A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

Wang, Ji; Du, Jianke; Pan, Qiaoqiao

doi:10.1007/s11433-007-0059-1

Cited by 11 publications

(8 citation statements)

References 27 publications

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“…We found that the two surface acoustic wave modes had velocities normalized by the transverse wave velocity c T as 0.90717921 and 0.91541065, which are the exact results from the earlier study [19] . The displacements of the two modes are shown in Figures 2 and 3.…”

Section: Numerical Examplessupporting

confidence: 84%

“…For an infinite plate with uniform thickness and waves traveling in the x 1 direction, we assume that the displacements are [19][20][21] …”

Section: Surface Acoustic Waves In a Layered Platementioning

confidence: 99%

“…It is generally conceivable that by using thin layers we should be able to analyze plates of any property variation schemes provided that the computational challenges can be overcome with large number of layers and accompanying variables. This has been a general practice in the analysis of structures of FGMs [17][18][19][20][21][22][23][24][25][26] . In this study, this method is also employed to obtain simple and direct solutions for a few property variation schemes we are interested in.…”

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confidence: 99%

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An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

Gao

Wang

Zhong

et al. 2008

Sci. China Ser. G-Phys. Mech. Astron.

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In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing different features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with general material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grading schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applications of such structures in engineering.Rayleigh wave, surface acoustic wave, vibration, plate, layered structure, functionally graded material (FGM) Surface acoustic waves (SAW), also known as Rayleigh waves, exist in a semi-infinite solid with a free plane surface. Since its discovery by Rayleigh in 1885 [1] , surface acoustic waves have found wide engineering applications including piezoelectric surface acoustic wave resonators [2] . More general applications in foundations for vibration control and isolation caused by moving loads are also important because surface waves have been the destructive wave component due to its lower velocity (frequency) and energy concentration [3][4][5][6] . Although these applications are drastically different by nature, the common feature we can summarize is that both surface wave velocity and displacements are the major concerns for given structures. For SAW devices, which are widely

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Section: Numerical Examplessupporting

confidence: 84%

“…For an infinite plate with uniform thickness and waves traveling in the x 1 direction, we assume that the displacements are [19][20][21] …”

Section: Surface Acoustic Waves In a Layered Platementioning

confidence: 99%

mentioning

confidence: 99%

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An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

Gao

Wang

Zhong

et al. 2008

Sci. China Ser. G-Phys. Mech. Astron.

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“…As a results, analytical and design efforts have been directed to the precise prediction of wave propagation in the complicated structure and optimization of geometric parameters to achieve better performance in electrical circuit applications [13][14][15][16]. As an electrical circuit element, the electrical parameters such as the resistance and capacitance are closely related to the configuration of the resonator, then the elastic deformation of the finite piezoelectric solid.…”

Section: Introductionmentioning

confidence: 99%

P3K-3 Surface Acoustic Waves in an Infinite Plate of Functionally Graded Materials

Wang

Zhou

2006

2006 IEEE Ultrasonics Symposium

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We have found that the spatial variation of material properties such as elastic constants and density will result in significant changes in surface acoustic waves (Rayleigh waves) in a semi-infinite substrate including the wave velocity and deformation, implying potential advantages in modifying the velocity (frequency) and changing the surface deformation which are directly related to device performance and packaging, since it is generally required to obtain large electrical charge through surface deformation and minimizing energy leaking by limiting the deformation of bottom surface. With these positive results, we further consider the case that the substrate is finite in thickness, making the analytical model close to actual surface acoustic wave (SAW) resonators. Again by assuming the material properties varying along the thickness direction uniformly, we obtained the frequency equation by satisfying boundary conditions on the faces.Consequently, the deformation variation along the thickness is also obtained with specified variation parameters for possible optimal selection in variation schemes. Using the exponential variation of material properties in an isotropic plate as an example, we calculated the surface acoustic wave velocity and deformation for different parameters. It is found that unlike a homogeneous plate, the symmetric and anti-symmetric wave modes will not merge to one velocity even for smaller grading parameters and the deformation will also be distinctive. The gap between two velocities will be larger as the property variation increases. Also the surface acoustic wave modes exist for very small thickness of the plate. For surface acoustic wave resonators, such a phenomena demonstrates a possible way to have velocity (frequency) selectivity based on different operating modes, and the frequency selectivity can be further modified by using different material variation parameters.With the rapid advances of material processing techniques, such benefits of functionally graded materials (FGMs) in surface acoustic waves have great potential in the new generations of devices.

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“…The wave method has been used to solve the structural vibration problem [13][14][15][16][17][18][19][20]. Cremer et al [13] used the wave propagation concept to describe the dynamic responses of beams and plates.…”

Section: Introductionmentioning

confidence: 99%

Vibration control of the finite L-shaped beam structures based on the active and reactive power flow

Liu

Tang

et al. 2010

Sci. China Phys. Mech. Astron.

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This paper analyzes the physical meaning of the active and reactive power flow in the finite L-shaped beams and studies the active vibration control of the structures based on the active and reactive power flow. The traveling wave approach is used to calculate the structural dynamic responses. Because the error of control force is inevitable in practical applications, the effects of the error of control force on the control results are studied. The study indicates that the error of control force has pronounced influence on the control results of the acceleration and reactive power flow. It is obvious that the reactive power flow can represent the vibration strength component of the complex intensity, and the active power flow strongly depends on the structural damping of the finite beams.finite L-shaped beam, active power flow, reactive power flow, active vibration control, traveling wave method PACS: 46.70.De, 43.40.+s, 45.80.+r, 42.25.Bs

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A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

Cited by 11 publications

References 27 publications

An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

P3K-3 Surface Acoustic Waves in an Infinite Plate of Functionally Graded Materials

Vibration control of the finite L-shaped beam structures based on the active and reactive power flow

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