This study theoretically and numerically explores a dynamic design to control elastic wave actively in a piezoelectric phononic crystal beam using tunable LRC shunt circuits. Based on piezoelectric constitutive equations and electromagnetic resonance principles, the equivalent elastic modulus of the piezoelectric patches is derived as a circuit-dependent complex parameter. By systematically adjusting resistance, inductance, and capacitance, the position and attenuation strength of the electromagnetic oscillation bandgap (EOBG) can be effectively tuned. Results indicate that variations in R alter only the transmission loss without affecting the bandgap frequency. In contrast, increasing L or C reduces the bandgap frequency, while simultaneously enhancing wave energy dissipation through intensified electromagnetic oscillation. Reducing R, increasing L, or decreasing C amplifies the magnitude and phase angle of the equivalent modulus, leading to improved vibration attenuation within the bandgap. The study demonstrates that real-time tuning of LRC circuits enables precise and adaptive control over wave propagation, offering a practical strategy for designing smart metamaterials with customized wave manipulation and vibration suppression capabilities.

Hanbo Shao, Xiaochen Hang, Weiyu Chen. Dynamic Design and Active Control of Piezoelectric Phononic Crystal Beams for Vibration Suppression. Academic Journal of Engineering and Technology Science (2025), Vol. 8, Issue 5: 10-18. https://doi.org/10.25236/AJETS.2025.080502.

[1] Sheng P, Zhang X X, Liu Z, et al. Locally resonant sonic materials[J]. Science, 2000, 338(1):201-205.

[2] Mei J, Ma G, Yang M, et al. Dynamic Mass Density and Acoustic Metamaterials[J]. Physica B Physics of Condensed Matter, 2007, 394(2):256-261.

[3] Wang Y F, Wang Y S, Laude V. Wave propagation in two-dimensional viscoelastic metamaterials[J]. Physical Review B, 2015, 92(10).

[4] Mei J, Liu Z, Wen W, et al. Effective dynamic mass density of composites[J]. Physical Review B Condensed Matter, 2007, 76(13):134205.

[5] Charles C, Bonello B, Ganot F. Propagation of guided elastic waves in 2D phononic crystals [J]. Ultrasonics, 2006, 44(4):1209.

[6] Liu S, Li S, Shu H, et al. Research on the elastic wave band gaps of curved beam of phononic crystals[J]. Physica B Physics of Condensed Matter, 2015, 457(457):82-91.

[7] Taniker S, Yilmaz C. Phononic gaps induced by inertial amplification in BCC and FCC lattices[J]. Physics Letters Section A General Atomic & Solid State Physics, 2013, 377(31–33):1930-1936.

[8] Han L, Zhang Y, Ni Z Q, et al. A modified transfer matrix method for the study of the bending vibration band structure in phononic crystal Euler beams[J]. Physica B Physics of Condensed Matter, 2012, 407 (23): 4579-4583.

[9] Mei J, Ma G, Yang M, et al. Dark acoustic metamaterials as super absorbers for low-frequency sound[J]. Nature Communications, 2012, 3(2):756.

[10] Lu K, Wu J H, Guan D, et al. A lightweight low-frequency sound insulation membrane-type acoustic metamaterial[J]. Aip Advances, 2016, 6(2):1373. 

[11] Tanaka Y, Tamura S I. Surface acoustic waves in two-dimensional periodic elastic structures[J]. Physical Review B, 1998, 58(12):7958-7965.

[12] Hua L, Wang G X, Liu X M. Manipulation of light in MIM plasmonic waveguide systems[J]. Chinese Science Bulletin, 2013, 58(30):3607-3616.

[13] Zhang X J, Guo C J. Cubature Kalman filters: Derivation and extension[J]. Chinese Physics B, 2013, 22(12):497-502. 

[14] Shelby R A, Smith D R, Schultz S. Experimental Verification of a Negative Index of Refraction[J]. Science, 2001, 292(5514):77.

[15] Sukhovich A, Merheb B, Muralidharan K, et al. Experimental and theoretical evidence for subwavelength imaging in phononic crystals [J]. Physical Review Letters, 2009, 102(15):154301.

[16] Zhang S, Yin L, Fang N. Focusing ultrasound with an acoustic metamaterial network[J]. Physical Review Letters, 2009, 102(19):194301.

[17] Liu X F, Wang Y F, Wang Y S, et al. Wave propagation in a sandwich plate with a periodic composite core[J]. Journal of Sandwich Structures & Materials, 2014, 16(3):319-338.

[18] Yang Z, Mei J, Yang M, et al. Membrane-type acoustic metamaterial with negative dynamic mass[J]. Physical Review Letters, 2010, 101(20):204301.

[19] Thorp O, Ruzzene M, Baz A. Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings[J]. Smart Materials & Structures, 2005, 14(4):594.

[20] Tang J, Wang K W. Vibration Control of Rotationally Periodic Structures Using Passive Piezoelectric Shunt Networks and Active Compensation[J]. Journal of Vibration & Acoustics, 1999, 121(3):379-390.

[21] Baz A M. Active control of a two-dimensional periodic structure[J]. Proceedings of SPIE - The International Society for Optical Engineering, 2004, 53:86.

[22] Akl W, Baz A. Multi-cell Active Acoustic Metamaterial with Programmable Bulk Modulus[J]. Journal of Intelligent Material Systems & Structures, 2010, 21(5):541-556.

[23] Baz A. The structure of an active acoustic metamaterial with tunable effective density[J]. New Journal of Physics, 2009, 11(11):123010.

[24] Popa B I, Zigoneanu L, Cummer S A. Tunable active acoustic metamaterials[J]. Physical Review B, 2013, 88(2).

[25] Cheng Z, Shi Z. Vibration attenuation properties of periodic rubber concrete panels[J]. Construction & Building Materials, 2014, 50:257-265. 

[26] Modinos A. Stefanou N. and Yannopapas V. Applications of the layer-KKR method to photonic crystals [J]. Optics Express, 2001, 8(3): 197-229.

[27] E. Waks, K. Inoue, C. Santori, et al. Secure communication: Quantum cryptography with a photon turnstile [J]. Nature, 2002, 420: 762.