A Review on Statistical Energy Analysis of Composite Structure

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1 A Review on Statistical Energy Analysis of Composite Structure Devendra Kamble 1 Assistant Professor Sharad Institute of technologycollege of engineering, yadrav M.B. Mandale Assistant Professor Rajarambapu Institute of technology, Sakharale Dhiraj Patil Assistant Professor Sharad Institute of technologycollege of engineering, yadrav ABSTRACT The aim of this paper is to review method for structure born noise propagation assessment in composite structure. In application where, the lightweight structure is an important parameter, the introduction of a composite structure, which has several advantages, such as their high strength-to-weight ratio, excellent thermal insulation etc. So in recent years, such structures have become used increasingly in aerospace, marine, automotive and other applications. Care must be taken in their design to ensure that their sound insulation capabilities are good enough to sustain at high frequency. Statistical energy analysis is frame- work to study the vibro-acoustic behavior of structure at high frequency. This review includes the Basic of statistical energy analysis, methods of estimation of statistical energy analysis parameter (Modal density, damping loss factor and coupling loss factor) of a composite structure as well as conventional material, study of fiber reinforced composites. Keywords Statistical energy analysis, modal density, damping loss factor (DLF). INTRODUCTION Composite materials are used extensively in many applications because of their high strength-to-weight ratio as compared to metal plates. Statistical energy analysis (SEA) is a way of studying dynamical system. Statistical energy analysis is first introduced by Lyon in 1960 to analyze the vibro-acoustic behaviour in complex structure [1]. These vibro-acoustic responses are at high frequency range and solved by statistical approach [1-3]. SEA can provide reliable estimates of vibration levels on complicated system by using very simple model. The method is well suited for system level response prediction at early design stage of a product, for predicting responses at high frequencies [4]. In many industries there are design requirements to ensure vibro-acoustic performance is met. They needs to reduce interior noise to acceptable levels, and ensure that radiated noise level are in compliance with regulations. In space industry vibration must be assessed to ensure that vibration both during launch and in orbital operation will not damage electronic equipment s. The traditional structural design technique based on normal modes using natural frequency and corresponding mode shape of structures, was not useful in designing such space structure. Vibro-acoustic is mainly depends on propagation of wave and this has application in statistical energy analysis. There are three parameters in SEA which needs to study, they are modal density, damping loss factor, coupling loss factor. The SEA is a framework which is mainly used for determine the energy flow relation for finding the dynamic characteristics 1226 Devendra Kamble, M.B. Mandale, Dhiraj Patil

2 1227 Devendra Kamble, M.B. Mandale, Dhiraj Patil International Journal of Engineering Technology Science and Research of the complex structure, and it is also used in high frequency analysis. In this method the system is divided into subsystem and correlate with the energy flow between the subsystems [1-4 ]. The basic concept of SEA is to group the resonant modes into different frequency bandwidth i.e. the ratio of number resonant modes to frequency bandwidth is called modal density [16].Damping loss factor is a measure of loss of energy from the system. The methods used to find out the damping loss factor are, decay rate method, half power bandwidth method (3 db method) and power injection method. Coupling loss factor means the transmission of energy from one subsystem to another [1]. Recently, a displacement field measurement has been used by RaefCherif et al. [5] to estimate the damping loss factor of two-dimensional orthotropic structures. In this work the chosen method based on a scanning laser vibrometer measurement. A wave based method has been used by McDaniel et al. [6] to estimate frequency dependant loss factors in one-dimensional structures. In this work they put number of accelerometer on a beam to identify the complex wavenumbers of flexural and evanescent waves at each frequency. The damping loss factor is then co-related to the imaginary part of estimated wavenumber. AbderrazakMejdi et al. [7] describes the prediction of sound transmission loss (STL) and damping loss factor of sandwich panel of different configurations. Euler- Bernoulli composite beam has been used by C. Mei [8] in this study, influence of frequency on torsional mode and flexural mode of vibration is considered and coupling effect taken into account. L.S.Teoh et al. [9] has considered shear and rotary inertia effect on a cantilever beam. A wavenumber integration method has been used by G. Xie et al [11] to discuss the effect of boundary conditions on mode count and modal density of a one-dimensional and two-dimensional structural system like beam, plate respectively. In this paper it is demonstrated that average mode count is reduced by between 0 and 1 for each boundary constraints, depending upon the type of boundary condition. Also they said the modal density of one-dimensional system is independent on boundary condition and for two-dimensional system it is largely dependent on boundary conditions. P.J. Shorter et al. [24] has been used a non-iterative hybrid for presenting transmission of noise and vibrations in a complex system. In this they combine the deterministic and statistical technique to produce a non-iterative method. Stefan Dancila et al. [46] has developed a solution for anisotropic thin walled closed section laminated composite beam. J.R. Banrjee [12] investigated the expression for the frequency equation and mode shape of a coupled composite beam with cantilever end condition. Omer Civalek [13] investigated a numerical solution on free vibration analysis of laminated conical and cylindrical shell and also discussed the effect of circumferential wave number, number of layers on frequencies characteristics. C.H. Ziang et al [14] used FEA model to verify the correctness of any analytical model prepared for vibration analysis of laminated composite plate. In this paper they studied the analytical and experimental method of elastically restrained composite plate for investigating the vibration characteristics. Different connection has been used by R. Panuszka et al. [15] to find the coupling loss factor. In this they used perpendicular connection for finding the coupling loss factor. The point and line welded connections effects are discussed. R. Bachoo et al. [16] has investigated an analytical expression for finding the modal density of fiber reinforced composite beam coupled in bending and torsion. They also found the effect of fiber orientation on beam and effect orientation on modal density. Modal based approach has been used by L.Ji et al [17] for the mid frequency vibration analysis of a complex structure built from a long wavelength source and short wavelength receiver. The both source and receiver have low and high modal density and modal overlap. The SEA parameter such modal spacing, coupling loss factor, input power are numerically determined for directly coupled symmetrical composite plate [18]. The method used to determine the modal density of any one-dimensional system requires that relationship for the mode count in terms of wavenumber, this can be done by neglecting the evanescent wave and applying the principle of wave train phase closure [23]. Analytical expression for the modal density of anisotropic plates and shell [22]. A wave based approach for evaluating damping loss factor of thick composite laminate plate with linear visco-elastic damping is done [23]. Damping loss factor values for different material have been compared. For this, different material like steel, brass, aluminum, plexiglass, rectangular plate, trapezoidal corrugated plate etc. are used [19]. Damping loss factor of composite beam made up of FRP material. They have considered volume fraction of 15% and 45%. The fiber is oriented in different angle and find out the effect of orientation on damping capacity [20]. Concept of modal density or density of eigen-values for various structural elements

3 1228 Devendra Kamble, M.B. Mandale, Dhiraj Patil International Journal of Engineering Technology Science and Research [25] discussed. Extended modal overlap factor has been used by G. Rabbiolo et al. [26] to show a high frequency threshold for plates and acoustical spaces depends upon parameters of system, damping and bandwidth of frequency averaging. A modal impedance technique has been used by A. Secgin et.al [28] for mid frequency analysis, but the approach used is statistical energy analysis (SEA). In this paper geometrical complexity and boundary condition are considered to handle mid-frequency effect. Content of this paper is used to vibration analysis of a complex structure at mid and high frequency. Damped and undamped coupled oscillator has been considered by Dante Tufanoet. al [29] for finding the transient coupling loss factor and the steady state coupling loss factor of classical SEA. The author shows the classical Statistical energy analysis method is not useful for undamped system because the undamped coupling loss factor does not converge to steady state value. Parameter variation and random excitation has been used by Xu Wang [30] to find out coupling loss factor of linear vibration energy harvesting system. This paper gives idea of Statistical energy analysis in linear vibration energy harvesting system for reliable performance, optimization under parameter variation of material, manufacturing process and random excitation. A hybrid FE-SEA method and montecarlo simulation method has been used by Yunju Yan et.al [31] to check the energy response analysis of a beam-plate built-up structure. The FE-SEA method the structural vibration and the cabin noise field response under vibro-acoustic coupling for an air-craft model and experiment is carried out to verify the simulated results. The hybrid FE-SEA method can obtain relatively precise result. This provides a new approach for the prediction of complex vibro-acoustic issue in aero-space engineering. Y. Lei et al. [32] were used statistical energy analysis method to investigate the structural response. In this they have considered structural-structural coupling and acoustical structural coupling for noise reduction. S.JosephineKelvina Florence et.al [33] investigated the modal density of composite cylindrical shell. In this paper they have discuss characteristic and sensitivity is also analyzed. In this paper modal density of composite cylindrical shell is increases with frequency and it is maximum at certain frequency beyond which it converges to modal density of flat panel. A new approach statistical modal energy distribution analysis has been used by L.Maxit et.al [34] to estimate the transmission loss ( TL) of a structure between two cavity. Statistical modal energy distribution analysis ( SmEDA ) is used as an alternative method to statistical energy analysis ( SEA ) for describing subsystem with low modal overlap. In this paper extension of SmEDA, this takes into account non-resonant modes of thin structure for estimation of transmission loss. BadrAloufi et.al [35] developed a model for vibro-acoustic behaviour of aircraft window. The result shows that at frequency sound transmission loss (STL) performance can be improved by increasing the number of window panel. A modal based technique has been used by V. Denis et.al [36] with high resolution to show acoustic black hole (ABH) significantly increases the modal overlap factor (MOF) of the beam and reducing the resonant behaviour of the structure. Transient SEA method has been used by B.Y. Mao et.al [37] to identify the impact load. In this identification first location and input energy of impact are identified by using energy balance equation, second is impact load amplitude spectrum is derived by using Parseval theorem and finally a parametric fitting approach is developed to reconstruct further time history of impact load. The present approach gives an effective and feasible way for impact load identification of engineering structure. A graph theory approach has been used by Angels Aragones et.al [38] for prediction of transmission of noise and vibration at mid-frequency range. In this paper author investigated the analogy between the graph obtained by statistical energy analysis and statistical modal energy distribution analysis. Mehran Sadri et al. [39] are used random excitation for investigating the vibroacoustic behaviour of coach platform. In this paper structure borne noise of rail was analytically studied. A plate-cavity model is considered for solving the problem and free-free condition was employed to found out the natural frequency and response of the system. Hyun-Sil Kim et al. [40] has been derived formula for insertion loss of large acoustical enclosure. In this paper they have discussed, how critical frequency affects the insertion loss of enclosure. Power injection method has been used by A. Secgin et al. [41] to find out the loss factor of different types of composite structure. Composite structure are of point connected ( I, L, and T ) type. The improved ordinary sandwich panel theory has been used by Jingyong Han et al [42] for estimating the modal density of sandwich panel. Sandwich panel composed of composite face sheet and orthotropic core for finding modal density. The wavenumber space integration method has been used to find the modal density. Hybrid power flow analysis technique has been used by Young-Ho Park et.al.[43] to predict the vibrational

4 and acoustic responses of the low-damping system in mid-to-high frequency range. In this paper hybrid boundary condition method used 3-D model. Statistical modal energy distribution analysis has been used by N. Totaro et.al. [44] to estimate the kinetic and potential energy density in coupled subsystem. Finite element analysis method has been used by A.N Thite et.al [45] to estimate the coupling loss factor. They used robust method that gives good estimation of coupling loss factor (CLF). Researcher have found out statistical energy analysis (SEA) parameter of different component like rectangular plate, right angled structure, rectangular and trapezoidal corrugated plate, ship structural panel etc. made up different materials like steel, aluminium, brass, FRP etc. in their work. The scope lies to estimate SEA parameter of simple structure made up of different material and with one of the available method which has not yet been carried out. Conclusion From this review paper it is conclude that Statistical energy analysis (SEA) method is mainly used for prediction structure born noise and Air born noise. This paper gives idea of statistical energy analysis parameter of the simple structure made up composite or conventional material. It is very useful method for prediction of transmission loss of noise and vibration in complex system. It is best suit at the system having large degree of freedom.statistical energy analysis is used for high frequency analysis. REFERENCES Text (Times New Roman, 10 points) [1] R. H. Lyon, R. G. Dejong, (1960) Theory and application of SEA, second ed. [2] Lyon RH, Maidanik G, (1962) Power flow between linearly coupled oscillator, Journal of Acoustic society, America, 34, [3] Lyon RH, Eichler E, (1964) Random vibration of connected structures, Journal of Acoustic society, America, 36, [4] Smith. P.W, (1962), Response and radiation of structural modes excited by sound, Journal of Acoustic society, America,34.5, [5] RaefCherif, Jean-Daniel Chazot, NoureddineAtalla, (2015) Damping loss factor estimation of two -dimensional orthotropic structure from a displacement field measurement, Journal of Sound and Vibration, 356, [6] J. McDaniel, P. Dupont, L. Salvino, (2000) A wave approach to estimate frequency dependent damping under transient loading, Journal of Sound vibration 231 (2) [7] AbderrazakMejdi, NoureddinAtalla, Sebastian Ghinet, (2015), Wave spectral finite element model for the prediction of sound transmission loss and damping of sandwich panels, Computers and Structures, 158, [8] C.Mei, (2005) Effect of material coupling on wave vibration of composite Euler-Bernoulli beam structure, journal of sound and vibraton288 (1-2) [9] L. S. Teoh, C. C. Huang, (1977) The vibration of beam of fiber reinforced material, Journal of sound and Vibration51 (4) [10] Richard Bachoo, (2013) Jacqueline Bridge, The modal distribution and density of fiber reinforced composite beam, Journal of sound and vibration [11] G. Xie, D.J. Thompson, C.J.C. Jones, (2004) Mode count and modal density of structural systems: relationships with boundary conditions Journal of Sound and Vibration 274, [12] J.R. Banerjee, (2001), Explicit analytical expression for fre quency equation and mode shape of composite beam, International Journal of solid and structure, 38, [13] Omer Civalek, (2007), Numerical analysis of free vibration of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach, 205, [14] C.H. Ziang, T.Y. Kam, (2013), Vibration analysis of restrained laminated composite sound radiation plate via finite element approach, 67, [15] R. Panuszka, J. Wiciak, M. Iwaniec, (2005), Experiment assessment of coupling loss factor of thin rectangular plate, Devendra Kamble, M.B. Mandale, Dhiraj Patil

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