Research on Radial Vibration of a Circular Plate

Abstract

Radial vibration of the circular plate is presented using wave propagation approach and classical method containing Bessel solution and Hankel solution for calculating the natural frequency theoretically. In cylindrical coordinate system, in order to obtain natural frequency, propagation and reflection matrices are deduced at the boundaries of free-free, fixed-fixed, and fixed-free using wave propagation approach. Furthermore, radial phononic crystal is constructed by connecting two materials periodically for the analysis of band phenomenon. Also, Finite Element Simulation (FEM) is adopted to verify the theoretical results. Finally, the radial and piezoelectric effects on the band are also discussed.

Free Vibration and Transmission Response Analysis for Torsional Vibration of Circular Annular Plate

“…And they calculated the natural frequency of the radial vibration for these annular plates. Through adopting wave propagation technique, Liu et al (2016) investigated the free vibration of piezoelectric circular plate for the radial vibration, and the effect of inner radius and piezoelectric effect on the transmission response is also discussed. Bahrami and Teimourian (2017) applied the wave approach to analyze the vibration, wave transmission and reflection in composite rectangular membranes.…”

“…In our previous study, wave approach has been applied to analyze the radial vibration (Liu et al 2016) and transverse vibration (Liu et al 2018) of annular plate. However, to the author's knowledge, few studies on torsional vibration can be found.…”

Smart piezoelectric phononic crystals and metamaterials:State-of-the-art review and outlook

“…Aghakhani 等人 [104] 也提出了一个二维压电复合板理论模型， 用于在频域内分析压电片不同的粘贴方 式、电路参数对于弯曲波传播的影响。Lian 等人 [105] 则将电压作为未知量改进了传统的平面波展开 法，并用改进的平面波展开法计算了不同的分流电路对于弯曲波传播的影响。 在实际工程应用中，结构的减振降噪非常重要。而二维压电复合板的研究结果可以直接应用于 实际的工程结构中。例如 Mokrani 等人 [106] 利用压电片降低了鼓风机叶片的振动。Dai 等人 [107] ，Shu 等人 [108] ，Liu 等人 [109] 则将压电片以环状贴在圆形板上，并研究了不同分流电路对于弯曲波在其中 传播的影响。Ouisse 等人 [110] 将压电片贴在金字塔蜂窝点阵夹芯结构中提高了其隔振降噪的性能。 Koutsianitis 等人 [111] 利用遗传算法以最宽带隙为优化目标，优化了拉胀结构中最佳的压电片分布位 置。Wu 等人 [112] 通过将压电复合梁呈十字型相连接，并用谱元法求解了弯曲波的传输谱以及频域相 应。Xiao 等人 [96] 将压电片贴在碳钎维增强聚合物上，研究了负电容电路和材料参数对于弯曲波传 播的影响，如图 5(c)所示。结果表明，负电容值的增加会使带隙变宽。Chen 等人 [113] 将压电片贴在 蜂窝晶格夹芯板上，以便提高夹芯板的减振性能。 除了外接电路的调控方式之外，也可通过主动控制的措施对二维复合压电声子晶体/超材料实 施调控。Li 等人 [94]…”

Out-of-Plane Free Vibration and Forced Harmonic Response of a Curved Beam

“…e natural frequencies of a continuous curved beam are calculated when the effects of shear deflection and rotary inertia are considered [6]. Liu presented the radial vibration of the circular plate using the wave propagation approach and the classical method containing Bessel solution and Hankel solution for calculating the natural frequency theoretically [7]. Based on the in-plane and out-of-plane governing equation of the curved beam, Liu analyzed the transmission response of periodic curved beams by using the transfer matrix method and Bloch theorem.…”