In-plane P-SV waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions

The derivation of plate equations for a plate consisting of two layers, one anisotropic elastic and one piezoelectric, is considered. Power series expansions in the thickness coordinate for the displacement components and the electric potential lead to recursion relations among the expansion functions. Using these in the boundary and interface conditions, a set of equations is obtained for some of the lowest-order expansion functions. This set is reduced to six equations corresponding to the symmetric (in-plane) and antisymmetric (bending) motions of the elastic layer. These equations are given to linear (for the symmetric equations) or quadratic (for the antisymmetric equations) order in the thickness. It is noted that it is, in principle, possible to go to any order, and that it is believed that the corresponding equations are asymptotically correct. A few numerical results for guided waves along the plate and a 1D actuator case illustrate the accuracy.

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“…by using the present equations or by using equivalent boundary conditions [9,11] and comparing with exact calculations for simple cases.…”

Section: A15mentioning

confidence: 99%

“…All lengthy analytical calculations involved are performed with Mathematica. This approach has previously been adopted for an isotropic plate, see Boström et al [8], and for deriving equivalent boundary conditions for a thin piezoelectric layer, see Johansson and Niklasson [9], Zhang et al [10], and Boström and Zhang [11].…”

Section: Introductionmentioning

confidence: 99%

Modelling of thin piezoelectric layers on plates

2008

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“…2.19, 2.20, 2.22 and 2.23, also used by Gopinathan et al (2000) and Boström and Zhang (2005), have the advantage that they, together with the electric boundary condition (2.21), make it possible to expand the fields inside the two layers in simple trigonometric series in x. This is used in the exact solution of the problem in Section 5.…”

Section: ð2:13þmentioning

confidence: 99%

“…Also the derivation of these plate equations are based on the same series expansion approach. The exact solution of the problem follows an approach based on Fourier series expansions, similar to one adopted by Boström and Zhang (2005) for a piezoelectric strip actuator. In Section 6 numerical calculations of the displacement field are compared between the three theories.…”

Section: Introductionmentioning

confidence: 99%

Modelling of finite piezoelectric patches: Comparing an approximate power series expansion theory with exact theory

Mauritsson

2009

International Journal of Solids and Structures

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a b s t r a c tPlate equations for a plate consisting of one elastic layer and one piezoelectric layer with an applied electric voltage have previously been derived by use of power series expansions of the field variables in the thickness coordinate. These plate equations are here evaluated by the consideration of a time harmonic 2D vibration problem with finite layers. The boundary conditions at the sides of the layers then have to be considered. Numerical comparisons of the displacement field are made with solutions from two other theories; a solution with equivalent boundary conditions for a thin piezoelectric layer applied on an elastic plate and an exact solution based on Fourier series expansions. The two approximate theories are shown to be equally good and they both yield accurate results for low frequencies and thin plates.

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“…For that reason, its use is somewhat rare. The analysis of contact interaction between a surface-bonded piezoelectric actuator and an elastic half-space was carried out, for example, in [5,6]. The case of a waveguide of finite thickness was considered in [7] and in the authors' articles [8,9,10].…”

mentioning

confidence: 99%

Resonance excitation and mode selection in smart structures with piezoelectric patch actuators

Глушков

Glushkova

Kvasha

et al. 2008

Proc Appl Math and Mech

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A system of piezoelectric flexible patch actuators bonded to an elastic layered substrate is considered. An integral equation based model for the smart structure under consideration has been developing. The rigorous solution to the patch-substrate dynamic contact problem extends the range of the model's utility far beyond the bounds of conventional simplified models that rely on plate, beam or shell equations for the waveguide part. The developed approach provides the possibility to reveal the effects of resonance energy radiation associated with higher modes that would be inaccessible using models accounting for the fundamental modes only. Algorithms that correctly account for the mutual wave interaction among the actuators via the host medium, for selective mode excitation in a layer as well as for body waves directed to required zones in a half-space, have also been elaborated and implemented in computer code. Electromechanical systems with distributed piezoelectric actuators and sensors in the form of flexible patches bonded to or embedded in elastic waveguide structures serve as a basis for modern material systems with intelligence and life features integrated in the microstructure that are referred to as smart materials and smart structures. They find a wide variety of applications in ultrasonic non-destructive evaluation and structural health monitoring, e.g. shell structures in aerospace units, active systems of vibration damping, precision mechanical positioning gears, ultrasonic surface wave motors etc.We consider elastodynamic behavior of substructures (layers or half-spaces) with sets of thin and flexible piezoelectric strip actuators bonded to their surface (typical configurations are shown in Fig. 1). The longitudinal deformation of the piezoelectric strips in response to a transverse electromagnetic field causes contact shear tractions generating a 2D in-plane harmonic wave field u(x, z)e −iωt in the waveguide. Conventionally, such piezoelectrically excited devices are simulated using simplified mathematical models with mechanical elements (elastic waveguides) described by beam, plate or shell equations and actuating contact forces replaced by concentrated bending moments applied at the points of patch edges (pin-force models; see, for example, surveys in [1, 2]). However, these models may be used in a low-frequency range only, first of all, because they do not account for the higher normal modes inherent to elastic layer waveguides. For instance, the comparison of the dispersion curves for an elastic layer and a Kirchhoff's plate are shown in Fig. 2). Here and in the numerical examples below ω = 2πf h/v s is a dimensionless angular frequency composed of the dimensional frequency f , waveguide's thickness h and S-wave velocity v s . The dimensionless parameters are introduced so that h = 1, v s = 1 and the material density ρ = 1; the Poisson's ratio ν = 0.3.The wave numbers ξ n of two plate traveling waves (bending and longitudinal) given in Fig. 2 by the dashed lines coincide with the wave number...

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In-plane P-SV waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions

Cited by 8 publications

References 11 publications

Modelling of thin piezoelectric layers on plates

Modelling of thin piezoelectric layers on plates

Modelling of finite piezoelectric patches: Comparing an approximate power series expansion theory with exact theory

Resonance excitation and mode selection in smart structures with piezoelectric patch actuators

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