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Genc, G., and Koruk, H. (2017). "Identification of the dynamic characteristics of luffa fiber reinforced bio-composite plates," BioRes. 12(3), 5358-5368.

Abstract

Luffa cylindrica plant fiber is a new biodegradable engineering material. However, the dynamic behaviors of these new green materials or their composites should be explored to consider them for practical applications. The dynamic characteristics including modal behavior and the elastic and sound isolation properties of luffa-based bio-composite plates were explored in this study. Structural frequency response function measurements were conducted using a few luffa bio-composite plates to identify their modal behavior. The modal frequencies and loss factors of the luffa bio-composite plates were identified by analyzing the frequency response function measurements using a few modal analysis methods such as half-power, circle-fit, and line-fit. The same luffa bio-composite structures were modelled using a finite element formulation with damping capability, and the elastic moduli of the composite plates were identified. In addition, the transmission loss levels of the same luffa composite samples were measured using the impedance tube method. The results showed that luffa composite structures have considerably high stiffness (elasticity modulus: 2.5 GPa), damping levels (loss factor: 2.6%), and transmission loss level (25 to 30 dB for a 1 cm thickness), and their mechanical properties are promising as an alternative disposable material for noise and vibration control engineering applications.


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Identification of the Dynamic Characteristics of Luffa Fiber Reinforced Bio-Composite Plates

Garip Genc,a,* and Hasan Koruk b

Luffa cylindrica plant fiber is a new biodegradable engineering material. However, the dynamic behaviors of these new green materials or their composites should be explored to consider them for practical applications. The dynamic characteristics including modal behavior and the elastic and sound isolation properties of luffa-based bio-composite plates were explored in this study. Structural frequency response function measurements were conducted using a few luffa bio-composite plates to identify their modal behavior. The modal frequencies and loss factors of the luffa bio-composite plates were identified by analyzing the frequency response function measurements using a few modal analysis methods such as half-power, circle-fit, and line-fit. The same luffa bio-composite structures were modelled using a finite element formulation with damping capability, and the elastic moduli of the composite plates were identified. In addition, the transmission loss levels of the same luffa composite samples were measured using the impedance tube method. The results showed that luffa composite structures have considerably high stiffness (elasticity modulus: 2.5 GPa), damping levels (loss factor: 2.6%), and transmission loss level (25 to 30 dB for a 1 cm thickness), and their mechanical properties are promising as an alternative disposable material for noise and vibration control engineering applications.

Keywords: Bio-composites; Luffa Composites; Elastic Properties; Damping Levels; Transmission Loss; FEM Modeling

Contact information: a: Mechanical Department, Marmara University, 34722, Istanbul, Turkey; b: Mechanical Engineering Department, MEF University, 34396 Istanbul, Turkey;

* Corresponding author: ggenc@marmara.edu.tr

INTRODUCTION

Petroleum-based materials are widely used in the industry due to their superior features such as high strength and low density. However, finding and developing new materials as alternatives to these chemical materials is necessary due to their adverse effects including the enormous amount of carbon dioxide released into the atmosphere resulting from the burning of such substances (Wambua et al. 2003). The use of natural fibers for the reinforcement of composite structures has received increasing attention (Wambua et al. 2003; Chen and Lin 2005; Cheung et al. 2009; Xu et al. 2012). Luffa cylindrica fibers (also called loofah or sponge gourd) are a noteworthy alternative to mineral fibers. Their low cost and low density are the major benefits for their use in composites (Boynard and d’Almeida 2000; Chen and Lin 2005; Paglicawan et al. 2005; Zampieri et al. 2006; Demir et al. 2008; Kocak 2008; Seki et al. 2012; Shen et al. 2013). However, the characteristics (especially the dynamic or modal properties) of these new materials should be investigated in order to use them effectively in practical applications such as vibration attenuation of machines and sound isolation of conference rooms.

As reported in the literature, the sound absorption coefficient of flax fiber reinforced composites is approximately 25% higher than that of glass fiber reinforced composites, and the vibration damping of flax fiber reinforced composites is approximately 50% higher than that of glass fiber reinforced composites (Prabhakaran et al. 2014). Some other studies on natural fibers such as ramie, flax, jute, and broom fibers (Zhu et al. 2014; Yang and Li 2012; Umberto et al. 2017) suggest that natural fibers and their composites could be a viable candidate for noise and vibration applications.

There have been some studies on the morphology, thermodynamics, energy absorption, and elastic properties of luffa materials (Boynard and D’Almeida 2000; Chen and Lin 2005; Paglicawan et al. 2005; Zampieri et al. 2006; Demir et al. 2008; Kocak 2008; Ghali et al. 2009; Satyanarayana et al. 2009; Seki et al. 2012; Shen et al. 2012, 2013; Kocak et al. 2013; Genc 2015; Genc and Koruk 2016a). Koruk and Genc (2015) showed that the sound absorption of luffa composites is considerably high. It was shown that the sound absorption coefficients of luffa composite samples (with a thickness of 10 mm) are 0.3 and 0.7 when the luffa/epoxy ratio is 1.5 and 4, respectively, for the frequency of 6 kHz. It is seen that that the sound absorption coefficients of luffa fiber and their composites are comparable with those of traditional acoustic materials (Ersoy and Kucuk 2009; Koruk 2014a). It is worth remembering that the sound absorption coefficient of a widely used conventional material, i.e., a polyester and poly-propylene based material with a thickness of 10 mm, is 0.5 for the frequency of 6 kHz (Ersoy and Kucuk 2009). On the other hand, as previously reported (Genc and Koruk 2016b), the difficulties and restrictions during the manufacturing process of the composites combined with the defects and structural differences in raw bio materials such as luffa plant result in large variations in mechanical properties. This is a disadvantage of all natural fibers.

For practical applications, composites of natural fibers including luffa should have not only superior acoustic properties (i.e., sound absorption and transmission loss) but also acceptable elastic and damping properties. In this study, the modal behavior of a few luffa bio-composite plates were explored based on structural frequency response function measurements. The elastic properties of these structures were extracted by using a finite element formulation with damping capability, and the transmission loss levels of luffa bio-composite samples were determined using impedance tube measurements.

EXPERIMENTAL AND THEORY

Materials

Luffa cylindrica fibers of the Mediterranean region of Turkey were used to prepare composites. Hybrid composites (without any modification) were produced in this study, though some previous studies (Kocak et al. 2013; Jayamani et al. 2014; Wang et al. 2016) studied the effect of surface modification. It should be noted that sufficient adhesion was observed at the interface between the fiber and matrix. Epoxy resin was used as a matrix to produce the composite specimens. The volume fraction of the luffa fiber was 60 percent, and the material was compressed with a pressure of p = 500 kPa and cured at T = 80 C for 300 minutes. Three L. cylindrica plants with an approximate diameter of 110 mm and length of 225 mm (Fig. 1a) were used to manufacture three composite plates (Fig. 1b) in this study.

The length and width of the plates were 200 mm and 100 mm, respectively. The densities and thicknesses of the composite plates had small differences because the three different L. cylindrica fibers were used. The density and thickness values for the so called Luffa-1, Luffa-2, and Luffa-3 plates were ρ = 777.8, 800.0, and 857.1 kg/mand h = 5.4, 4.5, and 4.9 mm, respectively. Here, the density of each plate was calculated by using its measured mass and dimensions (or volume).

Methods

Frequency response function measurements

The frequency response function measured using the luffa bio-composite plates is expressed by Eq. 1 (Ewins 2000),

(1)

where and are the Fourier transforms of the time domain excitation force  applied at the point j and the vibration acceleration  measured at point i, respectively, t is time, ω is the excitation frequency, and the superscript  indicates the complex conjugate. A instrumented impact hammer (Endevco 2302-10) and a lightweight piezoelectric (B&K 4507B) accelerometer (mass of about 4.5 g) were used for the frequency response function measurements. First, preliminary Hij () measurements were conducted to determine the best signal processing parameters. For example, the measurement period was selected to be long enough so that there was no need to apply any windowing functions to the signals. Therefore, there was minimal uncertainty in the identified modal loss factors. The experiments were also performed under free-free boundary conditions to eliminate uncertainty due to boundary damping and stiffness. The free-free boundary conditions were provided by hanging the test sample using a fishing line. This method is quite common in practice as the effect of the interaction between a light fishing line and test structure is almost negligible (Ewins 2000; Koruk 2014b). The Hij () measurements were conducted with a frequency resolution of  = 2 Hz (or with a period of T = 0.5 s), and each power spectrum was estimated using N = 5 averages. The auto spectrum of the force signal was examined to ensure that the structure was adequately excited over the frequency range of interest. The coherence function ij () was also checked to assess the quality of measurements.

Extraction of modal parameters

Half-power, circle-fit and line-fit methods were used to identify modal loss factors using measured structural frequency response functions . In the half-power method (Ewins, 2000), the loss factor (  ) for mode r is determined by Eq. 2,

 (2)

where  and  are the frequencies corresponding to half power points around  In the circle-fit method (Kennedy 1947), the modal loss factor is determined by Eq. 3,

 (3)

where the frequencies r,a and r,b correspond to the angles r,a and r,b around r when the  function is plotted using the Nyquist diagram (Kennedy 1947; Ewins 2000). In the line-fit method (Dobson 1987), which is very effective for the determination of modal parameters (Koruk and Sanliturk 2011a), an inverse parameter is defined for modal analysis given by Eq. 4,

 (4)

where  is the so called modal constant for the mode corresponding to i and j. The inverse parameter in Eq. 4 is separated into real and imaginary parts, which fit onto a line when plotted against ω2.

The modal parameters are then estimated by determining the best lines that provide the best fits for the measured data (Kennedy 1947; Dobson 1987; Ewins 2000; ICATS 2009; Koruk and Sanliturk 2011a; Koruk et al. 2014).

Extraction of elastic properties of luffa bio-composites

Notably, luffa material has a special structure in which the fibers are interlocked. A recently developed finite element formulation with damping capability (Sanliturk and Koruk 2013, Sanliturk and Koruk 2014; Koruk 2014b) was used to model the luffa composite plates. This formulation is based on complex eigenvalue method, and the damping capability is added to the element by defining the complex elasticity modulus of the material as  , where E and are the storage elasticity modulus and the loss factor, respectively.

The specific shell element utilized in this formulation includes the physical drilling degrees of freedom in the normal direction to the element (Sanliturk and Koruk 2013). After the elemental stiffness and mass matrices are obtained, these matrices are transformed to a common global coordinate system and the modal frequencies and damping levels for a bio-composite luffa plate can be obtained by solving the conventional eigenvalue problem given by Eq. 5,

 (5)

where K and M are the global stiffness and mass matrices of the structure, respectively, 2 is the eigenvalue, and is the eigenvector. The solution of the eigenvalue problem above results in eigenvalues (r2) and eigenvectors (r). The natural frequencies (r) and loss factors (r) are determined by defining  and using the following equations. Here, the plates are modelled using a fine mesh (n = 800 elements).

 (6)

 (7)

Measurement of transmission loss levels of luffa bio-composites

The transmission loss levels of the luffa bio-composite samples were identified using an impedance tube with four microphones. A B&K Type 4206 T small tube setup was used for measurements, and the calculation of the transmission loss levels was based on the four-microphone transfer-function method (ASTM E2611-09 Standard 2009; Bolton et al. 2007; Pulse LabShop 2013). For this purpose, circular luffa bio-composite samples with a diameter d of approximately 30 mm were prepared.

As it was difficult to measure the transmission loss of the luffa bio-composite samples with thicknesses of h = 5 mm using the impedance tube, thicker samples (h = 10 mm) were prepared using the manufacturing method explained before.

RESULTS AND DISCUSSION

Frequency Response Function Measurements

A number of frequency response function measurements were conducted for various impact and response locations of the plate samples. The sample time domain  and  signals, and  spectrums, and  frequency response and  coherence functions for the Luffa-1 composite plate are plotted in Fig. 2. The signals approached zero at the end of the measurement period. Also, the force spectrum decreased dramatically after f = 1.5 kHz due to the inability to properly excite the structure beyond this frequency, and the effect of damping at higher frequencies; hence, the measurements were conducted up to f = 1.5 kHz. Furthermore, the coherence function was at least  = 0.999 at and around the natural frequencies. Notably, the frequency domain based methods used data at and around natural frequencies to identify modal parameters. It should be noted that coherence function indicates how much of the output is due to the input and it is an indicator of the quality of the frequency response function measurement (Ewins 2000). Overall, the  functions were measured using the Luffa-1, 2, and 3 composite plates using the determined data acquisition and signal processing parameters. Their modal parameters (below f = 1.5 kHz) were extracted as described in the next section.

Extraction of Modal Parameters

The natural frequencies and modal loss factors of three luffa bio-composite plates are listed in Tables 1 through 3. The modal frequencies for the three luffa plates were similar, with less than 10% standard deviations in modal frequencies for the given first six modes. While some variations were due to the small differences in densities and thicknesses of the plates, some deviations may have occurred due to differences of the properties of different cylindrica fibers.

Table 1. Identified Natural Frequencies and Modal Loss Factors of the Luffa-1 Bio-Composite Plate

Table 2. Identified Natural Frequencies and Modal Loss Factors of the Luffa-2 Bio-Composite Plate

*Could not be identified with high accuracy using the individual response function

Table 3. Identified Natural Frequencies and Modal Loss Factors of the Luffa-3 Bio-Composite Plate

*Could not be identified with high accuracy using the individual response function

The differences between the modal loss factors identified using the half-power, circle-fit, and line-fit methods were small. For example, the average loss factors of the Luffa-1 bio-composite plate in the frequency range of interest were η = 2.65, 2.68, and 2.53% when the half-power, circle-fit, and line-fit methods, respectively, were used. In general, the identified damping levels using the line-fit method were a little bit smaller than those of the other methods. The modal loss factors for the three luffa plates were quite close. The standard deviation in the first modal frequencies was 9.4%, and the deviations were less than 2.2% for the second to sixth modes. Although the modal loss factors of the first modes of the bio-composite plates were a bit higher, the damping variation with respect to the frequency was low. A few potential reasons for the higher levels and larger variations for the damping of the first mode are the mass loading effect of the accelerometer, the adverse effect of the frequency resolution and the additional damping due to the air around the structure being more apparent at lower modes (ICATS 2009; Koruk and Sanliturk 2011a; Sanliturk and Koruk 2013; Koruk 2014b; Koruk et al. 2014). Overall, the average loss factors of the Luffa-1, 2, and 3 bio-composite plates in the frequency range of interest were η = 2.62, 2.53, and 2.57%, respectively. It is seen that the modal loss factors of luffa composite samples are higher than those of conventional materials such as glass composites and steel (Prabhakaran et al. 2014; Koruk and Sanliturk 2010) though the modal loss factors of luffa composite samples are less than those of conventional viscoelastic damping materials (Koruk and Sanliturk 2011b). The modal frequencies and loss factors for the three luffa plates produced from different L. cylindrica fiber materials were similar to each other (Tables 1 through 3). The standard deviations in modal frequencies and loss factors were less than 10% for the given first sixth modes; some variations were due to the small differences in densities and thicknesses of the plates. It is clear that the modal properties of luffa bio-composite structures can be maintained within some limits.

Extraction of Elastic Properties of Luffa Bio-composites

The elasticity moduli of the luffa bio-composite plates were determined by comparing experimental and theoretical modal parameters. Importantly, the loss factors for the Luffa-1, 2, and 3 bio-composite plates used in modal analyses were c,Luffa-1 =2.62%, c,Luffa-2 =2.53%, and c,Luffa-3 =2.57%, respectively, in the frequency range of interest. The Poisson’s ratio was assumed to be v = 0.3 (Wang et al. 2015). Overall, the elasticity moduli of the luffa bio-composite plates were Ec,Luffa-1 = 2.55 GPa, Ec,Luffa-2 = 2.45 GPa, and Ec,Luffa-3 = 2.40 GPa.

Table 4. Differences between the Measured and Predicted Natural Frequencies of the Luffa Bio-Composite Plates using the Identified Material Properties

The differences between the measured and predicted natural frequencies of the luffa bio-composite plates using the identified material properties are compared in Table 4. The experimental and theoretical natural frequencies of the luffa bio-composite plates were similar; the average differences between the experimental and theoretical natural frequencies were 1.3, 0.5, and 1.1% for the Luffa-1, 2, and 3 bio-composite plates, respectively, when the identified material properties of the luffa bio-composite plates are used.

Transmission Loss Levels of Luffa Bio-composites

The transmission loss levels of the luffa bio-composite samples are presented for f = 500 to 6400 Hz in Fig. 3. The transmission loss values of the luffa bio-composite samples were similar. The transmission loss decreased from f = 0.5 to 1 kHz and then increased from f = 1 to 2 kHz. There was approximately a 3 dB/octave increase in the region of approximately f = 2 to 5 kHz. The transmission loss values of the luffa bio-composite samples with h = 1 cm were 25 to 30 dB for f = 2 to 6 kHz.

Fig. 3. The measured transmission loss levels of the luffa bio-composite samples

The elasticity modulus and loss factors of the three bio-composite structures were Ec = 2.47 ± 0.06 kPa and c = 2.57 ± 0.04%, respectively. High values of transmission loss and damping levels are desired for sound isolation and vibration attenuation. The transmission loss values of the thin luffa bio-composite samples with h = 1 cm were quite high, being 25 to 30 dB for f= 2 to 6 kHz. It should be underlined that the transmission loss level of a cement panel of 1 cm is 25 to 30 dB at 2 kHz (Ng and Hui 2008). The considerably high values of both elasticity moduli and damping levels as well as high values of transmission loss levels for luffa bio-composite structures make them very attractive for a variety of applications, including sound isolation and vibration attenuation in practical applications.

The surface chemical modification on the fibers improves the bonding between the fiber and the matrix interface; hence, it changes the mechanical properties of luffa composites (Kocak et al. 2013). The structural defects and differences caused between the sowing and harvesting periods of natural fibers result in some variations in the mechanical properties of luffa composites (Genc and Koruk 2016b).

It should be noted that the examined composite is not fully environmental friendly because of the chemical resin used. The search for natural resins that are alternatives to chemical resins is ongoing. Consequently, it might be possible to manufacture a green luffa composite in near future.

CONCLUSIONS

  1. Modal frequencies and loss factors of a few luffa bio-composite plates were identified by analyzing the frequency response functions measured using the luffa composite plates and a few modal analysis methods.
  2. The elastic moduli of luffa composites were determined by modelling the luffa composite plates using a finite element formulation with damping capability.
  3. The transmission loss levels of the luffa composite samples were determined using the impedance tube experiments.
  4. Modal frequencies and loss factors of composite plates made from different luffa cylindrica fiber materials are close to each other.
  5. The identified loss factors of luffa composite plates are quite high (i.e., 2.6%).
  6. The luffa bio-composite plates have considerably high elasticity moduli (i.e., 2.5 GPa) and transmission loss levels (i.e., 25 to 30 dB for a thickness of 1 cm).
  7. These superior features of luffa composites as well as their low densities, costs, and degradability feature make the luffa composites very attractive for various noise and vibration control engineering applications.

ACKNOWLEDGEMENTS

This research is supported by Marmara University, Scientific Research Projects Committee (BAPKO) with grant number FEN-A-110913-0377. The authors would like to thank Prof. H. Temel Belek (Pro-Plan Proje Müh. San. ve Tic. Ltd. Şti., Istanbul, Turkey) and Mr. Philippe Callec (Brüel & Kjær Sound & Vibration Measurement A/S, Nærum, Denmark) for fruitful discussions on dynamic behavior of luffa composites and sound transmission loss measurements of plates using the impedance tube method.

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Article submitted: Dec. 1, 2016; Peer review completed: March 3, 2017; Revised version received and accepted: April 18, 2017; Published: June 7, 2017.

DOI: 10.15376/biores.12.3.5358-5368