Analysis of multilayered two-dimensional decagonal piezoelectric quasicrystal beams with mixed boundary conditions. (English) Zbl 07867754
Summary: Piezoelectric quasicrystals have a broad spectrum of promising applications and research value due to their unique atomic arrangement and multi-field coupling effects. This paper presents a mechanical analysis of the static bending and free vibration problems of two-dimensional multilayered decagonal piezoelectric quasicrystal laminated beams. Mechanical models of the beams are established, and the differential quadrature method in conjunction with the state-space method is utilized to obtain the solutions for the beams with mixed boundary conditions. We first investigated the static response and free vibration problem of quasicrystal laminated beams. By degrading them into crystalline materials, we verified the accuracy of the method by comparing the results with the existing ones. Then, the effects of different boundary conditions and slenderness ratios on the stresses, displacements, electric potentials, and electric displacements of quasicrystal laminated beams under normal mechanical loading and free vibration are investigated. Subsequently, the effects of different laying modes on the mechanical properties of the quasicrystal laminated beams when the material principal axis of the beam is changed are also analyzed.
MSC:
| 74-XX | Mechanics of deformable solids |
References:
| [1] | Agiasofitou, E.; Lazar, M., On the equations of motion of dislocations in quasicrystals, Mech. Res. Commun., 57, 27-33, 2014 |
| [2] | Agiasofitou, E.; Lazar, M., The elastodynamic model of wave-telegraph type for quasicrystals, Int. J. Solid Struct., 51, 5, 923-929, 2014 |
| [3] | Agiasofitou, E.; Lazar, M., On the constitutive modelling of piezoelectric quasicrystals, Crystals, 13, 12, 2023 |
| [4] | Bak, P., Phenomenological theory of icosahedral incommensurate (quasiperiodic) order in Mn-Al alloys, Phys. Rev. Lett., 54, 14, 1517-1519, 1985 |
| [5] | Bak, P., Symmetry, stability, and elastic properties of icosahedral incommensurate crystals, Phys. Rev. B, 32, 9, 5764-5772, 1985 |
| [6] | Bellman, R.; Kashef, B. G.; Casti, J., Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, J. Comput. Phys., 10, 1, 40-52, 1972 · Zbl 0247.65061 |
| [7] | Bert, C. W.; Malik, M., Differential quadrature: a powerful new technique for analysis of composite structures, Compos. Struct., 39, 3/4, 179-189, 1997 |
| [8] | Chen, W. Q.; Lü, C. F.; Bian, Z. G., A semi-analytical method for free vibration of straight orthotropic beams with rectangular cross-sections, Mech. Res. Commun., 31, 6, 725-734, 2004 · Zbl 1098.74592 |
| [9] | Ding, D. H.; Yang, W. G.; Hu, C. Z., Generalized elasticity theory of quasicrystals, Phys. Rev. B Condens. Matter, 48, 10, 7003-7010, 1993 |
| [10] | Fan, T.; Wang, X.; Li, W., Elasto-hydrodynamics of quasicrystals, 89, 6, 501-512, 2009 |
| [11] | Fan, C.; Li, Y.; Xu, G., Fundamental solutions and analysis of three-dimensional cracks in one-dimensional hexagonal piezoelectric quasicrystals, Mech. Res. Commun., 74, 39-44, 2016 |
| [12] | Feng, X.; Fan, X.; Li, Y., Static response and free vibration analysis for cubic quasicrystal laminates with imperfect interfaces, Eur. J. Mech. Solid., 90, Article 104365 pp., 2021 · Zbl 1486.74092 |
| [13] | Feng, X.; Zhang, L.; Wang, Y., Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions, Appl. Math. Mech., 42, 11, 1599-1618, 2021 · Zbl 1492.74102 |
| [14] | Feng, X.; Hu, Z.; Zhang, H., Semi-analytical solutions for functionally graded cubic quasicrystal laminates with mixed boundary conditions, Acta Mech., 233, 6, 2173-2199, 2022 · Zbl 1493.74019 |
| [15] | Feng, X.; Zhang, L.; Zhang, H., Semi-analytical solution for mixed supported and multilayered two-dimensional thermo-elastic quasicrystal plates with interfacial imperfections, J. Therm. Stresses, 46, 2, 91-116, 2023 |
| [16] | Gao, Y., The exact theory of one-dimensional quasicrystal deep beams, Acta Mech., 212, 3-4, 283-292, 2010 · Zbl 1397.74115 |
| [17] | Gao, Y., Decay conditions for 1D quasicrystal beams, IMA J. Appl. Math., 76, 4, 599-609, 2011 · Zbl 1390.74116 |
| [18] | Hu, K.; Gao, C.; Fu, J., Interference of two cylindrical inclusions in an infinite piezoelectric quasicrystal medium, J. Inn. Mong. Univ. Technol. (Soc. Sci. Ed.), 42, 3, 230-236, 2023 |
| [19] | Huang, Y. Z.; Li, Y.; Yang, L. Z., Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach, J. Zhejiang Univ. - Sci., 20, 2, 133-147, 2019 |
| [20] | Jang, S., Free vibration of stepped beams: exact and numerical solutions, J. Sound Vib., 130, 2, 342-346, 1989 · Zbl 1235.74083 |
| [21] | Ji, Antong X. M., Dependence and monotonicity of eigenvalues on some parameters for a class of third-order differential operator, J. Inn. Mong. Univ. Technol. (Soc. Sci. Ed.), 42, 1, 1-7, 2023 |
| [22] | Landau, L. D.; Lifshitz, E. M., Course of Theoretical physics[M], 2013, Elsevier |
| [23] | Li, Y. S.; Xiao, T., Free vibration of the one-dimensional piezoelectric quasicrystal microbeams based on modified couple stress theory, Appl. Math. Model., 96, 733-750, 2021 · Zbl 1481.74282 |
| [24] | Li, X. Y.; Li, P. D.; Wu, T. H., Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect, Phys. Lett., 378, 10, 826-834, 2014 · Zbl 1323.82048 |
| [25] | Li, Y.; Yang, L. Z.; Gao, Y., Bending analysis of laminated two-dimensional piezoelectric quasicrystal plates with functionally graded material properties, Acta Phys. Pol., A, 135, 3, 426-433, 2019 |
| [26] | Lubensky, T.; Ramaswamy, S.; Toner, J., Hydrodynamics of icosahedral quasicrystals, Phys. Rev. B, 32, 11, 7444, 1985 |
| [27] | Lubensky, T. C.; Ramaswamy, S.; Toner, J., Dislocation motion in quasicrystals and implication for macroscopic properties, Phys. Rev. B, 33, 11, 7715-7719, 1986 |
| [28] | Nagem, R. J.; Williams, Jr J. H., Dynamic analysis of large space structures using transfer matrices and joint coupling matrices, J. Struct. Mech., 17, 3, 349-371, 1989 |
| [29] | Rochal, S.; Lorman, V., Anisotropy of acoustic-phonon properties of an icosahedral quasicrystal at high temperature due to phonon-phason coupling, Phys. Rev. B, 62, 2, 874, 2000 |
| [30] | Rochal, S.; Lorman, V., Minimal model of the phonon-phason dynamics in icosahedral quasicrystals and its application to the problem of internal friction in the i-AlPdMn alloy, Phys. Rev. B, 66, 14, Article 144204 pp., 2002 |
| [31] | Shechtman, D.; Blech, I.; Gratias, D., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., 53, 20, 1951-1953, 1984 |
| [32] | Shu, C., Differential Quadrature and its Application in engineering[M], 2012, Springer Science & Business Media |
| [33] | Shu, C.; Chen, W.; Xue, H., Numerical study of grid distribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximation, 51, 2, 159-179, 2001 · Zbl 1169.74657 |
| [34] | Sun, T.; Guo, J., Free vibration and bending of one-dimensional quasicrystal layered composite beams by using the state space and differential quadrature approach, Acta Mech., 233, 8, 3035-3057, 2022 · Zbl 1498.74031 |
| [35] | Wang, X.; Bert, C.; Striz, A., Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates, Comput. Struct., 48, 3, 473-479, 1993 |
| [36] | Yang, L.; Li, Y.; Gao, Y., Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading, Compos. Struct., 171, 198-216, 2017 |
| [37] | Zhang, L.; Zhang, Y.; Gao, Y., General solutions of plane elasticity of one-dimensional orthorhombic quasicrystals with piezoelectric effect, Phys. Lett., 378, 37, 2768-2776, 2014 · Zbl 1298.74027 |
| [38] | Zhang, L.; Wu, D.; Xu, W., Green’s functions of one-dimensional quasicrystal bi-material with piezoelectric effect, Phys. Lett., 380, 39, 3222-3228, 2016 |
| [39] | Zhang, L.; Guo, J. H.; Xing, Y. M., Bending deformation of multilayered one-dimensional hexagonal piezoelectric quasicrystal nanoplates with nonlocal effect, Int. J. Solid Struct., 132, 278-302, 2018 |
| [40] | Zhang, L.; Guo, J. H.; Xing, Y. M., Nonlocal analytical solution of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal nanoplates, Acta Mech., 230, 5, 1781-1810, 2019 · Zbl 1428.74076 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
