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Vibrations of piezoelectric plates without and with dissipation.

機(jī)譯：壓電板的振動(dòng)，無(wú)耗散。

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摘要

Exact and closed-form solutions are obtained from three-dimensional equations for free vibrations of an infinite, asymmetric bimorph plate of piezoelectric ceramics. Dispersion curves are calculated for different materials as well as for various thickness ratios. The solutions reduce to those of homogeneous plate as rt = 0 and to those of symmetric bimorph plate as rt = 1. The effects of changes in thickness ratios on the behavior of various frequency branches are examined in details.; Energy dissipation attributed to acoustic viscosity as well as electric current conductivity is investigated for high-frequency vibrations and wave propagation in unbounded solids and along infinite plates of piezoelectric ceramics and various cuts of quartz. Free and piezoelectrically forced thickness-vibrations are studied and the mode shapes of displacements and potentials are obtained. Effects of the viscosity and conductivity on the resonance frequency, modes, attenuation coefficients, time constants and coupling factor are calculated and examined.; In the extended framework incorporating the two aforementioned dissipation factors, solutions of plane harmonic wave of arbitrary direction in an infinite and dissipative piezoelectric plate with general symmetry are obtained. Dispersion curves are computed and plotted for real frequencies and complex wave numbers and are compared with those obtained from the linear 3-D theory without dissipation. Effects of energy loss on the wave propagation are examined in detail for AT-cut of quartz as well as ceramic plate of barium titanate.; Piezoelectric ceramic plate of finite length with a pair of free edges is studied. First, we study a non-dissipative plate with a pair of traction-free and charge-free surfaces. Second, under dissipative assumptions, we study a plate with alternating voltage applied to its two surfaces. The solutions are expanded in series of exact functions obtained from the exact solutions. Frequency spectrums are computed and plotted from solving both the free vibration and forced vibration problems for the non-dissipative model and dissipative model, respectively. Mode shapes at various points of the frequency spectrum, both along the length as well as along the thickness directions, are calculated and explained.
機(jī)譯：精確和封閉形式的解決方案是從三維方程獲得的，用于無(wú)限長(zhǎng)，不對(duì)稱的壓電陶瓷雙壓電晶片的自由振動(dòng)。計(jì)算出不同材料以及各種厚度比的色散曲線。當(dāng)rt = 0時(shí)，解為均質(zhì)板的解；當(dāng)rt = 1時(shí)，解為對(duì)稱雙壓電晶片的解。詳細(xì)研究了厚度比變化對(duì)各個(gè)頻率分支行為的影響。對(duì)于在無(wú)界固體中以及沿著無(wú)限長(zhǎng)的壓電陶瓷和各種石英切割的高頻振動(dòng)和波傳播，研究了由于聲學(xué)粘度和電流傳導(dǎo)性引起的能量耗散。研究了自由和壓電強(qiáng)迫的厚度振動(dòng)，并獲得了位移和電勢(shì)的振型。計(jì)算并檢查了粘度和電導(dǎo)率對(duì)諧振頻率，模式，衰減系數(shù)，時(shí)間常數(shù)和耦合因子的影響。在結(jié)合了上述兩個(gè)耗散因子的擴(kuò)展框架中，獲得了具有一般對(duì)稱性的無(wú)限耗散壓電板中任意方向的平面諧波的解。計(jì)算色散曲線并繪制實(shí)頻率和復(fù)波數(shù)，并將其與從線性3-D理論獲得的無(wú)色散的曲線進(jìn)行比較。仔細(xì)研究了AT切割石英以及鈦酸鋇陶瓷板的能量損耗對(duì)波傳播的影響。研究了具有一對(duì)自由邊緣的有限長(zhǎng)度的壓電陶瓷板。首先，我們研究具有一對(duì)無(wú)牽引力和無(wú)電荷表面的非耗散板。其次，在耗散假設(shè)下，我們研究了在其兩個(gè)表面上施加交流電壓的板。從精確解中獲得的一系列精確函數(shù)擴(kuò)展了解。通過(guò)分別求解非耗散模型和耗散模型的自由振動(dòng)和強(qiáng)迫振動(dòng)問(wèn)題來(lái)計(jì)算和繪制頻譜。計(jì)算并解釋了沿頻譜長(zhǎng)度方向和沿厚度方向在頻譜各個(gè)點(diǎn)的模式形狀。

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  • 作者

    Liu, Ninghui.;

  • 作者單位

    Princeton University.;

  • 授予單位 Princeton University.;
  • 學(xué)科 Applied Mechanics.
  • 學(xué)位 Ph.D.
  • 年度 2006
  • 頁(yè)碼 156 p.
  • 總頁(yè)數(shù) 156
  • 原文格式 PDF
  • 正文語(yǔ)種 eng
  • 中圖分類 應(yīng)用力學(xué);
  • 關(guān)鍵詞

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