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

Abstract

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...