The dynamic behavior of a sandwich beam with a porous core and carbon nanotube-reinforced polymer facesheets subjected to a moving mass on simple supports was investigated using the quasi-3D theory of shear deformation. The system of equations was determined using the energy technique. In order to solve the equations of motion, the analytical Navier’s approach in the space domain and the numerical Newmark’s method in the time domain were employed. Additionally, the natural frequencies of the free vibrations of beam were studied and evaluated. To validate the accuracy of the results obtained, comparisons were made with existing responses for specific circumstances reported in the literature. The effect of various parameters such as carbon nanotube volume percentage, porosity coefficient and distribution pattern, ratio of geometric and dimensional parameters, speed of moving mass, and facesheet-to-core thickness ratio on the dynamic response, critical speed of moving mass, and natural frequency of the sandwich beam with a porous core and nanocomposite surfaces were investigated. The results showed that by increasing the core porosity, the natural frequencies and critical speeds were increased. Because the intrinsic holes in the core structure get bigger, the stiffness and mass of the beam decrease. However, the effect of the mass reduction is greater than the effect of the stiffness reduction, so the frequency and critical speed of the system are increased.
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References
J. R. Vinson, “Sandwich structures,” Appl. Mech. Rev., 54, No. 3, 201-214 (2001).
H. H. Jeffcott, “On the vibration of beams under the action of moving loads,” London, Edinburgh, Dublin Philos. Mag. J. Sci., 8, No. 48, 66-97 (1929).
M. H. Kadivar and S. R. Mohebpour, “Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads,” Finite Elem. Anal. Des., 29, No. 3, 259-273 (1998).
M. Olsson, “On the fundamental moving load problem,” J. Sound Vib., 145, No. 2, 299-307 (1991).
C. E. Smith, “Motions of a stretched string carrying a moving mass particle,” J. Appl. Mech., 31, No. 1, 29-37 (1964).
M. M. Stanišić, J. A. Euler, and S. T. Montgomery, “On a theory concerning the dynamical behavior of structures carrying moving masses,” Ingenieur-Archiv, 43, No. 5, 295-305 (1974).
S. E. Azam, M. Mofid, and R. Afghani Khoraskani, “Dynamic response of Timoshenko beam under moving mass,” Scientia Iranica, 20, 50-56 (2013).
I. Esen, “A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory,” Lat. Am. J. Solids Struct., 12, No. 4, 808-830 (2015).
I. Esen, “A modified FEM for transverse and lateral vibration analysis of thin beams under a mass moving with a variable acceleration,” Lat. Am. J. Solids Struct., 14, No. 3, 485-511 (2017).
L. Vu-Quoc and M. Olsson, “A computational procedure for interaction of high-speed vehicles on flexible structures without assuming known vehicle nominal motion,” Comput. Methods Appl. Mech. Eng., 76, No. 3, 207-244 (1989).
Cao, Chang-yong, Zhong, and Yang, “Dynamic response of a beam on a Pasternak foundation and under a moving load,” (2008).
M. Zehsaz, M. ~H. Sadeghi, and A. Z. Asl, “Dynamics response of railway under a moving load,” J. Appl. Sci., 9, No. 8, 1474-1481 (2009).
B. Jin, “Dynamic displacements of an infinite beam on a poroelastic half space due to a moving oscillating load,” Arch. Appl. Mech., 74, 277-287 (2004).
H. S. Zibdeh and M. Abu-Hilal, “Stochastic vibration of laminated composite coated beam traversed by a random moving load,” Eng. Struct., 25, 397-404 (2003).
J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC press (2003).
J. Yang, Y. Chen, Y. Xiang, and X. L. Jia, “Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load,” J. Sound Vib., 312, 166-18 (2008).
I. Esen, “Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass,” Int. J. Mech. Sci., 153-154, 21-35 (2019).
S. M. R. Khalili, N. Nemati, K. Malekzadeh, and A. R. Damanpack, “Free vibration analysis of sandwich beams using improved dynamic stiffness method,” Compos. Struct., 92, No. 2, 387-394 (2010).
M. Şimşek and T. Kocatürk, “Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load,” Compos. Struct., 90, No. 4, 465-473 (2009).
M. Şimşek and S. Cansız, “Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load,” Compos. Struct., 94, No. 9, 2861-2878 (2012).
D. Chen, J. Yang, and S. Kitipornchai, “Free and forced vibrations of shear deformable functionally graded porous beams,” Int. J. Mech. Sci., 108-109, 14-22 (2016).
I. Esen, “Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load,” Eur. J. Mech. / A Solids, 78, 103841 (2019).
L.-L. Ke, J. Yang, and S. Kitipornchai, “Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams,” Compos. Struct., 92, No. 3, 676-683 (2010).
M. Heshmati and M. H. Yas, “Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads,” Mater. Des., 49, 894-904 (2013).
F. V. Tahami, H. Biglari, and M. Raminnea, “Optimum design of FGX-CNT-reinforced reddy pipes conveying fluid subjected to moving load,” J. Appl. Comput. Mech., 2, No. 4, 243-253 (2016).
S. Kitipornchai, D. Chen, and J. Yang, “Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets,” Mater. Des., 116, 656-665 (2017).
D. Chen, J. Yang, and S. Kitipornchai, “Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams,” Compos. Sci. Technol., 142, 235-245 (2017).
I. Esen, “Dynamics of size-dependant Timoshenko micro beams subjected to moving loads,” Int. J. Mech. Sci., 175, 105501 (2020).
A. G. Shenas, P. Malekzadeh, and S. Ziaee, “Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment,” Compos. Struct., 162, 325-340 (2017).
Y. Kiani, “Analysis of FG-CNT reinforced composite conical panel subjected to moving load using Ritz method,” Thin-Walled Struct., 119, 47-57 (2017).
M. Şimşek and M. Al-shujairi, “Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads,” Compos., Part B., 108, 18-34 (2017).
Y. Wang, K. Xie, T. Fu, and C. Shi, “Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses,” Compos. Struct., 209, 928-939 (2019).
S. S. Mirjavadi, B. M. Afshari, M. R. Barati, and A. M. S. Hamouda, “Transient response of porous inhomogeneous nanobeams due to various impulsive loads based on nonlocal strain gradient elasticity,” Int. J. Mech. Mater. Des., 16, No. 1, 57-68 (2020).
Y. Li, W. Yao, and T. Wang, “Free flexural vibration of thin-walled honeycomb sandwich cylindrical shells,” Thin-Walled Struct., 157, 107032 (2020).
C. Li, P. Li, B. Zhong, and X. Miao, “Large-amplitude vibrations of thin-walled rotating laminated composite cylindrical shell with arbitrary boundary conditions,” Thin-Walled Struct., 156, 106966 (2020).
J.-S. Chen, S.-Y. Chen, and W.-Z. Hsu, “Effects of geometric nonlinearity on the response of a long beam on viscoelastic foundation to a moving mass,” J. Sound Vib., 497, 115961 (2021).
B. Fahsi, R. B. Bouiadjra, A. Mahmoudi, S. Benyoucef, and A. Tounsi, “Assessing the effects of porosity on the bending, buckling, and vibrations of functionally graded beams resting on an elastic foundation by using a new refined quasi-3d theory,” Mech. Compos. Mater., 55, No. 2, 219-230 (2019).
S. S. Akavci and A. H. Tanrikulu, “Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories,” Compos. Part B Eng., 83, 203-215 (2015).
H. Akbari, M. Azadi, and H. Fahham, “Flutter prediction of cylindrical sandwich panels with saturated porous core under supersonic yawed flow,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., 235, No. 16, 2968-2984 (2020).
A. G. Arani, F. Kiani, and H. Afshari, “Free and forced vibration analysis of laminated functionally graded CNTreinforced composite cylindrical panels,” J. Sandw. Struct. Mater. 23, No. 1, 255-278 (2019).
M. M. Stanišić and J. C. Hardin, “On the response of beams to an arbitrary number of concentrated moving masses,” J. Franklin Inst., 287, No. 2, 115-123 (1969).
M. Şimşek, “Vibration analysis of a functionally graded beam under a moving mass by using different beam theories,” Compos. Struct., 92, No. 4, 904-917 (2010).
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Appendix
Appendix
The coefficients of Eqs. (19) to (22) are defined as follows:
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Biglari, H., Teymouri, H. & Shokouhi, A. Dynamic Response of Sandwich Beam with Flexible Porous Core Under Moving Mass. Mech Compos Mater 60, 163–182 (2024). https://doi.org/10.1007/s11029-024-10181-7
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DOI: https://doi.org/10.1007/s11029-024-10181-7