Abstract
Non-propagating waves have great potential for crack evaluation, but it is difficult to obtain the complex solutions of the transcendental dispersion equation corresponding to the non-propagating wave. This paper presents an analytical approach based on the orthogonal function technique to investigate non-propagating Lamb-like waves in a functionally graded piezoelectric spherical curved plate. The presented approach can transform the set of partial differential equations for the acoustic waves into an eigenvalue problem that can give the generally complex wave numbers and the field profiles. A comparison of the obtained results with the well-known ones in plates is provided. The obtained solutions of the dispersion equation are shown graphically in three dimensional frequency-complex wave number space, which aids in understanding the properties of non-propagating waves better. The properties of the guided wave, including real, purely imaginary, and complex branches in various functionally graded piezoelectric spherical curved plates, are studied. The effects of material piezoelectricity, graded fields, and mechanical and electrical boundary conditions on the dispersion characteristics, are illustrated. The amplitude distributions of displacement and electric potential are also discussed, to analyze the specificities of non-propagating waves.
Highlights
Guided ultrasonic waves (GUW) are widely used as a tool for various problems in structural health monitoring and nondestructive evaluation
We present a method that is based on the orthogonal function technique, to determine the complex dispersion solution, and to study the characteristics of non-propagating guided waves in a functionally graded piezoelectric materials (FGPMs) spherical curved plate
The FGPM spherical curved plate is composed of PZT-4 and
Summary
Guided ultrasonic waves (GUW) are widely used as a tool for various problems in structural health monitoring and nondestructive evaluation. Dubuc et al [24] studied propagating and non-propagating guided waves in a nonuniformly stressed plate. Non-propagating waves in functionally graded piezoelectric cylindrical structures with sectorial cross-sections, and in functionally graded piezoelectric-piezomagnetic plates, were investigated by Zhang et al [25] and Zhang et al [26] without considering the different mechanical and electrical boundary conditions. To the best of the authors’ knowledge, the non-propagating waves in FGPM spherical curved structures, with different mechanical and electrical boundary conditions, have not been studied before. We present a method that is based on the orthogonal function technique, to determine the complex dispersion solution, and to study the characteristics of non-propagating guided waves in a FGPM spherical curved plate.
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