Vibration response and band gap characteristics of the functionally graded frame structures are investigated based on the first-order shear deformation theory. The material properties of functionally graded material rods vary continuously in thickness direction according to a power law. Spectral stiffness matrix of the periodic functionally graded material frame structure in the global coordinate system is derived in detail. Consequently, the vibration band gap properties of the functionally graded material frame structure can be calculated and analyzed by using the spectral element method. The calculation accuracy for dynamic responses of the functionally graded material frame structure is validated by the finite element method. The results demonstrate that the wider band gaps in the low and medium frequency ranges can be achieved for the functionally graded frame structures comparing with the homogeneous ones. Moreover, the frequency windows and ranges for the band gaps of the functionally graded material frame structure can be effectively adjusted through designing the gradient indexes for the functionally graded material rods, which provide a novel idea for vibration suppression of frame structures.
AkbasSD (2016) Wave propagation in edge cracked functionally graded beams under impact force. Journal of Vibration and Control22(10): 2443–2457.
2.
AlshorbagyAEEltaherMAMahmoudFF (2011) Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling35(1): 412–425.
3.
AydogduMTaskinV (2007) Free vibration analysis of functionally graded beams with simply supported edges. Materials and Design28(5): 1651–1656.
4.
BanerjeeJRAnanthapuvirajahA (2018) Free vibration of functionally graded beams and frameworks using the dynamic stiffness method. Journal of Sound and Vibration422: 34–47.
5.
BednariMCervenkaMGrobyJP, et al. (2018) One-dimensional propagation of longitudinal elastic waves through functionally graded materials. International Journal of Solids and Structures146: 43–54.
6.
ChakraborthyAGopalakrishnanSReddyJN (2003) A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences45(3): 519–539.
7.
ChakrabortyAGopalakrishnanS (2003) A spectrally formulated finite element for wave propagation analysis in functionally graded beams. International Journal of Solids and Structures40(10): 2421–2448.
8.
FomenkoSIGolubMVZhangC, et al. (2014) In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals. International Journal of Solids and Structures51(13): 2491–2503.
9.
GolubMVFomenkoSIBuiTQ, et al. (2012) Transmission and band gaps of elastic SH waves in functionally graded periodic laminates. International Journal of Solids and Structures49(2): 344–354.
10.
GulUAydogduMKaracamF (2019) Dynamics of a functionally graded Timoshenko beam considering new spectrums. Composite Structures207: 273–291.
11.
GuoXWeiPLiL, et al. (2018) Effects of functionally graded interlayers on dispersion relations of shear horizontal waves in layered piezoelectric/piezomagnetic cylinders. Applied Mathematical Modelling55: 569–582.
12.
GuoZShengM (2018) Bandgap of flexural wave in periodic bi-layer beam. Journal of Vibration and Control24(14): 2970–2985.
13.
GuptaATalhaM (2015) Recent development in modeling and analysis of functionally graded materials and structures. Progress in Aerospace Sciences79: 1–14.
14.
HajhosseiniMEbrahimiS (2019) Analysis of vibration band gaps in an Euler–Bernoulli beam with periodic arrays of meander-shaped beams. Journal of Vibration and Control25(1): 41–51.
15.
HuangXSuJRenL, et al. (2017) Development of curved beam periodic structure in broadband resonance suppression for cylindrical shell structure. Journal of Vibration and Control23(8): 1267–1284.
16.
KoizumiM (1997) FGM activities in Japan. Composites Part B: Engineering28: 1–4.
17.
LeeJWLeeJY (2017) Free vibration analysis of functionally graded Bernoulli–Euler beams using an exact transfer matrix expression. International Journal of Mechanical Sciences122: 1–17.
18.
LiLHuYLingL (2015) Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Composite Structures133: 1079–1092.
19.
LiNWangYZWangYS (2019) Active control of elastic metamaterials consisting of symmetric double Helmholtz resonator cavities. International Journal of Mechanical Sciences153: 287–298.
20.
RenTLiuCLiF, et al. (2020) Active tuning of the vibration band gap characteristics of periodic laminated composite metamaterial beams. Journal of Intelligent Material Systems and Structures31: 843–859.
21.
SlavisaSAleksandarOAleksandarT (2018) Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. Composites Part B: Engineering150: 135–143.
22.
SofiyevAH (2019) Review of research on the vibration and buckling of the FGM conical shells. Composite Structures211: 301–317.
23.
TrinhLCVoTPOsoferoAI, et al. (2016) Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach. Composite Structures156: 263–275.
24.
WangPYiQZhaoC, et al. (2019) Elastic wave propagation characteristics of periodic track structure in high-speed railway. Journal of Vibration and Control25(3): 517–528.
25.
WangZHWangXHXuGD, et al. (2016) Free vibration of two-directional functionally graded beams. Composite Structures135: 191–198.
26.
WattanasakulpongNCharoensukJ (2015) Vibration characteristics of stepped beams made of FGM using differential transformation method. Meccanica50: 1089–1101.
27.
WeiDLiuYXiangZ (2012) An analytical method for free vibration analysis of functionally graded beams with edge cracks. Journal of Sound and Vibration331(7): 1686–1700.
28.
WuMLWuLYYangWP, et al. (2009) Elastic wave band gaps of one-dimensional phononic crystals with functionally graded materials. Smart Materials and Structures18(11): 115013.
29.
YingZGNiYQ (2018) Dynamic characteristics of infinite-length and finite-length rods with high-wave-number periodic parameters. Journal of Vibration and Control24(11): 2344–2358.
30.
ZhuLFKeLLZhuXQ, et al. (2019) Crack identification of functionally graded beams using continuous wavelet transform. Composite Structures210: 473–485.
31.
ZuoSLLiFMZhangC (2016) Numerical and experimental investigations on the vibration band-gap properties of periodic rigid frame structures. Acta Mechanica227(6): 1653–1669.
