Measurement of damping properties of beeswax and cosmetic wax using Oberst beam method

Damping treatment is a standard practice in many industries for controlling excessive vibration at resonance. Different damping materials are available for various engineering applications. Wax is one of them, and it’s mostly used in musical instruments. There are two types of wax are available namely beeswax (natural wax) and cosmetic wax. The aim of the present study is to measure damping properties of these two types of wax using Oberst Beam Method (OBM). The effects of damping material’s thickness and bare sample on damping loss factor are studied

Vibro-Acoustic behaviour of Flexible Rectangular Ducts

Ducts are extensively used in Heating, Ventilation and Air Conditioning (HVAC) applications and gas industries for transmission of substance, especially liquid or gas. These ducts carry the noise generated by Air-Handling Units (AHU) in axial and transverse directions. Sound radiated in the transverse direction due to acoustic excitation of duct walls is known as ‘Breakout noise’. Sound radiation from duct depends on its structural properties as well as the medium’s acoustic properties. The present research interest is to study sound radiation and vibration characteristics of rectangular ducts using direct and inverse techniques. First part of the work describes analytical, experimental and numerical models to understand sound radiation characteristics of a flexible rectangular duct. Firstly, an analytical model is developed based on an ‘equivalent plate model’ of the rectangular duct. This model has considered the coupled and uncoupled behaviour of both, acoustic and structural subsystems. Modal radiation efficiencies of a rectangular duct are estimated and compared to those of simple rectangular plate. This comparison shows a similarity between duct sound radiation behaviours in terms of plate modes. The analytical model results are validated using Finite Element-Boundary Element Method (FEM-BEM) numerical results. As a part of the study, sound radiation behaviour of a duct is studied to understand its equivalence with monopole and dipole sources. As second step, an experimental setup is developed to measure the breakout noise in terms of Transverse Transmission Loss (TTL) and radiation efficiency, by providing a plane-wave excitation. A methodology is developed to calculate input sound power from measured pressure signals inside the cylindrical tube using an autospectrum of a progressive wave. Radiated sound power is measured using two different methods, namely- intensity probe method (P-P method) and Microflown technique (P-U method). Using the measured input and radiated sound power, TTL and radiation efficiency are calculated. These results have been corroborated with analytical results of ‘equivalent plate model’ and FEM-BEM numerical results. Second part of the current study is to understand the effect of duct joints on modal parameters. In this study, three different rectangular ducts with two types of joints (welded and adhesive joints) are considered. Pre-test analysis is performed to know the number of measuring points and their locations. Then, Experimental Modal Analysis (EMA) is performed on these three ducts to identify natural frequencies and mode shapes. These EMA (measured) results are compared to Numerical Modal Analysis (NMA) results (predicted). It has been observed from all cases that natural frequencies are in good agreement. Mode shapes of measured and predicted results are compared in terms of Modal Assurance Criteria (MAC) plot, mode pair table and visual inspection. Low MAC values are observed for the duct with welded joints. However, a duct with an adhesive joint similar to the ideal shape has good MAC value. Detailed section analysis is performed on a duct with a two-welded joint configuration to understand mode shape deviation. It is observed from experimental and numerical results that joints play a critical role in deviation of mode shapes for thin flexible structures. Hence, as next part of the study, an analytical model is developed to incorporate joint effects in estimating the modal parameters. Here, the joint condition is represented using linear and rotational spring’s stiffness. Natural frequencies and mode shapes of a rectangular duct are found analytically by Rayleigh-Ritz method using an ‘equivalent plate model’. These results are validated with experimental results for a rectangular duct with Pittsburgh lock joint. Natural frequencies of the duct in both cases are in good agreement. Mode shapes of symmetric modes remained same for both ducts, whereas antisymmetric modes deviated from each other. This deviation is observed only in duct walls next to the joint. Third part of the study focuses on sound source reconstruction using two inverse techniques such as Inverse Numerical Acoustics (INA) and Near-field Acoustic Holography (NAH) methods. Here, INA is used to reconstruct the vibration velocity on a flexible duct surface in structural-acoustic coupled system. Effect of measurement locations, measurement points and mesh density on reconstruction results is discussed at both coupled and uncoupled frequencies. L-curve regularization parameter selection method is used to overcome the ill-posed problem. It is verified from reconstruction results that vibration velocity can be obtained accurately with less than 10% error. Four different NAH techniques are used in the present investigation to identify distribution of fan noise source strength and radiation pattern. Firstly, number of reference microphones needed to find the incoherent sources by Singular Value Decomposition (SVD) is evaluated. Later, sound source is reconstructed with measured sound pressure using different NAH techniques. The reconstructed results showed that ESM method is best to reconstruct fan noise sources with minimal error. The behaviour of a fan at blade passing frequency (BPF) is akin to a dipole sound source. A comparison of reconstructed pressures with measured values indicates that reconstructed pressure correlates very well with measured pressure. As part of study, ESM is used to reconstruct sound source at uncoupled and coupled frequencies for a rectangular box with a single compliant wall. Sound pressure data for reconstruction is generated from numerical simulations instead of actual measurements. Reconstructed results are compared to actual results at both frequencies. Effect of noise on accuracy of the reconstruction is studied for different signal to noise ratio (SNR) values. Higher SNR values led to good accuracy in reconstruction. Based on the regularization studies, it can be concluded that L-curve method is better compared to GCV method for reconstruction at uncoupled and coupled frequencies. Finally, from the present research work it is concluded that vibro-acoustic behaviour of the flexible rectangular ducts is studied effectively using direct (sound intensity method, Microflown technique) and inverse techniques (INA and NAH)

Free vibrational analysis of rectangular ducts with different joint conditions

Rectangular ducts are fabricated using thin sheets of a metal with different joint conditions. Due to the presence of these joints, ducts deviate from their assumptive ideal shapes. The objective of the present work is to study the effect of different joint conditions and wall thickness on dynamic characteristics of the ducts. Experimental Modal Analysis (EMA) is performed on three rectangular ducts of different joint types. Numerical Modal Analysis (NMA) is also performed by considering that the ducts are of ideal rectangular shape (without joint condition). Correlation analysis is performed between EMA and NMA in terms of Modal Assurance Criteria (MAC), Relative Frequency Difference (RFD) plots and auto-MAC. It is observed that natural frequencies are in good agreement but there is a discrepancy in mode shapes

Study on Effect of Joints on the Modal Parameters of Rectangular Duct.

A duct is an enclosed passage for transmission of a substance, especially liquid or gas with extensive usage in heating, ventilation, and air conditioning (HVAC) applications and gas industries. Practically, duct shapes have deviations from ideal geometric shapes, predominantly in thin-walled structures due to joint conditions. The aim of the present research is to understand the effect of duct joints on modal parameters. In this study, Experimental Modal Analysis (EMA) is carried out on three different rectangular ducts having different joints and materials. Numerical Modal Analysis (NMA) is then performed on these ducts by modelling the corresponding joints. The Modal Assurance Criteria (MAC), frequency comparison, and auto-MAC plots are used to check the correlation between the experimental and numerical results. Based on these comparisons, a good match in natural frequencies but a mismatch in mode shapes are observed

Sound Source Reconstruction on Flexible Plate backed by a Cavity using Equivalent Source Method

Characterization of sound radiation from thin flexible structures, which encloses sound sources, is required for noise control studies. It involves structural-acoustic coupling between flexible structure and acoustic cavity. The aim of present study is to reconstruct the sound source at uncoupled and coupled frequencies using Equivalent Source Method (ESM) for a rectangular box with the single compliant wall. Data for reconstruction is generated from numerical simulations instead of actual measurements. Effect of the regularization and Signal-toNoise Ratio (SNR) on the accuracy of reconstruction is discussed. The numerical model is developed to understand the coupling phenomena between structural and acoustic subsystem

Application of NAH method for the prediction of sound radiation from a flexible box structure

Prediction of noise radiation from the thin flexible structures, which encloses sound sources is important for the structural design to develop a quieter product. There are different direct and indirect techniques are existing to know the sound radiation of the machine or structure. The direct method such as sound intensity method and indirect methods or inverse techniques includes Near-field Acoustic Holography (NAH) and beam forming. NAH is one of the good inverse techniques to predict the vibro-acoustic properties of the sound source. In this method, acoustic quantities can be reconstructed on the surface of a vibrating structure based on sound pressure measurements made at a set of points in the near-field of the source. These NAH methods are the ill-posed inverse problems due to the existence of strongly decaying, evanescent like waves. Regularization is used to overcome the ill-posed problem. The purpose of this investigation is to predict the sound radiation characteristics of a box structure with one flexible wall. The acoustic quantities are reconstructed with NAH technique

Effect of a joint on breakout noise characteristics of rectangular duct

Breakout from a flexible rectangular duct depends on its structural properties as well as acoustic properties of the medium. Majority of duct breakout noise prediction models in the literature consider an ideal duct (without joint). However, ducts used in applications have joints. So, current research interest is to study the effect of duct joint in predicting the breakout noise and its influence on modal parameters. For this purpose, duct with a joint is considered in the experimental study and an ideal duct for numerical analysis. As a first step, an experimental setup is developed to measure breakout noise in terms of transverse transmission loss and radiation efficiency, and furthermore an experimental modal analysis is performed to measure modal parameters of the duct. Numerical analysis is performed on an ideal rectangular duct (without considering the joint condition) to calculate the breakout noise and modal parameters. Both, experimental and numerical results are compared, and it is observed that joint has a less significant influence on breakout noise as compared with modal parameters

Experimental study of breakout noise characteristics of flexible rectangular duct

Breakout noise is prominent at low frequencies in a rectangular shaped duct due to strong structural–acoustic coupling and is characterized in terms of transverse transmission loss (TTL). The main objective of the present investigation is, to implement intensity based experimental techniques for measuring breakout noise and validate “equivalent unfolded plate” analytical model available in the literature. An experimental test setup is developed to measure input and radiated sound power along with vibration displacement and particle velocity. Using the obtained input and radiated sound power, transverse transmission loss (TTL) and radiation efficiency are calculated. Input sound power is calculated by using an autospectrum of a progressive pressure wave. Radiated sound power is measured using two different methods, namely- intensity probe method (P-P method) and Microflown technique (P-U method). In this present study, numerical model is also developed to predict transverse transmission loss (TTL), radiation efficiency and these results have been corroborated with experimental and analytical result