We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known...We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10^-6 which is not insignificant,and an amplitude change of the order of 10^-8. The effects are expected to be stronger under real damping of 10^-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.展开更多
We study shear-horizontal （SH） waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used...We study shear-horizontal （SH） waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used for the quartz plate and the elastic layer,respectively.A transcen-dental frequency equation that determines the dispersion relations of the waves is obtained.The dispersion relations are obtained and plotted by solving the frequency equation using MATLAB.Approximate dispersion relations are also obtained analytically for two special cases.One is for long waves whose wavelength is much larger than the plate thickness.The other is for the case of a very thin elastic layer.The effects of the elastic layer on the dispersion relations are exam-ined.The results obtained are fundamental and useful to acoustic wave sensors for measuring the mechanical and geometric properties of the elastic layer.展开更多
This paper deals with indirect effects of major impacting throughout the Early Paleozoic resp. with those of super plume activity during the Early Cretaceous, both applied to the siliciclastic series of Jordan deposit...This paper deals with indirect effects of major impacting throughout the Early Paleozoic resp. with those of super plume activity during the Early Cretaceous, both applied to the siliciclastic series of Jordan deposited on the Arabian Platform, Arabian Plate. Its focus is mainly directed on gases released by both processes (CO2, SO2, NOx, HCl, HF) and the relating acids, challenged by experiments and microscopic analysis of grain mounts and thin sections that reveal chemical instability of quartz and ultrastable heavy minerals (i.e. tourmaline) under high acidity (pH °C - 90°C). According to Lopatin’s Time/Temperatur-Index the Lower Cambrian reached the onset of hydrocarbon generation (liquid window) during the Lower Early Cretaceous. Unstable heavy minerals (apatite, garnet, hornblende, epidote, zoisite/clinozoisite) are generally absent in quartz arenites while in arkosic sandstones of marine environment carbonate cement and primary clay minerals (illite) provide conservation. As known since the eighties, the K/T-event’s indirect effects had global influence on Earth’s surface sediments and atmospheric chemistry by wildfires, hot whirl storms, acidic “sturz rain”, dust, soot, darkness, loss of photosynthesis, toxic metals, gases and relating acids. All of them are here concerned and applied to major impacting throughout the Early Paleozoic using the impact data of Price (2001);while superplume volcanism during Cretaceous led to the opening of the South Atlantic accompanied by the cyclic outflow of the Para?a/Etendeka Flood Basalts and relating gases in a gigantic scale (137 - 127 Ma). Assuming that the gases cause similar global effects on Earth’s surface sediments, an according result may be expected in form of quartz arenites and their sequence-analytical patterns (cyclic SBs, MFSs).*展开更多
The thickness-shear （TS） and thickness-twist （TT） vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural v...The thickness-shear （TS） and thickness-twist （TT） vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone fam- ilies of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acous- tic wave resonators and filters.展开更多
We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed....We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases： pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.展开更多
Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration a...Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.展开更多
This research aims to use several kind of rare earth oxides, such as Nd2O3, Yb2O3, Ce2O3 and La2O3, to improve the electroless plating and electroplating processes for surface metallization of quartz optical fiber (si...This research aims to use several kind of rare earth oxides, such as Nd2O3, Yb2O3, Ce2O3 and La2O3, to improve the electroless plating and electroplating processes for surface metallization of quartz optical fiber (silicon fiber) for its practical uses. The effects of the rare earth oxides on the deposition rate of Ni-P-B, the stability of the plating solution and the surface property of the film were investigated and the comparisons of their behaviours were made. The effects of rare earth oxide of La2O3 on the hardness and surface property of the Ni film prepared by electroplating process were studied. The surface morphonogies, compositions and hardness of the Ni-P-B and Ni films were characterized and analyzed by SEM, MSM, ICP and DIMHM, respectively. The experimental results showed that Ce2O3 with the concentration of 4 mg·L-1 was the best one among the four rare earth oxides with suitable concentrations in increasing the deposition rate, enhancing the stability of the electroless plating solution and improving the surface property of the Ni-P-B film. The improvements of the hardness and surface property of the Ni film prepared by electroplating with adding La2O3 were discovered. No obvious influences of Ce2O3 and La2O3 on the compositions of Ni-P-B and Ce free in the Ni-P-B film were found because of its much more nagative deposition potential than those of the used reducing agents in this experiment. The total diameter of the quartz optical fiber with deposited Ni-P-B film and Ni film was about 1.7 mm, which could be satisfactorily for the practical uses of quartz optical fiber in many fields.展开更多
基金supported by the Science and Technology Division of Zhejiang Provincial Government under the Key Technological Initiative Program(No.2006C14021)Additional supports are from Ningbo University through the K.C.Wong Magna Fund,the Qianjiang Fellow Fund,and the Research Promotion Initiative.
文摘We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10^-6 which is not insignificant,and an amplitude change of the order of 10^-8. The effects are expected to be stronger under real damping of 10^-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.
基金supported by the National Natural Science Foundation of China (Nos. 11072116,10772087 and 10932004)Key Team of Technological Innovation of Zhejiang Province (Grant 2009R50025)+2 种基金Key Industrial Project of Bureau of Science and Technology,City of Ningbo (No. 2005B100015)grants from the Bureau of Science and Technology,City of Ningbo,through the International Collaboration Initiative (Project 2007B10052)Sponsored by K.C.Wong MagnaFund in Ningbo University
文摘We study shear-horizontal （SH） waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used for the quartz plate and the elastic layer,respectively.A transcen-dental frequency equation that determines the dispersion relations of the waves is obtained.The dispersion relations are obtained and plotted by solving the frequency equation using MATLAB.Approximate dispersion relations are also obtained analytically for two special cases.One is for long waves whose wavelength is much larger than the plate thickness.The other is for the case of a very thin elastic layer.The effects of the elastic layer on the dispersion relations are exam-ined.The results obtained are fundamental and useful to acoustic wave sensors for measuring the mechanical and geometric properties of the elastic layer.
文摘This paper deals with indirect effects of major impacting throughout the Early Paleozoic resp. with those of super plume activity during the Early Cretaceous, both applied to the siliciclastic series of Jordan deposited on the Arabian Platform, Arabian Plate. Its focus is mainly directed on gases released by both processes (CO2, SO2, NOx, HCl, HF) and the relating acids, challenged by experiments and microscopic analysis of grain mounts and thin sections that reveal chemical instability of quartz and ultrastable heavy minerals (i.e. tourmaline) under high acidity (pH °C - 90°C). According to Lopatin’s Time/Temperatur-Index the Lower Cambrian reached the onset of hydrocarbon generation (liquid window) during the Lower Early Cretaceous. Unstable heavy minerals (apatite, garnet, hornblende, epidote, zoisite/clinozoisite) are generally absent in quartz arenites while in arkosic sandstones of marine environment carbonate cement and primary clay minerals (illite) provide conservation. As known since the eighties, the K/T-event’s indirect effects had global influence on Earth’s surface sediments and atmospheric chemistry by wildfires, hot whirl storms, acidic “sturz rain”, dust, soot, darkness, loss of photosynthesis, toxic metals, gases and relating acids. All of them are here concerned and applied to major impacting throughout the Early Paleozoic using the impact data of Price (2001);while superplume volcanism during Cretaceous led to the opening of the South Atlantic accompanied by the cyclic outflow of the Para?a/Etendeka Flood Basalts and relating gases in a gigantic scale (137 - 127 Ma). Assuming that the gases cause similar global effects on Earth’s surface sediments, an according result may be expected in form of quartz arenites and their sequence-analytical patterns (cyclic SBs, MFSs).*
基金supported by the Program for New Century Excellent Talents in Universities of the Ministry of Education of China(No.NCET-12-0625)the National Natural Science Foundation of China(Nos.11232007 and 11502108)+2 种基金the Science Foundation for Distinguished Young Scholars of Jiangsu Province(No.SBK2014010134)the Fundamental Research Funds for the Central Universities(Nos.NE2013101 and NZ2013307)funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘The thickness-shear （TS） and thickness-twist （TT） vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone fam- ilies of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acous- tic wave resonators and filters.
基金Project supported in part by the National Natural Science Foundation of China (Grant Nos. 10932004, 11072116, and 10772087)the Doctoral Program Fund of Ministry of Education of China (Grant No. 20093305110003/JW)+3 种基金Additional Funds were from the Sir Y. K. Pao Chair Professorshipthe K. C. Wong Magna Fund through Ningbo Universitythe K. C. Wong Education Foundation in Hong KongThe project also supported in part by the US Army Research Laboratory/US Army Research Office (Grant No. W911NF-10-1-0293)
文摘We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases： pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.
基金supported by a grant from the Science and Technology Division,Zhejiang Provincial Government,under the Key Project of the International Collaborative Program(Grant No.2006C14021)Additional support is from the K.C. Wong Magna Fund of Ningbo University.
文摘Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.
基金the State Special Programs for 973 Key Foundamental Pre-Research (2005cca04300)
文摘This research aims to use several kind of rare earth oxides, such as Nd2O3, Yb2O3, Ce2O3 and La2O3, to improve the electroless plating and electroplating processes for surface metallization of quartz optical fiber (silicon fiber) for its practical uses. The effects of the rare earth oxides on the deposition rate of Ni-P-B, the stability of the plating solution and the surface property of the film were investigated and the comparisons of their behaviours were made. The effects of rare earth oxide of La2O3 on the hardness and surface property of the Ni film prepared by electroplating process were studied. The surface morphonogies, compositions and hardness of the Ni-P-B and Ni films were characterized and analyzed by SEM, MSM, ICP and DIMHM, respectively. The experimental results showed that Ce2O3 with the concentration of 4 mg·L-1 was the best one among the four rare earth oxides with suitable concentrations in increasing the deposition rate, enhancing the stability of the electroless plating solution and improving the surface property of the Ni-P-B film. The improvements of the hardness and surface property of the Ni film prepared by electroplating with adding La2O3 were discovered. No obvious influences of Ce2O3 and La2O3 on the compositions of Ni-P-B and Ce free in the Ni-P-B film were found because of its much more nagative deposition potential than those of the used reducing agents in this experiment. The total diameter of the quartz optical fiber with deposited Ni-P-B film and Ni film was about 1.7 mm, which could be satisfactorily for the practical uses of quartz optical fiber in many fields.
