Study on Vibration Band Gap Characteristics of a Branched Shape Periodic Structure Using the GDQR
Subject Areas : Mechanics of Solids
1 - Department of Mechanical Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
2 - Department of Mechanical Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
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[1] Hajhosseini M., Rafeeyan M., 2016, Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting, Applied Mathematics and Mechanics 37(8): 1053-1066.
[2] Wen J.H., Wang G., Yu D.L., Zhao H.G., Liu Y.Z., 2008, Study on the vibration band gap and vibration attenuation property of phononic crystals, Science in China Series E-Technological Sciences 51(1): 85-99.
[3] Olhoff N., Niu B., Cheng G., 2012, Optimum design of band-gap beam structures, International Journal of Solids and Structures 49(22): 3158-3169.
[4] Kamotski L.V., Smyshlyaev V.P., 2019, Band gaps in two-dimensional high-contrast periodic elastic beam lattice materials, Journal of the Mechanics and Physics of Solids 123: 292-304.
[5] Xiang H.J., Cheng Z.B., Shi Z.F., Yu X.Y., 2014, In-plane Band Gaps in a Periodic Plate with Piezoelectric Patches, Journal of Solid Mechanics 6(2): 194-207.
[6] Zouari S., Brocail J., Génevaux J.M., 2018, Flexural wave band gaps in metamaterial plates: A numerical and experimental study from infinite to finite models, Journal of Sound and Vibration 435: 246-263.
[7] Hajhosseini M., Rafeeyan M., Ebrahimi S., 2017, Vibration band gap analysis of a new periodic beam model using GDQR method, Mechanics Research Communications 79: 43-50.
[8] Hajhosseini M., Mahdian Parrany A., 2019, Vibration band gap properties of a periodic beam-like structure using the combination of GDQ and GDQR methods, Waves in Random and Complex Media 2019: 1-17.
[9] Zhu Z.W., Deng Z.C., Huang B., Du J.K., 2019, Elastic wave propagation in triangular chiral lattices: Geometric frustration behavior of standing wave modes, International Journal of Solids and Structures 158: 40-51.
[10] Wu Z.J., Li F.M., Zhang C., 2014, Vibration properties of piezoelectric square lattice structures, Mechanics Research Communications 62: 123-131.
[11] Hajhosseini M., Ebrahimi S., 2019, Analysis of vibration band gaps in an Euler–Bernoulli beam with periodic arrays of meander-shaped beams, Journal of Vibration and Control 25(1): 41-51.
[12] Guo X., Liu H., Zhang K., Duan H., 2018, Dispersion relations of elastic waves in two-dimensional tessellated piezoelectric phononic crystals, Applied Mathematical Modelling 56: 65-82.
[13] Wang G., Wen J., Liu Y., Wen X., 2004, Lumped-mass method for the study of band structure in two-dimensional phononic crystals, Physical Review B - Condensed Matter and Materials Physics 69: 184302.
[14] Liang X., Wang T., Jiang X., Liu Z., Ruan Y., Deng Y., 2019, A numerical method for flexural vibration band gaps in a phononic crystal beam with locally resonant oscillators, Crystals 9(6): 293.
[15] Chang I.L., Liang Z.X., Kao H.W., Chang S.H., Yang C.Y., 2018, The wave attenuation mechanism of the periodic local resonant metamaterial, Journal of Sound and Vibration 412: 349-359.
[16] Zhou X., Xu Y., Liu Y., Lv L., Peng F., Wang L., 2018, Extending and lowering band gaps by multilayered locally resonant phononic crystals, Applied Acoustics 133: 97-106.
[17] Leissa A.W., Qatu M.S., 2011, Vibration of Continuous Systems, McGraw-Hill Professional.
[18] Kittel C., 2005, Introduction to Solid State Physics, John Wiley & Sons, New York.
[19] Bellman R., Casti J., 1971, Differential quadrature and long term integration, Journal of Mathematical Analysis and Applications 34(2): 235-238.
[20] Liang X., Zha X., Jiang X., Cao Z., Wang Y., Leng J., 2019, A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries, Ocean Engineering 178: 145-155.
[21] Liang X., Deng Y., Jiang X., Cao Z., Ruan Y., Leng J., Wang T., Zha X., 2019, Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions, Journal of Low Frequency Noise, Vibration and Active Control 39: 1002-1023.
[22] Wu T.Y., Liu G.R., 1999, A differential quadrature as a numerical method to solve differential equations, Computational Mechanics 24(3): 197-205.
[23] Hajhosseini M., 2020, Analysis of complete vibration bandgaps in a new periodic lattice model using the differential quadrature method, Journal of Vibration and Control 26: 1708-1720.
[24] Shu C., 2000, Differential Quadrature and its Applications in Engineering, Springer-Verlag, London.