Free Vibration analysis of circular membrane backed by a cylindrical cavity using Impedance-Mobility Approach

The membrane backed by a cavity is used in many applications like sensors, loudspeaker design and musical acoustics. There are two types of configurations existing in engineering applications such as single membrane cavity and double membrane cavity. The modal parameters of membrane are influenced by the supporting back cavity due to structural-acoustic coupling. In this study, pre-stressed membrane with back cavity has been analyzed by using Impedance Mobility Coupling Method (IMCM). The coupled behavior of the system is expressed in terms of the finite number of uncoupled subsystem modes. The present paper discusses a generalized formulation to calculate modal parameters of coupled system and has demonstrated it for a single membrane cavity problem. Coupling between acoustic and structural subsystem is expressed in terms of a mode coupling coefficient which describes spatial matching of both mode shapes. Acoustic uncoupled subsystem is a circular cavity at one end closed and other end open for the single membrane case. The length of the cavity is more than its diameter, and the cylindrical surface is acoustically rigid. The membrane is thin and is coupled to the closed end of the cavity by clamping its circular edge. Radial tension along the circumference of the thin membrane is applied to provide membrane pre-tension. For the theoretical analysis, the acoustic impedances of all the cavity modes and the structural mobility of all the membrane modes are calculated. The complex amplitudes of the acoustic pressure and vibration velocity are then arranged in a matrix form and modified suitably to prepare as a standard eigenvalue problem. The numerical estimation of the coupled frequencies is carried out by coupling structural and acoustic physics in a Finite Element (FE) environment. In structural case, membrane physics was established and the initial tension to the membrane was provided by giving initial in-plane forces. The membrane was provided with fixed constraints at the edge to replicate fixed constraints at the boundary in case of theoretical analysis. Zero acoustic pressure condition was imposed at one end of acoustic cavity to mimic the open-close boundary condition while remaining surfaces were defined acoustically rigid. Velocity continuity condition was defined as coupling boundary condition. The predicted numerical and theoretical coupled natural frequencies are in good agreement with each other. The proposed methodology is useful to predict the Eigen frequencies of the weakly coupled system

Acoustic Analysis of Additive Manufactured Multilayer Periodic Structures

Traditional acoustic materials like glass wool, fiber glass, foams etc. are extensively used to attenuate acoustic energy or noise along the propagation path. To have maximum absorption along the path, acoustic material requires thickness of at least quarter of wavelength. Therefore, at lower frequencies it demands thicker acoustic materials where wavelength of acoustic wave is much higher. These requires more space to put these materials and ultimately adds weight to the system. The current study is focused on design and fabrication of periodic structures inspired from natural honeybee hive to improve low frequency absorption with relatively lower thickness, as an alternative to traditional acoustic materials. The main objective of this study is to understand the acoustic energy attenuation through periodic structures with central membrane. First part of work describes the standard techniques available for measurement of acoustic absorption coefficient, and effects of manufacturing technique on absorption coefficient of the structure. The proposed periodic structure has three distinct features namely; narrow tubes, periodicity and structural flexibility. In this stage, narrow tubes and periodicity excluding flexibility has been studied extensively. A generalized mathematical formulation to predict absorption coefficient for single (hexagonal) as well as multi-periodic (octagonal) structure has been developed where shape dependent viscous and thermal effects are included. The proposed method is based on unit section analysis which significantly reduces the complexity during analysis of periodic structures. Additive Manufacturing (AM) has been extensively used to fabricate periodic structures to examine effect of various cell parameters like cell size, shape and cell length. The estimated absorption coefficients using unit section have been corroborated with measured results in impedance tube. Second part of thesis deals with the influence of membrane flexibility on acoustic absorption coefficient of complete periodic structure. This part emphases on development of a mathematical formulation of membrane, perforated membrane, membrane backed by a cavity and membrane sandwiched between two periodic layers. A mathematical formulation of the perforated membrane has been rewritten by combining individual impedances of membrane and perforations with modified boundary conditions (velocity continuity at perforation circumference). A mathematical formulation based on transfer matrix method has been developed to estimate absorption coefficient of complete multilayer periodic structure (two periodic narrow tube layers with central membrane). The formulation is capable of handling membrane tension as well as perforations in the membrane. The measured results are correlated with predicted results. Third part of current work deals with improving low frequency absorption coefficient of periodic structures without incorporating flexibility in to it. The four different configurations are studied by reducing the cell size, providing impedance mismatch, increasing effective length of wave travel, and providing perforations to face sheets of hexagonal periodic structures. These proposed configurations are fabricated using Additive Manufacturing (AM) method. The tuning of these structures to narrow as well as broad band sound absorption coefficient has been discussed. The predicted results based on viscous and thermal effects are validated with measured results. Finally, the last part of thesis summarizes current work based on above findings. The results and methodology presented in this study helps to understand the acoustic energy attenuation through the periodic structures. This study also paves the basic framework to design and fabricate periodic structures for acoustic applications like automobile, aviation and building acoustics

Acoustic characterization of additive manufactured layered porous materials

In the present study, acoustic properties of layered porous materials produced by Fused Filament Fabrication (FFF) technique of Additive Manufacturing (AM) have been investigated. The porous materials are fabricated by using different infill percentage of materials in the direction of fabrication, which leads to layered porous material of various pore sizes along the direction of fabrication. Samples with different combinations of infill percentages are fabricated, and their sound absorption coefficient is measured by using two microphone impedance tube technique. Measured results indicate that the sound absorption coefficient of additive manufactured porous materials can be tuned to the required frequency range by changing the combination of infill percentages. The results and fabrication technique presented here gives an alternative method to fabricate layered porous materials

Analytical investigation of propeller-wing interaction noise

This paper investigates the noise generated by propeller-wing configuration at take-off condition with the propeller mounted upstream. This study makes use of various axisymmetric noise models developed for contra-rotating propellers to estimate the noise generated by propeller-wing configuration and later integrate them to estimate total noise. First, using well-published theory, rotor-alone (loading, thickness, and self-noise) and interaction noise sources (viscous-wake, potential field, tip-vortex) including tonal and broadband components are estimated. Later, a systematic parametric study is carried out by changing the blade number and tip Mach, while maintaining the propeller thrust and blade solidity. The noise generated is represented by Overall Acoustic Sound Power Level (OSWLs), which is an integrated value over the emission angles and frequency range, in a matrix form for the range of blade number and tip Mach. This matrix shows the regions dominated by rotor-alone and interaction noise and found that the noise characteristics of a rotor in uninstalled conditions (rotor-alone) are significantly altered due to the presence of a wing (installed condition). Further, it is found that the balance between these regions shifts with the variation in separation distance between the propeller and the wing. These results are further discussed with the individual interaction noise source mechanism and their dominance at various blade numbers, tip Mach, and separation distances. In addition, the non-axisymmetric viscous-wake interaction noise is investigated for even and odd numbers of blades and found that viscous-wake interaction noise has considerable directivity in the azimuthal direction. The results presented in the study are preliminary findings of propeller-wing noise, however, it gives give a quantitative picture of the behaviour of various noise sources and their balance with respect to geometric and operating parameters. This study will help to understand the dominant noise sources involved in propeller-wing configuration and will provide a quick guide for designing a low-noise configuration

Acoustic characterization of additive manufactured perforated panel backed by honeycomb structure with circular and non-circular perforations

This paper studies the acoustic properties of an additive manufactured micro-perforated panel backed by a periodic honeycomb structure. Extrusion-based Fused Filament Fabrication (FFF) technique of Additive Manufacturing (AM) is used to fabricate the integrated honeycomb structures with a perforated face sheet. Normal absorption coefficient of the fabricated structure is measured in impedance tube using two microphone transfer function method. A generalized analytical formulation based on unit section analysis applicable to various cross sections of perforations has been proposed to predict the absorption coefficient, where shape dependent viscous effects in the perforation are incorporated by deriving effective complex density of the medium. To study the effect of perforation shape, three geometries viz., circular, triangular and square perforations are considered for analysis where triangular shape found to have more absorption coefficient and lower frequency of peak absorption. In addition, broadband absorption coefficient of proposed structure has been demonstrated by deploying hexagonal cells of different lengths in a unit section. The analytical results are compared with experimental results and a good agreement is observed between them. A parametric study is conducted to understand effect of perforated hole size and cell length on the absorption coefficient and peak frequency. Results show that the proposed structures can be tuned to desired frequency range by altering geometric parameters like cell length, shape and size of perforation hole. Technique and methodology presented in the current study gives an alternative way to design and fabricate honeycomb structures with perforations for acoustic applications such as aircraft cabins, ship structures and building acoustics

Acoustic characterization of additive manufactured perforated panel backed by honeycomb structure with circular and non-circular perforations

This paper studies the acoustic properties of an additive manufactured micro-perforated panel backed by a periodic honeycomb structure. Extrusion-based Fused Filament Fabrication (FFF) technique of Additive Manufacturing (AM) is used to fabricate the integrated honeycomb structures with a perforated face sheet. Normal absorption coefficient of the fabricated structure is measured in impedance tube using two microphone transfer function method. A generalized analytical formulation based on unit section analysis applicable to various cross sections of perforations has been proposed to predict the absorption coefficient, where shape dependent viscous effects in the perforation are incorporated by deriving effective complex density of the medium. To study the effect of perforation shape, three geometries viz., circular, triangular and square perforations are considered for analysis where triangular shape found to have more absorption coefficient and lower frequency of peak absorption. In addition, broadband absorption coefficient of proposed structure has been demonstrated by deploying hexagonal cells of different lengths in a unit section. The analytical results are compared with experimental results and a good agreement is observed between them. A parametric study is conducted to understand effect of perforated hole size and cell length on the absorption coefficient and peak frequency. Results show that the proposed structures can be tuned to desired frequency range by altering geometric parameters like cell length, shape and size of perforation hole. Technique and methodology presented in the current study gives an alternative way to design and fabricate honeycomb structures with perforations for acoustic applications such as aircraft cabins, ship structures and building acoustics

Acoustic characterization of additive manufactured micro-perforated panel backed by honeycomb structure

This paper studies the acoustic properties of an additive manufactured micro-perforated panel backed by a periodic honeycomb structure. Extrusion-based Fused Filament Fabrication (FFF) technique of Additive Manufacturing (AM) is used. Absorption coefficient of the proposed structure is measured using an Impedance tube. An analytical model is developed to predict the acoustic absorption coefficient. The analytical results are compared with the experimental results and a good agreement is observed between them. A parametric study is conducted to understand the effect of perforated hole size on the absorption coefficient and peak frequency

A Performance Study on Indirect Static Flow Resistivity Measurement Methods for Acoustic Materials

Various empirical models have emphasized the dependence of sound absorption coefficient on static airflow resistivity, and thus its measurement becomes essential. In this paper, the two-cavity and two-thickness indirect acoustic methods are implemented based on a standard impedance tube for evaluating the static flow resistivity of foam. A comparison is made between the resistivity results obtained by the two-cavity and two-thickness method , and later validated with results of an alternating air-flow test setup which is developed as per the ISO 9053 guidelines. Further, the empirical relations are utilized to estimate the absorption coefficientfrom measured values ​​of flow resistivity and are compared with measured absorption coefficient in an impedance tube . The results discussed in this study presents the feasibility and suitability of the indirect acoustic methods for evaluating the flow resistivity