https://oldena.lpnu.ua/handle/ntb/39553| Title: | Dynamic properties predictions for laminated plates by high order theories |
| Authors: | Diveyev, Bohdan |
| Affiliation: | Lviv Polytechnic National University, Lviv, Ukraine |
| Bibliographic description (Ukraine): | Diveyev B. Dynamic properties predictions for laminated plates by high order theories / Bohdan Diveyev // Ukrainian Journal Of Mechanical Engineering Andmaterials Science. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 3. — No 1. — P. 43–72. |
| Is part of: | Ukrainian Journal Of Mechanical Engineering Andmaterials Science, 1 (3), 2017 |
| Issue: | 1 |
| Issue Date: | 1-Jan-2017 |
| Submitted date: | 7-Feb-2017 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Lviv |
| Keywords: | composite materials laminated plates Timoshenko beam stress distribution damping |
| Number of pages: | 30 |
| Page range: | 43-72 |
| Start page: | 43 |
| End page: | 72 |
| Abstract: | The main aim of this study is to predict the elastic and damping properties of composite laminated plates. Some approximate methods for the stress state predictions for laminated plates are presented. For simple uniform bending and transverse loading conditions, this problem has an exact elasticity solution. This paper presents a new stress analysis method for the accurate determination of the detailed stress distributions in laminated plates subjected to cylindrical bending. The present method is adaptive and does not rely on strong assumptions about the model of the plate. The theoretical model described here incorporates deformations of each sheet of the lamina, which account for the effects of transverse shear deformation, transverse normal strain-stress and nonlinear variation of displacements with respect to the thickness coordinate. Dynamic and damping predictions of laminated plates for various geometrical, mechanical and fastening properties are defined. The comparison with the Timoshenko beam theory is systematically done for analytical and approximation variants. The values of damping are got at a bend in three- and five-layered plates. For the threelayered plates the equivalent beam of Timoshenko exactly approximates a “sandwich” (with a soft damping kernel) dynamic properties of sandwich in a wide frequency range. For a plate with soft external layers the equivalent beam needs to be found in every frequency range separately. A hard bounded layer multiplies damping in a plate with soft external layers, however only at higher frequency of vibrations. For the high-frequency vibrations of plates the anomalous areas of diminishing of damping (for sandwiches) and increase are got for plates with soft covers. At the moderate amount of approximations the exact divisions of tensions are got in the layers of plates, thus the stresses continuity and surface terms are approximated exactly enough. Unlike the widespread theories of plates with the terms set a priori on surfaces (as a rule levels to the zero tensions) the offered equations allow to satisfy and complicated boundary conditions, instead of only free fastened plates. It allowed to explore the row of important examples for plates fastened in a hard holder and to explore influence of not only plates but also construction of holder on damping. |
| URI: | https://ena.lpnu.ua/handle/ntb/39553 |
| ISSN: | 2411-8001 |
| Copyright owner: | © Національний університет "Львівська політехніка" © Diveyev B., 2017 |
| References (Ukraine): | [1] D. Ross, E. E. Ungar, E. M. Kerwin. Damping of plate flexural vibrations by means of viscoelastic laminate. ASME. Structural Damping. 1959. pp. 49–88. [2] E. M. Kerwin. Damping of flexural waves by a constrained viscoelastic layer. Journal of the Acoustical Society of America. 31 (7). 1959. pp. 952–962. [3] R. A. DiTaranto. Theory of vibratory bending for elastic and viscoelastic layered finite length beams. Transactions of the ASME. Journal of Applied Mechanics. 32. 1965. pp.881–886. [4] D. J. Mead, S. Markus. The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions. Journal of Sound and Vibration. 10. 1969. pp. 163–175. [5] J. M. Whitney, C. T. Sun, A higher order theory for extensional motion of laminated anisotropic shells and plates. J. Sound Vib. 30. 1973. pp. 85–97. [6] R. B. Nelson, D. R. Lorch. A refined theory for laminated orthotropic plates. ASME. J. Appl. Mech. 41.1974. pp. 177–183. [7] J. N. Reddy. A simple higher-order theory for laminated composite plates. ASME. J. Appl. Mech. 51. 1984. pp. 745–752. [8] K. P. Soldatos, T. Timarci. A unified formulation of laminated composite, shear deformable five-degreeof- freedom cylindrical shell theories. Compos. Struct. 25. 1993. pp. 165–171. [9] T. Kant, K. Swaminathan. Estimation of transverse-interlaminar stresses in laminated composites – a selective review and survey of current developments. Compos. Struct. 49.2000. pp. 65–75. [10] N. J. Pagano. Exact solutions for composite laminates in cylindrical bending. Journal of Composite Materials. 3. 1969. pp. 398–411. [11] S. Srinivas, C. V. Joga Rao, A. K. Rao. Flexural vibration of rectangular plates. J. Appl. Mech. 23. 1970. 430–436. [12] A. K. Noor. Free vibration of multilayered composite plates. AIAA J.11.1973. pp. 1038–1039. [13] K. Swaminathan, S. S. Patil. Analytical solutions using a higher order refined computational mode with 12 degrees of freedom for the free vibration analysis of antisymmetrical angle-ply plates. Composite structures. 82. 2008. pp. 209–216. [14] K. H. Lo, R. M. Christensen. E. M. A. Wu. High-Order Theory of Plate Deformation. Part 2: Laminated Plates. Journal of Applied Mechanics. 44. Trans. ASME, Series E. 1977. pp. 669–676. [15] B. M. Diveyev, M. M. Nykolyshyn. Refined numerical schemes for a stressed-strained state of structural joints of layered elements, Journal of Mathematical Sciences. 107. 2001. pp. 3666–3670. [16] Z. Wu, W. Chen. Free vibration of laminated composite and sandwich plates using global-local higherorder theory. Journal of Sound and Vibration. 298. 2006. pp. 333–349. [17] Reddy J. N. A review of refined theories of laminated composite plates. Shock and Vibration Digest. 22. 1990. pp. 3–17. [18] E. Carrera. Historical review of zig-zag theories for multilayered plates and shells. Appl. Mech. Rev. 56. 2003. pp. 287–308. [19] Hu Heng, Belouettar Salim, Potier-Ferry Michel, Daya El Mustafa. Review and assessment of various theories for modeling sandwich composites. Compos. Struct. 84. 2008. pp.282–292. [20] Z. Li, M. J. Crocker. A review of vibration damping in sandwich composite structures, International Journal of Acoustics and Vibration, 10. 2005. pp. 159–169. [21] Carrera E., Demasi L. Multilayered finite plate element based on Reissner mixed variational theorem. Part II: numerical analysis. Int. J. Numer. Methods Eng. 55. 2002. pp. 253–296. [22] L. Demasi. 13 hierarchy plate theories for thick and thin composite plates. Compos. Struct. 84. 2008. pp. 256–270. [23] S. H. Zhang, H. L. Chen, X. P. Wang. Numerical parametric investigation of loss factor of laminated composites with interleaved viscoelastic layers. Int. J. of Vehicle Noise and Vibration. 2. 2006. pp. 62–74. [24] A. L. Araujo, C. M. Mota Soares, J. Herskovits, P. Pedersen. Estimation of piezoelastic and viscoelastic properties in laminated structures. Composite Structures. 87. 2009. pp. 168-174. [25] Jean-Marie Berthelot, Mustapha Assarar, Youssef Sefrani, Abderrahim El Mahi. Damping analysis of composite materials and structures. Composite Structures. 85. 2008. pp.189–204. [26] Yabin Liao, Valana Wells. Estimation of complex Young’s modulus of non-stiff materials using a modified Oberst beam technique. Journal of Sound and Vibration. 316.2008. pp. 87–100. [27] K. DeBelder, R. Pintelon, C. Demol, P. Roose. Estimation of the equivalent complex modulus of laminated glass beams and its application to sound transmission loss prediction. Mechanical Systems and Signal Processing. 24. 2010. pp. 809–822. [28] F. S. Barbosa, M. C. R. Farage. A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment. Journal of Sound and Vibration. 317. 2008. pp.91–111. [29] Reddy J. N. On refined computational models of composite laminates. Int. J. Numer. Meth. Eng. 27. 1989. pp. 361–382. [30] V. A. Matsagar, R. S. Jangid. Dynamic characterization of base-isolated structures using analytical shearbeam model. International Journal of Acoustics and Vibration. 11. 2006. pp. 132–136. [31] L. Gelman, P. Jenkins, I. Petrunin, M. J. Crocker. Vibroacoustical damping diagnostics: complex frequency response function versus its magnitude. International Journal of Acoustics and Vibration. 11. 2006. pp. 120–124. [32] Z. Li, M. J. Crocker. Effects of Thickness and Delamination on the Damping in Honeycomb-foam Sandwich Beams. J. Sound. Vib. 294. 2006. pp. 473–485. [33] K. H. Hornig, G. T. Flowers. Performance of Heuristic Optimisation Methods in the Characterisation of the Dynamic Properties of Sandwich Composite Materials. International Journal of Acoustics and Vibration. 12. 2007. pp. 60–68. [34] D. Backstrom, A.C. Nilsson. Modelling the vibration of sandwich beams using frequency-dependent parameters. Journal of Sound and Vibration. 300. 2007. pp. 589–611. [35] T. S. Plagianakos, D. A. Saravanos. High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams. International Journal of Solids and Structures. 41. 2004. pp. 6853–6871. [36] B. Diveyev, I. Butiter, N. Shcherbina. Identifying the elastic moduli of composite plates by using highorder theories. Pt 1. Theoretical approach. Mech. Compos. Mater. Vol. 44, No. 1. 2008. pp. 25–36. [37] B. Diveyev, I. Butiter, N. Shcherbina. Identifying the elastic moduli of composite plates by using highorder theories. Pt 2. Theoretical-experimental approach. Mech. Compos. Mater. Vol. 44, No. 2. 2008. pp. 139–144. [38] B. Diveyev, I. Butiter, N. Shcherbina. Influence of fixation conditions and material anisotropy on the frequency spectrum of laminated beams. Mech. Compos. Mater. Vol. 47, No. 2. 2011. pp. 149–160. [39] Bohdan Diveyev, Andrij Beshley, Solomiia Konyk, Ivan Kernytskyy. Identification of transverse elastic moduli of composite beams by using combined criteria. Materials of 22nd International Congress on Sound and Vibration. Vol. 2. 2015. Florence, Italy. (Electronic edition). [40] Bohdan Diveyev. Identifying the elastic moduli of composite plates by using high-order theories. Ukrainian Journal of Mechanical Engineering and Material Science. Vol. 1, No. 1. pp. 63–82. |
| References (International): | [1] D. Ross, E. E. Ungar, E. M. Kerwin. Damping of plate flexural vibrations by means of viscoelastic laminate. ASME. Structural Damping. 1959. pp. 49–88. [2] E. M. Kerwin. Damping of flexural waves by a constrained viscoelastic layer. Journal of the Acoustical Society of America. 31 (7). 1959. pp. 952–962. [3] R. A. DiTaranto. Theory of vibratory bending for elastic and viscoelastic layered finite length beams. Transactions of the ASME. Journal of Applied Mechanics. 32. 1965. pp.881–886. [4] D. J. Mead, S. Markus. The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions. Journal of Sound and Vibration. 10. 1969. pp. 163–175. [5] J. M. Whitney, C. T. Sun, A higher order theory for extensional motion of laminated anisotropic shells and plates. J. Sound Vib. 30. 1973. pp. 85–97. [6] R. B. Nelson, D. R. Lorch. A refined theory for laminated orthotropic plates. ASME. J. Appl. Mech. 41.1974. pp. 177–183. [7] J. N. Reddy. A simple higher-order theory for laminated composite plates. ASME. J. Appl. Mech. 51. 1984. pp. 745–752. [8] K. P. Soldatos, T. Timarci. A unified formulation of laminated composite, shear deformable five-degreeof- freedom cylindrical shell theories. Compos. Struct. 25. 1993. pp. 165–171. [9] T. Kant, K. Swaminathan. Estimation of transverse-interlaminar stresses in laminated composites – a selective review and survey of current developments. Compos. Struct. 49.2000. pp. 65–75. [10] N. J. Pagano. Exact solutions for composite laminates in cylindrical bending. Journal of Composite Materials. 3. 1969. pp. 398–411. [11] S. Srinivas, C. V. Joga Rao, A. K. Rao. Flexural vibration of rectangular plates. J. Appl. Mech. 23. 1970. 430–436. [12] A. K. Noor. Free vibration of multilayered composite plates. AIAA J.11.1973. pp. 1038–1039. [13] K. Swaminathan, S. S. Patil. Analytical solutions using a higher order refined computational mode with 12 degrees of freedom for the free vibration analysis of antisymmetrical angle-ply plates. Composite structures. 82. 2008. pp. 209–216. [14] K. H. Lo, R. M. Christensen. E. M. A. Wu. High-Order Theory of Plate Deformation. Part 2: Laminated Plates. Journal of Applied Mechanics. 44. Trans. ASME, Series E. 1977. pp. 669–676. [15] B. M. Diveyev, M. M. Nykolyshyn. Refined numerical schemes for a stressed-strained state of structural joints of layered elements, Journal of Mathematical Sciences. 107. 2001. pp. 3666–3670. [16] Z. Wu, W. Chen. Free vibration of laminated composite and sandwich plates using global-local higherorder theory. Journal of Sound and Vibration. 298. 2006. pp. 333–349. [17] Reddy J. N. A review of refined theories of laminated composite plates. Shock and Vibration Digest. 22. 1990. pp. 3–17. [18] E. Carrera. Historical review of zig-zag theories for multilayered plates and shells. Appl. Mech. Rev. 56. 2003. pp. 287–308. [19] Hu Heng, Belouettar Salim, Potier-Ferry Michel, Daya El Mustafa. Review and assessment of various theories for modeling sandwich composites. Compos. Struct. 84. 2008. pp.282–292. [20] Z. Li, M. J. Crocker. A review of vibration damping in sandwich composite structures, International Journal of Acoustics and Vibration, 10. 2005. pp. 159–169. [21] Carrera E., Demasi L. Multilayered finite plate element based on Reissner mixed variational theorem. Part II: numerical analysis. Int. J. Numer. Methods Eng. 55. 2002. pp. 253–296. [22] L. Demasi. 13 hierarchy plate theories for thick and thin composite plates. Compos. Struct. 84. 2008. pp. 256–270. [23] S. H. Zhang, H. L. Chen, X. P. Wang. Numerical parametric investigation of loss factor of laminated composites with interleaved viscoelastic layers. Int. J. of Vehicle Noise and Vibration. 2. 2006. pp. 62–74. [24] A. L. Araujo, C. M. Mota Soares, J. Herskovits, P. Pedersen. Estimation of piezoelastic and viscoelastic properties in laminated structures. Composite Structures. 87. 2009. pp. 168-174. [25] Jean-Marie Berthelot, Mustapha Assarar, Youssef Sefrani, Abderrahim El Mahi. Damping analysis of composite materials and structures. Composite Structures. 85. 2008. pp.189–204. [26] Yabin Liao, Valana Wells. Estimation of complex Young’s modulus of non-stiff materials using a modified Oberst beam technique. Journal of Sound and Vibration. 316.2008. pp. 87–100. [27] K. DeBelder, R. Pintelon, C. Demol, P. Roose. Estimation of the equivalent complex modulus of laminated glass beams and its application to sound transmission loss prediction. Mechanical Systems and Signal Processing. 24. 2010. pp. 809–822. [28] F. S. Barbosa, M. C. R. Farage. A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment. Journal of Sound and Vibration. 317. 2008. pp.91–111. [29] Reddy J. N. On refined computational models of composite laminates. Int. J. Numer. Meth. Eng. 27. 1989. pp. 361–382. [30] V. A. Matsagar, R. S. Jangid. Dynamic characterization of base-isolated structures using analytical shearbeam model. International Journal of Acoustics and Vibration. 11. 2006. pp. 132–136. [31] L. Gelman, P. Jenkins, I. Petrunin, M. J. Crocker. Vibroacoustical damping diagnostics: complex frequency response function versus its magnitude. International Journal of Acoustics and Vibration. 11. 2006. pp. 120–124. [32] Z. Li, M. J. Crocker. Effects of Thickness and Delamination on the Damping in Honeycomb-foam Sandwich Beams. J. Sound. Vib. 294. 2006. pp. 473–485. [33] K. H. Hornig, G. T. Flowers. Performance of Heuristic Optimisation Methods in the Characterisation of the Dynamic Properties of Sandwich Composite Materials. International Journal of Acoustics and Vibration. 12. 2007. pp. 60–68. [34] D. Backstrom, A.C. Nilsson. Modelling the vibration of sandwich beams using frequency-dependent parameters. Journal of Sound and Vibration. 300. 2007. pp. 589–611. [35] T. S. Plagianakos, D. A. Saravanos. High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams. International Journal of Solids and Structures. 41. 2004. pp. 6853–6871. [36] B. Diveyev, I. Butiter, N. Shcherbina. Identifying the elastic moduli of composite plates by using highorder theories. Pt 1. Theoretical approach. Mech. Compos. Mater. Vol. 44, No. 1. 2008. pp. 25–36. [37] B. Diveyev, I. Butiter, N. Shcherbina. Identifying the elastic moduli of composite plates by using highorder theories. Pt 2. Theoretical-experimental approach. Mech. Compos. Mater. Vol. 44, No. 2. 2008. pp. 139–144. [38] B. Diveyev, I. Butiter, N. Shcherbina. Influence of fixation conditions and material anisotropy on the frequency spectrum of laminated beams. Mech. Compos. Mater. Vol. 47, No. 2. 2011. pp. 149–160. [39] Bohdan Diveyev, Andrij Beshley, Solomiia Konyk, Ivan Kernytskyy. Identification of transverse elastic moduli of composite beams by using combined criteria. Materials of 22nd International Congress on Sound and Vibration. Vol. 2. 2015. Florence, Italy. (Electronic edition). [40] Bohdan Diveyev. Identifying the elastic moduli of composite plates by using high-order theories. Ukrainian Journal of Mechanical Engineering and Material Science. Vol. 1, No. 1. pp. 63–82. |
| Content type: | Article |
| Appears in Collections: | Ukrainian Journal of Mechanical Engineering And Materials Science. – 2017. – Vol. 3, No. 1 |
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| UJMEMS_2017v3n1_Diveyev_B-Dynamic_properties_predictions_43-72.pdf | 1.22 MB | Adobe PDF | View/Open | |
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