mode shapes and power transmission coefficients of acoustic transmission lines are performed to test the proposed DSC implementation. Power transmission coefficients are obtained through the two-load method using the data provided by the DSC approach. The results are compared with finite element method and analytical solutions (if applicable), and the analytical transfer matrix method is also used for validating the power transmission coefficients. This paper shows that the DSC method is accurate and reliable, and so applicable for acoustic transmission line analysis.
Statistical energy analysis is a widely used high frequency vibro-acoustic analysis tool. It is based on power flow balance between subsystems. Its accuracy mainly depends on precise determination of ...energy loss factors. In the paper, three different types of composite structures (point-connected I, L and T types) made of laminated plates are of concern to determine in-situ energy loss factors by using power injection method1 (PIM). The results are compared with those obtained by approximate analytical determinations, thus accuracy of numerical and experimental PIM is discussed for point-connected composite plates. Analytical loss factors are computed by an iterative procedure to consider indirect coupling for the structures having more than two subsystems.
This study is concerned with the mathematical modelling of the vibration response characteristic of a special dissimilar composite beam based on experimental modal analysis. Here, experimental modal ...analyses of three different dissimilar polyamide 6 composite beams, which are connected to each other by hot plate welding are performed. The measured natural frequencies are compared with finite element predictions for verification purposes. Modal information obtained by experiments is used to construct a mathematical model representing vibration response characteristic of beams by applying multi degree of freedom curve fitting method. The model showing modal characteristics of dissimilar beams is now ready to be used in different kinds of excitations to predict the frequency response of vibration.
The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters predicting these characteristics is a necessary and ...important step of the acoustic design and optimization process. Acoustic design sensitivity analysis includes the computation and evaluation of the sensitivity information required for this procedure. In this study, a boundary element code performing the sensitivity analysis of the acoustic pressure by using the matrix sensitivities with respect to different design variables has been developed. The effect of the precision of boundary element discretization on the acoustic pressure sensitivity is examined via this code. The formulation is applied to a multi-source system and the dimension sensitivity analysis of near field pressures of two-dilating-spherical source is performed. The last application is devoted to a real sound source: a washing machine sitting on the floor. Sensitivity of the field pressures to the machine’s dimensions (size), surface velocity and frequency is examined on the bases of the boundary element model of the machine and half-space condition. The impacts of these variables are compared; and a limiting speed for the machine responding both the acoustical and operational requirements is determined.
The boundary element method (BEM) is a widely used technique in vibro-acoustics. This method is effective not only in the determination of exterior and interior sound fields but also for the sound ...source localization of complex systems. In this chapter, the Helmholtz integral equation formulation and its boundary element discretization are presented. Half-space algorithm and half-space-contact version of this algorithm feasible for most machine locations are introduced. Some theoretical examples, for a dilating sphere in half-space, are presented. The chapter continues with a case study: Sound source identification and characterization of a refrigerator, via a cost-effective and easy-to-use technique, based on surface velocity measurements and BEM computation of surface and field acoustic pressures.
This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, ...specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.
Brass materials are widely used in many fields of machinery, especially plumbing applications. Parts produced from brass are processed in lathes or milling machines during the manufacturing phase. In ...this study, 6-corner pieces were produced by machining the MS58 brass alloy on the
C
-axis lathe with an end mill. As machining parameters, tool diameter, feedrate and rotation speed were selected. The effects of these parameters on average surface roughness (Ra), cutting time (
t
) and dimensional deviation (dev) were determined by the surface response method. Regression equations were created separately for surface roughness, cutting time and dimensional deviation. Later, parameter levels that optimize all three dependent variables together were obtained by grey relationship analysis. It was determined that the most effective parameter on surface roughness and dimensional deviation is the tool diameter. The most effective parameter on cutting time was found to be feedrate. The best combination of machining parameters was 10 mm tool diameter, 150 mm/min feedrate and 1000 rev/min rotation speed. The selection of parameters depends on the requirements based on better surface roughness, minimum cutting time, minimum dimensional deviation. Parameter levels that optimize surface roughness only are 10 mm tool diameter, 50 mm/min feedrate and 1000 rev/min rotation speed. Parameter levels that optimize cutting time only are 8 mm tool diameter, 143 mm/min feedrate and 1525 rev/min rotation speed. Parameter levels that optimize cutting time only: 10.31 mm tool diameter, 50 mm/min feedrate and 1000 rev/min rotation speed.
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