Free Vibration Analysis of a Rectangular Duct with Different Axial Boundary Conditions

3This paper describes the free vibration analysis of a rectangular duct by using the Rayleigh-Ritz method. Static beam functions are used as admissible functions in the Rayleigh-Ritz method. These basis functions are the static solutions of a point-supported beam under a series of sinusoidal loads. The unique advantage of using this method is that it allows for the consideration of different axial boundary conditions of a duct. Computational results are validated with existing literature data for a simply supported rectangular duct and the finite element method (FEM) for other axial boundary conditions. A validated analytical model is used for generating natural frequency data for different dimensions of rectangular ducts. Further curve fitting has been done for the generated data, and an empirical relation has been presented to calculate the first fundamental natural frequency for different material properties of ducts and different axial boundary conditions, which can be used for any dimensions of the duct within the specified range

Effect of Micro-Pitting on Gear Vibrations and Dynamic Excitation Source

This paper quantitatively investigates the effect of micro-pitting on Transmission Error (TE) of a pair of spur gears and its correlation with vibrations. Micro-pitting is a gear surface failure phenomenon. It changes the gear profile form. The measured profile form variation can be used to calculate Transmission Error. This paper describes the micro-pitting test rig and profile form variation measurement. Calculation method of Transmission Error from profile form error data has also been presented

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

Statistical Processing of Subjective Test Data for Sound Quality Evaluation of Automotive Horn

Product sound quality has a significant role in buying decision and customer satisfaction. An often used method to assess the sound quality of any product or equipment is a subjective listening test where the sound is heard by a panel of subjects (jury) who then rate the sound quality. Subjects use a semantic differential rating wherein they evaluate the presented sounds based on a bipolar variable. The two extremes of the rating scale are labeled with an adjective and its antonym respectively. In the present study, a subjective listening test has been conducted to assess sound quality of automotive horns. The data obtained are then analyzed using statistics to gain insights. Twenty two horn sound samples were judged by thirty participants aged 20-40 years who had normal hearing. Binaural head set (BHS) instrument was used to record horn sound samples in open ground (neglecting wind noise effect). Sounds are recorded two meter from horn in front direction and used for subjective test. For the subjective test and subsequent statistical analysis, a four step procedure has been used. In the first step, the participants were asked to rate the sound quality for each horn based on seven bipolar variables. These bipolar variables are soft/loud, calm/frightening, slow/fast, relax/tense, safe/danger, vague/distinct and pleasant/unpleasant. For each bipolar variable, a seven verbal interval scale was used ranging from one extreme to another in degree, for example extremely pleasant to extremely unpleasant

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

Numerical Simulation of Hit Noise Generation Due to Sloshing Phenomenon in a Rectangular Tank Under Periodic Excitation

Sloshing in fuel tanks is one of the major sources of noise in hybrid and high-end vehicles. During sloshing, the fluid causes impacts on tank walls resulting in their vibration, which further leads to noise, referred to as “hit noise.” Therefore, hit noise generation is a multi-physics phenomenon involving fluid flow, structural response, and acoustic radiation. This paper presents a multi-physics approach to predict hit noise in a rectangular tank. The methodology involves the prediction of fluid loading on tank walls and their structural response using transient fluid and structural analyses which are weakly coupled. Radiated hit noise is predicted using acoustic finite element analysis. Longitudinal periodic excitation is applied to the fluid domain at different frequencies to simulate the sloshing regime which has dominant fluid–structure interactions. Parameters like tank wall pressures, the resulting dynamic acceleration, and radiated sound pressure levels are monitored and validated with the experimental results available in the literature

Analytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls: Application to a triangular duct

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ElsevierAn analytic mode-matching method suitable for the solution of problems involving scattering in three-dimensional waveguides with flexible walls is presented. Prerequisite to the development of such methods is knowledge of closed form analytic expressions for the natural fluid–structure coupled waveforms that propagate in each duct section and the corresponding orthogonality relations. In this article recent theory [J.B. Lawrie, Orthogonality relations for fluid–structural waves in a 3-D rectangular duct with flexible walls, Proc. R. Soc. A. 465 (2009) 2347–2367] is extended to construct the non-separable eigenfunctions for acoustic propagation in a three-dimensional rectangular duct with four flexible walls. For the special case in which the duct cross-section is square, the symmetrical nature of the eigenfunctions enables the eigenmodes for a right-angled, isosceles triangular duct with flexible hypotenuse to be deduced. The partial orthogonality relation together with other important properties of the triangular modes are discussed. A mode-matching solution to the scattering of a fluid–structure coupled wave at the junction of two identical semi-infinite ducts of triangular cross-section is demonstrated for two different sets of “junction” conditions

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 Vibration Analysis of HVAC Ducts

Free vibration analysis of ducts is the first step to understand the coupling between structural and acoustic modes in Heating, Ventilation and Air Conditioning (HVAC) ducts. This thesis covers free vibration analysis of different duct shapes like rectangular, circular, flat oval and elliptical. These types of ducts are extensively used in HVAC systems. Transfer Matrix (TM) method is used to calculate natural frequencies and mode shapes for rectangular and flat oval ducts with simply supported boundary conditions. Free vibration analysis of cylindrical ducts and curved plates is explained as subsections of flat oval ducts. TM method is only useful for simply supported boundary conditions

An Experimental and Multiphysics Based Numerical Study to Predict Automotive Fuel Tank Sloshing Noise

With significant decrease in the background noise in present day automobiles, liquid slosh noise from an automotive fuel tank is considered as a major irritant during acceleration and deceleration. All major international OEMs and their suppliers try to reduce sloshing noise by various design modifications in the fuel tank. However, most major activities reported in open literature are primarily based on performing various CAE and experimental studies in isolation. However, noise generation and its propagation is a multiphysics phenomenon, where fluid mechanics due to liquid sloshing affects structural behaviour of the fuel tank and its mountings which in turn affects noise generation and propagation. In the present study a multiphysics approach to noise generation has been used to predict liquid sloshing noise from a rectangular tank. Computational Fluid dynamics (CFD), Finite Element Analysis (FEA) and Boundary Element Method (BEM) simulation studies have been performed in a semi-coupled manner to predict noise. VOF based multiphase model along with k-ε turbulence model was used to perform the CFD studies. Sloshing Noise generated due to fluid interaction with structural walls is simulated using Vibro-acoustic model. An integrated model is developed to predict dynamic forces and vibration displacement on tank walls due to dynamic pressure loading on tank walls. Noise radiated from tank walls is modelled by Harmonic Boundary Element Method. Experimental and numerical studies have been performed to understand the mechanics of sloshing noise generation. Images from high speed video camera and noise measurement data have been used to compare with numerical models