Makine Mühendisliği Bölümü Koleksiyonu
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Article Citation - WoS: 1Citation - Scopus: 21441. Quantification of the Flow Noise in Household Refrigerators(JVE INTERNATIONAL LTD., 2014) Körük, Hasan; Arısoy, Ahmet; Bilgin, NecatiThe flow noise in household refrigerators is quantified in this study. First, the sound pressure measurements in a quiet room using typical household refrigerators are conducted and the noise characteristics of the refrigerators are presented. Then, the flow noise in household refrigerators is quantified using the results of the overall analysis and Fourier transform of the measured sound pressure data. After that, the flow noise in household refrigerators is quantified using the sound pressure measurements conducted using a specially designed test rig. The frequency characteristics of the flow noise in household refrigerators are also explored and the contribution of the flow noise is identified.Editorial 17th International Conference on Mechatronics Technology, October 15-18, 2013, Jeju Island, Korea(Elsevier, 2015) Hwang, Sung Ho; Kim, Joon-wan; Dorantes-Gonzalez, Dante JorgeIn recent years, Mechatronics has gained a lot of interest as more applications have been introduced to industry and society. The need for new mechatronic technologies in the form of advanced production systems, mechatronic devices, control systems, robotics, biomedical applications, MEMS, and measurement systems, among others, is very much required in improving productivity and competitiveness in many industries. Thus, this conference was organized to address the state-of-the-art technology for the benefit of researchers and users, and this time the conference made a special focus on the topic: Sustainable Mechatronics Technology.Article Citation - WoS: 6Citation - Scopus: 6A New Approach for Measuring Viscoelastic Properties of Soft Materials Using the Dynamic Response of a Spherical Object Placed at the Sample Interface(Springer, 2023) Besli, Ayça; Koç,Ömer Hayati; Körük,Hasan; Yurdaer, Berk SalihBackground: There are several techniques to characterize the mechanical properties of soft materials, such as the indentation method and the method based on the application of a spherical object placed inside the sample. The indentation systems usually yield the elastic properties of materials and their mathematical models do not consider the inertia of the sample involved in motion and radiation damping, while placing an object inside the sample is not practical and this procedure can alter the mechanical properties of the sample for the method based on the application of a bubble/sphere placed inside the sample. Objective: A new approach for the identification of the viscoelastic properties of soft materials using the dynamic response of a spherical object placed at the sample interface was proposed. Methods: The spherical object placed at the sample interface was pressed using an electromagnet and the dynamic response of the spherical object was tracked using a high-speed camera, while the dynamic response of the spherical object placed at the sample interface was estimated using a comprehensive analytical model. The effects of the shear modulus, viscosity, Poisson’s ratio and density of the soft sample, the radius and density of the spherical object and the damping due to radiation were considered in this mathematical model. The shear modulus and viscosity of the soft sample were determined by matching the experimentally identified and theoretically estimated responses of the spherical object. Results: The shear moduli and viscosities of the three phantoms with the gelatin mass ratios of 0.20, 0.25 and 0.29 were measured to be 3450, 4300 and 4950 Pa and 12.5, 14.0 and 15.0 Pa⋅s, respectively. The shear modulus and viscosity of the phantom increases as the gelatin mass ratio increases. The frequency of oscillations of the hemisphere placed at the phantom interface increases as the gelatin mass ratio increases due to stiffness increase. Conclusions: After matching the experimental and theoretical steady-state displacements and amplitudes of oscillations of the hemisphere at the sample interface, the comparison of the experimentally identified and theoretically predicted frequency of oscillations further confirmed the identified material properties of the samples. The approach presented here is expected to provide valuable information on material properties in biomedical and industrial applications.Article Citation - WoS: 9Citation - Scopus: 12A New Triangular Composite Shell Element With Damping Capability(Elsevier, 2014) Körük, Hasan; Şanlıtürk, Kenan YüceThis paper presents a new triangular composite shell element with damping capability. Formulation of the composite triangular shell element is based on stacking individual homogeneous triangular shell ele- ments on top of each other. The homogeneous shell element is an assembly of a triangular membrane element with drilling degrees of freedoms and a plate element. Damping capability is provided by means of complex element stiffness matrix of individual flat layers of the composite element. These elements with damping capability allow modelling general structures with damping treatments. A few test cases are modelled using triangular finite element developed here and the results of the complex eigenvalue analyses are compared with those of the quadrilateral shell elements proposed recently. The results obtained using the presented triangular and previous quadrilateral composite elements are also com- pared with those based on modal strain energy method and experimental results. Comparisons of the experimental and the theoretical results confirm that the modal properties including modal damping lev- els of structures with damping treatments can be predicted with high accuracy using the proposed finite element.Book Part Citation - WoS: 29Citation - Scopus: 36Acoustic and Mechanical Properties of Luffa Fiber-Reinforced Biocomposites(Elsevier, 2019) Genç, Garip; Körük, HasanThis chapter presents an overview of acoustic and mechanical behaviors of luffa fiber reinforced biocomposites. A growing number of studies are examining the composites of biodegradable fibers such as flax, hemp, kenaf and luffa due to the adverse effects of chemical materials on nature. The low cost and superior acoustic and acceptable mechanical properties of biocomposites make them very attractive for practical applications such as sound and vibration isolation. However, the acoustic and mechanical characteristics of biocomposites and their dynamic behaviors should be fully determined before considering them for practical applications. In this chapter, acoustic properties, such as sound absorption and transmission loss, and mechanical properties, such as damping and elasticity of luffa fiber reinforced composites, are presented. The variations in acoustic and mechanical properties due to different samples and manufacturing process are explored.Article Citation - WoS: 1Citation - Scopus: 1Acoustic Cavitation Model Based on a Novel Reduced Order Gas Pressure Law(2021) Pasinlioğlu, Şenay; Delale, Can FuadThe thermal behavior of a spherical gas bubble in a liquid excited by an acoustic pressure signal is investigated by constructing an iterative solution of the energy balance equations between the gas bubble and the surrounding liquid in the uniform pressure approximation. This iterative solution leads to hierarchy equations for the radial partial derivatives of the temperature at the bubble wall, which control the temporal rate of change of the gas pressure and gas temperature within the bubble. In particular, a closure relation for the hierarchy equations is introduced based on the ansatz that approximates the rapid change of state during the collapse of the bubble from almost isothermal to almost adiabatic behavior by time averaging the complex dynamics of change of state over a relatively short characteristic time. This, in turn, leads to the desired reduced order gas pressure law exhibiting power law dependence on the bubble wall temperature and on the bubble radius, with the polytropic index depending on the isentropic exponent of the gas and on a parameter that is a function of the Péclet number and a characteristic time scale. Results of the linear theory for gas bubbles are recovered by identifying this parameter as a function of the Péclet number based on the Minnaert frequency. The novel gas pressure law is then validated against the near-isothermal solution and against the results of the numerical simulations of the original energy balance equations for large amplitude oscillations using spectral methods. Consequently, an acoustic cavitation model that accounts for phase change but that neglects mass diffusion is constructed by employing the reduced order gas pressure law together with the Plesset–Zwick solution for the bubble wall temperature and the Keller–Miksis equation for spherical bubble dynamics. Results obtained using variable interface properties for acoustically driven cavitation bubbles in water show that the time variations of the bubble radius and the bubble wall temperature lie between those obtained by the isothermal and adiabatic laws depending on the value of the Péclet number and the characteristic time scale.Article Citation - WoS: 25Citation - Scopus: 26Acoustic Particle Palpation for Measuring Tissue Elasticity(American Institute of Physics, 2015) El Ghamrawy, Ahmed; Körük, Hasan; Choi, James J; Pouliopoulos, Antonios NWe propose acoustic particle palpation—the use of sound to press a population of acoustic particles against an interface—as a method for measuring the qualitative and quantitative mechanical properties of materials. We tested the feasibility of this method by emitting ultrasound pulses across a tunnel of an elastic material filled with microbubbles. Ultrasound stimulated the microbubble cloud to move in the direction of wave propagation, press against the distal surface, and cause deformations relevant for elasticity measurements. Shear waves propagated away from the palpation site with a velocity that was used to estimate the material’s Young’s modulus.Article Citation - WoS: 13Citation - Scopus: 17Acoustic Streaming in a Soft Tissue Microenvironment(Elsevier, 2019) El Ghamrawy, Ahmed; Mohammed, Ali; Jones, Julian R; Körük, Hasan; Choi, James J; de Comtes, FlorentinaWe demonstrated that sound can push fluid through a tissue-mimicking material. Although acousticstreaming in tissue has been proposed as a mechanism for biomedical ultrasound applications, such as neuromodu-lation and enhanced drug penetration, streaming in tissue or acoustic phantoms has not been directly observed. Wedeveloped a material that mimics the porous structure of tissue and used a dye and a video camera to track fluidmovement. When applied above an acoustic intensity threshold, a continuous focused ultrasound beam (spatialpeak time average intensity: 238 W/cm2, centre frequency: 5 MHz) was found to push the dye axially, that is, in thedirection of wave propagation and in the radial direction. Dye clearance increased with ultrasound intensity andwas modelled using an adapted version of Eckart’s acoustic streaming velocity equation. No microstructuralchanges were observed in the sonicated region when assessed using scanning electron microscopy. Our study indi-cates that acoustic streaming can occur in soft porous materials and provides a mechanistic basis for future use ofstreaming for therapeutic or diagnostic purposes.Article Citation - WoS: 54Citation - Scopus: 64An Assessment of the Performance of Impedance Tube Method(Institute of Noise Control Engineering, 2014) Hasan KörükThe impedance tube method is widely used for measuring sound absorption (or reflection) coefficients of acoustic materials as a function of frequency. However, the sound absorption coefficients obtained using the impedance tube method may have some variations due to the dimensions (limits) of an impedance tube, sample preparation and sample mounting. This paper assesses the performance of the two-microphone impedance tube method as a function of frequency for different tube dimensions and materials and presents suggestions for increasing the reliability and repeatability of impedance tube measurements. First, after summarizing a systematic way for measuring acoustic transfer functions, sound absorption coefficients of a variety of materials ranging from conventional absorbing acoustic materials to samples with thin films are measured using two tubes with different tube diameter and microphone spacing. Uncertainty of sound absorption coefficients for various materials is discussed, and the frequency limits of impedance tubes are assessed. Then, a method for minimizing uncertainty due to sample mounting is proposed and the main findings are discussed.Article Citation - WoS: 4Citation - Scopus: 4Application of Ultrasonic Vibrations for Minimization of the Accumulation of Limescale in Steam Irons(Elsevier, 2018) Körük, Hasan; Şanlıtürk, Kenan Yüce; Serenli, MuzafferThe accumulation of limescale in steam irons can significantly reduce the ironing efficiency. It is this problem that inspired us to introduce ultrasonic vibrations to irons in order to minimize limescale accumulation. This study describes a methodology for designing, modelling and optimizing an iron fitted with an ultrasonic exciter in an attempt to minimize limescale accumulation. In our methodology, first, an experimental demonstration of the potential benefits of ultrasonic vibrations in steam irons was conducted, using two existing irons, one of which was equipped with an ultrasonic exciter. Having confirmed the benefits, an experimental iron was designed and then optimized to maximise ultrasonic vibrations using finite element analyses within a predefined frequency range. To validate the results of the finite element analyses, a prototype iron base was built, and forced vibrations of this prototype, at ultrasonic frequencies ranging from 35 to 40 kHz, were measured using a laser vibrometer. The results of the theoretical and experimental vibration analyses as well as the physical experiments on the steam irons indicate that it is possible for ultrasonic vibrations to be utilized in irons to minimize the accumulation of limescale.Article Citation - WoS: 2Citation - Scopus: 2Approximate Closed-Form Solutions for Vibration of Nano-Beams of Local/Non-local Mixture(Springer, 2022) Ruta, Giuseppe; Eroğlu, UğurcanThis paper presents an approach to natural vibration of nano-beams by a linear elastic constitutive law based on a mixture of local and non-local contributions, the latter based on Eringen's model. A perturbation in terms of an evolution parameter lets incremental field equations be derived; another perturbation in terms of the non-local volume fraction yields the variation of the natural angular frequencies and modes with the 'small' amount of non-locality. The latter perturbation does not need to comply with the so-called constitutive boundary conditions, the physical interpretation of which is still debated. The possibility to find closed-form solutions is highlighted following a thorough discussion on the compatibility conditions needed to solve the steps of the perturbation hierarchy; some paradigmatic examples are presented and duly commented.Article Citation - WoS: 10Citation - Scopus: 20Assessment of the Measurement and Prediction Methods for the Acoustic Properties of Natural Fiber Samples and Evaluation of Their Properties(Taylor & Francis, 2021) Körük, HasanAlthough some studies have been conducted to show how natural fibers canreplace synthetic materials, the use of many natural fibers is still limited. Onthe other hand, the use of natural fibers can become very common in manyapplications once their performance is fully understood. This paper aims topresent a critical assessment of the acoustic properties of natural fibersamples. First, the methods commonly used for the measurement and prediction of the acoustic properties of natural fiber samples are determined.Second, the common techniques for measuring sound absorption coefficients (SACs) and sound transmission losses (STLs) are presented, and theiradvantages and limitations are evaluated. After that, the models commonlyused for the prediction of acoustic properties are presented. Then, the SACsof many natural fiber samples are presented along with the thickness, bulkdensity and flow resistivity of the samples. Furthermore, the SACs of thesamples are normalized using sample thickness and bulk density, and thesound absorption performance of the fiber samples is evaluated. Based onthe results of many natural fiber samples, an empirical model for estimatingthe SACs of natural fiber samples is presented. Finally, the STLs of someporous natural fiber samples are presented.Article Citation - WoS: 15Citation - Scopus: 13Calibration of the Effective Spring Constant of Ultra-Short Cantilevers for a High-Speed Atomic Force Microscope(2015) Xu, Lin-Yan; Wu, Sen; Hu, Xiao-Dong; Song, Yun-Peng; Fu, Xing; Zhang, Jun-Ming; Dorantes-Gonzalez, Dante JorgeUltra-short cantilevers are a new type of cantilever designed for the next generation of high-speed atomic force microscope (HS-AFM). Ultra-short cantilevers have smaller dimensions and higher resonant frequency than conventional AFM cantilevers. Moreover, their geometry may also be different from the conventional beam-shape or V-shape. These changes increase the difficulty of determining the spring constant for ultra-short cantilevers, and hence limit the accuracy and precision of force measurement based on a HS-AFM. This paper presents an experimental method to calibrate the effective spring constant of ultra-short cantilevers. By using a home-made AFM head, the cantilever is bent against an electromagnetic compensation balance under servo control. Meanwhile the bending force and the cantilever deflection are synchronously measured by the balance and the optical lever in the AFM head, respectively. Then the effective spring constant is simply determined as the ratio of the force to the corresponding deflection. Four ultra-short trapezoid shape cantilevers were calibrated using this method. A quantitative uncertainty analysis showed that the combined relative standard uncertainty of the calibration result is less than 2%, which is better than the uncertainty of any previously reported techniques.Article Citation - WoS: 3Citation - Scopus: 3Characterization of Viscoelastic Materials Using Free-Layered and Sandwiched Samples: Assessment and Recommendations(Polish Physical Society, 2015) Özer, Mehmet Sait; Körük, Hasan; Şanlıtürk, Kenan YüceViscoelastic materials are widely used in many applications in practice. However, determination of the elastic and damping properties of these materials is quite difficult in the sense that the identified results may contain high degree of uncertainty. The characterization of viscoelastic materials using the Oberst beam method, based on non-contact excitation and response measurements, is revisited in this paper. The effects of signal processing parameters such as frequency resolution in Frequency Response Function (FRF) measurements, as well as the effects of various single-degree-of-freedom modal analysis methods, including circle-fit, half-power and line-fit are investigated first. Then, the modal loss factors, Young's modulus and shear modulus of some sample viscoelastic materials are identified using both the free-layered and sandwiched samples. The results obtained from different tests are compared, discussed and some recommendations are made so as to identify the damping and elastic properties of typical viscoelastic materials with better accuracy. Analyses of a large number of FRF measurements show that the selection of the appropriate signal processing parameters and the use of appropriate modal analysis method can be very significant during the identification of viscoelastic materials. By following the approach presented in this paper, the damping and elastic properties of viscoelastic materials can be identified with better accuracy using either free-layered or sandwiched samples. The material properties obtained by this approach can be used for developing valid structural models and/or for damping optimization purposes.Article Citation - WoS: 10Citation - Scopus: 11Computational Alloy Design, Synthesis, and Characterization of Wmonbvcrx Refractory High Entropy Alloy Prepared by Vacuum Arc Melting(Elsevier Ltd, 2024) Alkraidi, A.B.N.; Mansoor, M.; Boztemur, B.; Gökçe, H.; Kaya, F.; Yıldırım, C.; Öveçoğlu, M.L.Prior investigations have demonstrated enhanced mechanical properties, such as hardness and wear resistance, through high-entropy alloy designs that contain refractory metals. We propose the WMoNbVCrx alloy phase space as a single-phase BCC-structured, hard, and refractory high-entropy alloy for the first time. The WMoNbVCrx alloy (x = 0, 0.25, 0.5, 0.75, and 1) system is investigated computationally through CALPHAD and DFT for the equimolar and non-equimolar compositional phase spaces and synthesized through vacuum arc melting. The DFT calculations demonstrated the excellence of specific non-equimolar compositional spaces. It was found that stoichiometries rich in W and poor in V are exceptionally hard, while those rich in V and poor in W demonstrate unprecedented toughness, as determined by the ductility descriptor (Pugh's Ratio). The computational analysis shows the significance of microstructures that contain both (W-rich and W-poor) solid solution, where a synergy between hardness and toughness is created. Our experimental synthesis using vacuum arc melting demonstrated the possibility of successfully producing these alloys with W-rich (dendritic) and W-poor (interdendritic) solid solution regions, starting from elemental powders. The introduction of chromium (Cr) resulted in enhanced microhardness and wear resistance. The peak microhardness was attained when 0.5 moles of Cr were added, reaching 7.03 ±0.24 GPa, accompanied by the least wear volume loss. The produced alloys were found to align with the computationally predicted-designed alloys in terms of the hardness and Young's modulus trends that they follow. This comprehensive investigation underscores the synergistic application of CALPHAD and DFT techniques in the tailored design of novel high-entropy alloys, explaining their synthesis, structural correspondence, and the pivotal role of Cr in enhancing the mechanical properties of these alloys. © 2024 Elsevier B.V.Article Citation - WoS: 6Citation - Scopus: 10Detection of Air Leakage Into Vacuum Packages Using Acoustic Measurements and Estimation of Defect Size(Elsevier, 2019) Körük, Hasan; Şanlıtürk, Kenan YüceAir leakages in food and ingredient packages which are sealed in vacuum environments may cause a marked deterioration of the product, leading to a loss of functionality. Manufacturers of such products have very stringent but rather costly quality control procedures and there is a pressing need for developing more economical ways of automated quality control techniques to test the vacuum packages reliably. However, due to the fact that the defect size of a typical package with a leakage problem could be micro- or nano-scale, such faults are not detectable using conventional techniques. In this paper, the performance of a proposed acoustic method is assessed for the detection of air leakage in instant dry yeast packages sealed in a vacuum environment, which are typical of food and ingredients packaged under vacuum conditions. The investigation is carried out in both laboratory and in-situ environments. The acoustic pressure created by leaking air into the faulty packages is measured using a low-noise microphone in an acoustic chamber. Faulty packages are then identified using the changes in measured sound pressure levels within a certain frequency band. A mathematical model is also proposed to predict the pressure inside a yeast package with certain defect size as a function of time. The mathematical model is then used to determine the size of a defect causing the leakage, using the time required for the pressure inside a faulty yeast package to reach to a threshold level. The results of this investigation show that, using the state of the art measurement techniques, it is possible to detect packages with leakage problem if the diameter of the defect is greater than a few tens of micrometres.Article Citation - WoS: 44Citation - Scopus: 45Development of a Multigenerational Energy System for Clean Hydrogen Generation(Elsevier Ltd, 2021) Dinçer, İbrahim; Karapekmez, ArasThe existing fueling options for many power plants are still dependent primarily on fossil fuel resources, which in return cause serious local and global environmental problems. Therefore, in order to reduce the detrimental effects of greenhouse gas emissions, the use of cleaner production methods has been accelerated to develop and implement environmentally- friendly energy systems. In this regard, the combination of renewable energy systems and hydrogen production methods will definitely play a crucial role in the energy sector’s transition to a carbon-free production. In order to make the use of geothermal energy cleaner and more sustainable, some obstacles need to be eliminated. Most importantly, the hydrogen sulfide emissions may cause serious concerns in public acceptance of geothermal power plants. In the current study, solar, wind and geothermal energy resources are integrated to develop an integrated renewable-based energy system with a key objective of higher environmental and system performance. The underlying motivation is to propose a model which consists of a hydrogen sulfide abatement unit and an electrolyzer to produce hydrogen from hydrogen sulfide and hence eliminites the hydrogen sulfide emissions. A detailed thermodynamic analysis is carried out using Engineering Equation solver (EES) software. In addition, the effects of key design parameters and operating conditions (such as wind inlet speed and average hourly solar radiation) are analyzed, and their effects on the system overall performance are investigated. When 60 kg/s of geothermal fluid is supplied to the designed system, assuming that the NCG composition is equal to 15%, 0.7388 kg hydrogen sulfide will be emitted and 0.0433 kg hydrogen will be produced per second. The first-law (energy) and second-law (exergy) efficiencies are found to be 52.97% and 55.69% respectively.Article Citation - WoS: 27Citation - Scopus: 29Development of a New Integrated Energy System With Compressed Air and Heat Storage Options(Elsevier, 2020) Javania, Nader; Dinçer, İbrahim; Karapekmez, ArasThe present study investigates a biomass driven power plant integrated with compressed air and thermal energy storage subsystems. Compressed air energy storage system exploits the pressurized air at non-peak periods to be used in peak times when there is a need for extra energy. Thermal energy storage systems including phase change material, allow the solar subsystem to operate independently in order to produce hot air when solar irradiation is insufficient. The energy stored in the present system is then supplied to both the gasifier and combustion chamber in order to achieve a higher combustion efficiency. Three different phase change materials (PCMs) are investigated and their efficiencies are comparatively evaluated. Among the considered PCMs, LiNO3 is the most suitable material for the considered system with 82% energy efficiency and 84% exergy efficiency. The current study also aims at designing a renewable energy based power plant which operates continuously through using storage subsystems and is more environmental benign compared to fossil fuel based conventional systems. In this regard, wet wood (CH1.46O0.64N0.002) with 15% moisture content is selected as a fuel instead of fossil-based fuels in order to reduce the greenhouse gas emissions and eliminate the dep endency on fossil fuels. A comprehensive thermodynamic analysis is conducted to evaluate the entropy generations, exergy destructions, and energy and exergy efficiencies. The highest overall energy and exergy efficiencies are obtained as 28.58% and 24.08% in the discharging period, respectively.Article Citation - WoS: 34Citation - Scopus: 37Development of a New Solar, Gasification and Fuel Cell Based Integrated Plant(Elsevier, 2021) Dinçer, İbrahim; Karapekmez, ArasDespite its shortcomings, fossil-based fuels are still utilized as the main energy source, accounting for about 80% of the world's total energy supply with about one-third of which comes from coal. However, conventional coal-fired power plants emit relatively higher amounts of greenhouse gases, and the derivatives of air pollutants, which necessitates the integration of environmentally benign technologies into the conventional power plants. In the current study, a H2–CO synthesis gas fueled solid oxide fuel cell (SOFC) is integrated to the coal-fired combined cycle along with a concentrated solar energy system for the purpose of promoting the cleaner energy applications in the fossil fuel-based power plants. The underlying motivation of the present study is to propose a novel design for a conventional coal-fired combined cycle without altering its main infrastructure to make its environmentally hazardous nature more ecofriendly. The proposed SOFC integrated coal-fired combined cycle is modeled thermodynamically for different types of coals, namely pet coke, Powder River Basin (PRB) coal, lignite and anthracite using the Engineering Equation Solver (EES) and the Ebsilon software packages. The current results show that the designed hybrid energy system provide higher performance with higher energy and exergy efficiencies ranging from 70.6% to 72.7% energetically and from 35.5% to 43.8% exergetically. In addition, carbon dioxide emissions are reduced varying between 18.31 kg/s and 30.09 kg/s depending on the selected coal type, under the assumption of 10 kg per second fuel inlet.Article Citation - WoS: 9Citation - Scopus: 11Development of an Equivalent Shell Finite Element for Modelling Damped Multi-Layered Composite Structures(Elsevier, 2020) Şanlıtürk, Kenan Y.; Özer, Mehmet Sait; Körük, HasanA new equivalent shell finite element (FE) for modelling damped multi-layered structures is presented in this study. The method used for developing the new FE for such structures is based on the idea that the strain energy of the equivalent single-layer FE must be equal to the sum of the strain energies of individual layers. The so-called energy coefficients are defined for this purpose for the extensional, bending and shear deformations of the composite structure. These coefficients are then determined and used as correction multipliers during stacking the elemental matrices of individual layers. Two approaches, based on second-order strain or stress distribution assumption through the composite thickness, are investigated for deriving the shear energy coefficients. The damping capability of the FE developed here originates from using complex Young's modulus to define the material properties of individual layers. The resulting equivalent single-layer shell element with four nodes has six degrees-of-freedom per node. The accuracy, advantages and limitations of the composite FE developed in this work are investigated using experimental as well as theoretical results. In the light of the finding of these investigations, further enhancement in the formulation is made by also utilising a new shear correction factor for the individual layers in the equivalent shell element. Final results for free- and constrained-layered structures confirm that the equivalent shell FE developed here can be used effectively for the prediction of the modal properties of damped multi-layered structures.
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