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Some Dynamic Problems in the Theory of Piezoceramic Plates and Shells
Published in Nellya N. Rogacheva, The Theory of Piezoelectric Shells and Plates, 2020
where ωr is the resonance frequency and ωa is the antiresonance frequency. Another energy formula for the EMCC was suggested by W.J. Toulis [107], but R.S. Wollett [113, 114] showed that it was erroneous. Using some reasonable approaches of W.J Toulis [107], V.T. Grinchenko et al. [26] gave their own version of the formula for computing the EMCC: where () ke2=U(d)−U(sh)U(d)
Equivalent Circuits with Piezo Losses
Published in Kenji Uchino, High-Power Piezoelectrics and Loss Mechanisms, 2020
Figure 5.6 shows the PSpice simulation process of the IEEE Standard k31 type. Figure 5.6a shows an equivalent circuit for the k31 mode. L, C, and R values were calculated for PZT4 with 40 × 6 × 1 mm3 [Eqs. (5.14), (5.15), and (5.20)], and Figure 5.6b plots the simulation results on the current under 1 Vac, that is, admittance magnitude and phase spectra. IPRINT1 (current measurement), IPRINT2, and IPRINT3 are the measure of the total admittance (□ line), motional admittance (○ line), and damped admittance (∇ line), respectively. First, the damped admittance shows a slight increase with the frequency (jωCd) with +90° phase in a full frequency range. Second, the motional admittance shows a peak at the resonance frequency, where the phase changes from +90° (i.e., capacitive) to −90° (i.e., inductive). In other words, the phase is exactly zero at the resonance frequency. The admittance magnitude decreases above the resonance frequency with a rate of −20 dB down in a Bode plot. Third, by adding the above two, the total admittance is obtained. The admittance magnitude shows two peaks, maximum and minimum, which correspond roughly to the resonance and antiresonance points, respectively. You can find that the peak sharpness (i.e., the mechanical quality factor) is the same for both peaks, because only one loss is included in the equivalent circuit. The antiresonance frequency is obtained at the intersect of the damped and motional admittance curves. Because of the phase difference between the damped (+90°) and motional (−90°) admittance, the phase is exactly zero at the antiresonance and changes to +90° above the antiresonance frequency. Remember that the phase is −90° (i.e., inductive) at a frequency between the resonance and antiresonance frequencies.
Computer Simulation of Piezoelectric Devices
Published in Kenji Uchino, Micro Mechatronics, 2019
Figure 6.18 shows the PSpice simulation process for the IEEE-type k31 mode. (a) shows an equivalent circuit for k31 mode. L, C, and R values were calculated for PZT4 (Qm = 500) with 40 × 6 × 1 mm3, according to Equations 6.57–6.61. Figure 6.18b plots the simulation results on the currents under 1 Vac (constant voltage drive), that is, admittance magnitude and phase spectra. IPRINT1 (current measurement), IPRINT2, and IPRINT3 are the measure of the total admittance (□ line), motional admittance (○ line), and damped admittance (∇ line), respectively. First, the damped admittance shows a slight increase with the frequency (i.e., jωCd) with +90° phase in a full frequency range. Second, the motional admittance shows a peak at the resonance frequency, where the phase changes from +90° (i.e., capacitive) to –90° (i.e., inductive). In other words, the phase is exactly zero at the resonance. The admittance magnitude decreases above the resonance frequency with a rate of –40 dB down in the Bode plot. Third, by adding the above two, the total admittance is obtained. The admittance magnitude shows two peaks, maximum and minimum, that correspond to the resonance and antiresonance points, respectively. You can find that the peak sharpness (i.e., the mechanical quality factor) is the same for both peaks, because only one loss is included in the equivalent circuit. The antiresonance frequency is obtained at the intersect of the damped and motional admittance curves. Because of the phase difference between the damped (+90°) and motional (–90°) admittance, the phase is exactly zero at the antiresonance and changes to +90° above the antiresonance frequency. Remember that the phase is –90° (i.e., inductive) at a frequency between the resonance and antiresonance frequencies.
A study on the mechanism of vehicle body vibration affecting the dynamic interaction in the pantograph–catenary system
Published in Vehicle System Dynamics, 2021
Yongming Yao, Dong Zou, Ning Zhou, Guiming Mei, Jiangwen Wang, Weihua Zhang
When the excitation frequency satisfies: The antiresonance phenomenon will appear at the coordinate point i of the system. That is to say, under the harmonic excitation of antiresonance frequency, the displacement admittance of some parts of the system is 0 [35]. And Figure 15 shows that when the frequency of the excitation force is 3.5 Hz, the vertical displacement of the upper arm exceeds 1.5 mm, while the vertical displacement of the pantograph head is less than 0.2 mm. Under this excitation frequency, the displacement admittance of pantograph head is almost 0, so antiresonance frequency of the pantograph system at 3.5 Hz is verified.
Low frequency band gap and wave propagation mechanism of resonant hammer circular structure
Published in Mechanics of Advanced Materials and Structures, 2023
Shu-liang Cheng, Xiao-feng Li, Qun Yan, Bin Wang, Yong-tao Sun, Ya-jun Xin, Qian Ding, Hao Yan, Ya-jie Li
In complex working conditions, the problem of sound insulation and vibration reduction in the low frequency band below 1000 Hz becomes particularly difficult. The noise generated by low-frequency vibration has super penetrating power, long propagation distance and difficult to control, which makes it impossible for people to live a healthy productive life. Therefore, the design of periodic phonon crystals with suitable subwavelength dimensions to cope with vibration and noise reduction in the low-frequency band has become a hot research topic [36]. Currently, the band gap frequency can be effectively reduced by introducing the principle of local resonance composed of resonators. Liu et al [37], applied a high-density mass block wrapped with soft elastic material in a cubic lattice, which constitutes a local resonance unit, can effectively attenuate large wavelength vibrations, thus opening the band gap around 400 Hz. The conventional local resonance structure produces a narrow band gap, so Li et al [38] successfully opened a large broadband gap in the range of 256 Hz − 855 Hz by periodically setting a cylindrical phonon crystal on a thin plate, which is a new type of phonon crystal designed by applying the principle of "solid-state Helmholtz resonator". Ning et al [39] designed a tunable metamaterial consisting of a frame structure, an airbag and a weight. Wu et al [40] have developed a thin-film acoustic metamaterial structure by analogy with the local resonance theory, attaching a metal mass block and a metal crossbar to the circular thin-film structure to limit the propagation of elastic waves by anti-resonance. The antiresonance restricts the propagation of elastic waves, thus reducing the intrinsic frequency to achieve low frequency noise reduction. Most of the above designs achieve good vibration and noise control by sacrificing simplicity of manufacturing and miniaturization of size, so the design of a small-sized phononic crystal with both easy manufacturing and low frequency noise reduction has become a hot topic.