[15]
All the models used in numerical analysis share a common representation of the viscoelastic layer using solid CHEXA element. The lower layer and constraining layer are both modeled by solid element. First by using modal analysis of individual CLD beam, the frequency of bending modes are obtained and then the harmonic analysis corresponding to frequency of bending modes is performed . Numerical results in terms of the modal strain energy (MSE) are illustrated and the damping effects are emphasized. In the method of MSE, the system loss factor (system damping), ηr is directly proportional to the ratio of the energy dissipated in the viscoelastic elements to the energy stored in the entire system through one cycle of vibration.
DOI: 10.1002/9781118537619.ch5
Google Scholar
[16]
This ratio is then multiplied by the Loss factor of the viscoelastic material as explained in equation (1) ηr=ηv Uvr UTotr (1) By using above equation(1), the modal loss factor corresponding to mode 3 of three sandwich CLD beams are found and shown in Table 3. 5. Experimental investigation The damping performance of CLD beams is often quantified in terms of system loss factor and it is determined by ASTM beam test method.
Google Scholar
[17]
The symmetrical sandwich beam as shown in Fig. 2 is composed as per ASTM standard E-756(05). It consists of two layers of aluminum and the viscoelastic material in the core composed of a 3M 300 LSE High-Strength Acrylic double-face Adhesive.
Google Scholar
[18]
(a) (b) Fig. 2 Sandwich CLD beams The dynamic responses of the beams were measured by using accelerometer during a free vibration test performed by employing instantaneous hammer impact as excitation. The main features of the used equipment and the data acquisition are: accelerometer model uniaxial type 4515 (B&K) make, Impact Hammer 8206-002 (B&K) make and FFT Analyzer: 4 channel (B&K Photon +All in one). The result of beam FRF response are shown in RT Pro software.
Google Scholar
[19]
The typical experiment setup is shown in Fig. 3 Fig. 3 Experimental test setup Fig. 4 Comparison of frequency response curves By analyzing the resonant peaks for a particular mode, the loss factor, a measure of damping, is obtained from the real part of the response spectrum as shown in Fig. 4. These curves are presented using Matlab software.
DOI: 10.7717/peerj.6016/fig-14
Google Scholar
[20]
6. Results and discussion Half-power bandwidth method is used for calculating the loss factor at one of the natural modes of vibration for the system.
Google Scholar
[21]
By using half- power bandwidth method the modal loss factor corresponding to 3rd mode of all CLD beams are found. The comparison of result obtained by numerical analysis and experimental analysis are shown in Table 3. Table No. 3 Comparison of Numerical and Experimental Analysis results Sr. No. Beam type Natural frequency (Hz) Modal loss factor (ηr) Numerical Analysis Experimental Analysis Numerical Analysis Experimental Analysis 1 CLD beam-1 208 197 0. 412 0. 340 2 CLD beam-2 205 195 0. 502 0. 476 3 CLD beam-3 196 182 0. 456 0. 368 7. Conclusions This paper has presented the effect of appropriate thickness of damping VEM of CLD beam, on modal loss factor. The numerical results are well corroborated with experimental results. From comparison of results obtained by numerical analysis using MSE method and experimental investigation, it is observed that the modal loss factor of the sandwich CLD beam-2 is found to be more as compared to CLD beam-1 and CLD beam-3. As modal loss factor is more, the vibrational energy in the beam-2 decreases more. The damping of vibrations at high frequencies by the method of constrained layers is done best when the thickness of viscoelastic layer is half the thickness of constraining layer (CL). Hence to achieve maximum damping in the vibrating structure, the thickness ratio of constrained layer (damping material) to constraining layer (CL) should be equal to one half. Reference.
Google Scholar
[1]
Sun CT, Lu YP: Vibration damping of structural elements (New Jersey (USA): Prentice-Hall; 1995).
Google Scholar
[2]
Nashif AD, Jones DI and Henderson JP: Vibration damping. (New York (USA): John Wiley & Sons; 1989).
Google Scholar
[3]
Jones DIG: Handbook of viscoelastic vibration damping ( Chichester (England): John Wiley & Sons; 2001).
Google Scholar
[4]
Nakra BC: Vibration control in machines and structures using viscoelastic damping. Journal of Sound and Vibration, Vol. 211(1998), p.449–65.
DOI: 10.1006/jsvi.1997.1317
Google Scholar
[5]
Rao MD: Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes. Journal of Sound and Vibration, Vol. 262(2003), p.457–74.
DOI: 10.1016/s0022-460x(03)00106-8
Google Scholar
[6]
S.G. Won, S.H. Bae , J.R. Cho, S.R. Baec and W.B. Jeong : Three-layered damped beam element for forced vibration analysis of symmetric sandwich structures with a viscoelastic core. Finite Elements in Analysis and Design, Vol. 68 (2013), p.39–51.
DOI: 10.1016/j.finel.2013.01.004
Google Scholar
[7]
Richard C. Dickinson: Materials for noise and vibration control: what causes product variability? SAE International, Vol. 01, 3262 (2006).
Google Scholar
[8]
E M Kerwin: Damping of flexural waves by a constrained viscoelastic layer. Journal of the Acoustical Society of America. Vol. 31(1959), p.952–962.
DOI: 10.1121/1.1907821
Google Scholar
[9]
C.D. Johnson: Design of passive damping systems. Journal of Vibration Acoustic. Vol. 117 (1995), pp.171-176.
Google Scholar
[10]
D.K. Rao: Sandwich beams under various boundary conditions. Journal Mechanical Engineering Science, Vol. 20 No 5(1978).
Google Scholar
[11]
Raj V. Singh and Mike Pellny: Lightweight, high-performance, constrained-layer sound dampers. SAE International, Vol. 980466(1998).
DOI: 10.4271/980466
Google Scholar
[12]
J.S. Moita, A.L. Araujo and C.M. Mota Soares: Finite element model for damping optimization of viscoelastic sandwich structures. Advances in Engineering Software (2012).
DOI: 10.1016/j.advengsoft.2012.10.002
Google Scholar
[13]
Jay Tudor: Determination of Dynamic Properties and Modeling of Extensional Damping Materials. SAE International, Vol. 01, 1433(2003).
Google Scholar
[14]
Denys J Mead: Structural damping and damped vibration. Appl Mech Rev. Vol 55, no 6(2002).
Google Scholar
[15]
MSC. NASTRAN 12. 0 Software User Guide.
Google Scholar
[16]
C. D. Johnson, D.A. Kienholz: Finite element prediction of damping in structures with constrained viscoelastic layers. AIAA Journal, VOL. 20, No. 9(1981).
DOI: 10.2514/6.1981-486
Google Scholar
[17]
ASTM E-756-05: Standard Test Method for Measuring Vibration-Damping Properties of Materials.
Google Scholar
[18]
Min Hao, Mohan D. Rao : Vibration and damping analysis of a sandwich beam containing a viscoelastic constraining layer. Journal of Composite Materials. Vol. 39 (18), (2005), pp.1621-1643.
DOI: 10.1177/0021998305051124
Google Scholar
[19]
B&K Photon+ FFT RT Pro 2009 software Help.
Google Scholar
[20]
MATLAB 2010 Help, USA: The Math Works, Inc.
Google Scholar
[21]
M. D. Black, M. D. Rao: Material damping properties: a comparison of laboratory test methods and the relationship to in-vehicle performance. SAE International. Vol. 1, 1466(2001).
DOI: 10.4271/2001-01-1466
Google Scholar
