This paper investigates the Lamb wave generation by the surface bonded circular piezoelectric (PZT) actuator and wave propagation within the orthotropic Carbon Fiber Reinforced Plastic (CFRP) plate considering the anisotropy of the elastic and damping properties of the materials; existence of the adhesive layer; and dependence of the interfacial stress distribution on the surface between host plate and actuator, on the anisotropy of the plate material, and on the excited frequency, wavelength and plate thickness. This part of our investigation includes FE based study of the shear stress distribution on the interface between circular PZT actuator and surface of orthotropic CFRP plate, and its dependence on the excited wavelength and plate thickness. The anisotropic elastic and damping properties of the plate material, which are used in the implemented finite element (FE) model, have been preliminary determined in the first part of our investigation. We compare the behavior of the wave generation, propagation and attenuation that are studied using this model with the similar dependencies obtained at the simulation of the non-dissipating plate excited by the periodical radially oriented force, which is distributed along the circumference bounding the actuator, i.e. 3D pin-force excitation case. The proposed results can be used at the design of SHM for the composite structures with the structural anisotropy and damping, and at making a reasonable choice of the frequency, type, dimensions and optimum placement of the actuators and sensors.

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In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting properties of formal power series. Along the way, we show how formal power series can be used to solve combinatorial problems and also derive some results in calculus with a minimum of analytical machinery.

The article investigates the Lamb wave generation by the surface bonded circular actuator and wave propagation within the orthotropic Carbon Fiber Reinforced Plastic (CFRP) plate considering the anisotropy of the material elastic and damping properties. The first part of our investigation includes experimental determination of the elastic properties of CFRP, the wave attenuation, determination of the waves type that can be excited in the studied CFRP panel using a given frequency range. The model of anisotropic material damping has been proposed, which was further used in the Finite Element (FE) implementation of transient wave generation, propagation and attenuation that is present in the second part of the reported study. The proposed results can be used at the design of SHM for the composite structures with the structural anisotropy and damping, and for making a reasonable choice of the frequency and amplitude of excitation to provide the desired propagation distance and orientation of generated waves.

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The paper aims to develop improved acoustic-based structural health monitoring (SHM) and nondestructive evaluation (NDE) techniques, which provide the waves directivity emitted by the angle beam wedge actuators in thin-walled structures made of plastic materials and polymeric composites. Our investigation includes the dispersive analysis of the waves that can be excited in the studied plastic panel. Its results allowed to find two kinds of generated acoustic waves-anti-symmetric Lamb waves (A0) and shear horizontally polarized SH waves (SS0). The bounds of the chosen frequency range for the experimental and numerical studies were accepted as a compromise between the desire to obtain a high defect resolution by generating short waves, their adjustable directivity, and maximum propagation length. The finite element model for the transducer was built by using the results of an actuator structure experimental study. The frequency response functions for the actuator current and oscillation amplitude of the footprint surface demonstrated good agreement. The found eigenfrequencies of the actuator's structure were used for the numerical and experimental study of the Lamb and SH wave generation and propagation in a thin-walled plastic panel. Our results convincingly demonstrated the satisfactory directivity of the actuated waves at their excitation on the frequencies that corresponded to the natural modes of the actuator oscillation. The authors assume that an efficient use of the proposed technique for other analyzed quasi-isotropic materials and applied actuators can be provided by preliminary research using a similar approach and methods presented in this article.

This paper addresses investigation of guided-wave excitation by angle-beam wedge piezoelectric (PZT) transducers in multilayered composite plate structure with orthotropic symmetry of the material. The aim of the present study is to determine the capability of such actuators to provide the controlled generation of an acoustic wave of a desirable type with the necessary wavelength, propagation distance and directivity. The studied CFRP (Carbon Fiber Reinforced Plastic) panel is considered to be homogenous, with effective elastic moduli and anisotropic structural damping, whose parameters were determined experimentally. According to the results of dispersion analysis and taking into account the data of wave attenuation in a highly damping CFRP composite, the two types of propagating waves A0 and S0 were considered theoretically and experimentally in the frequency range of 10–100 kHz. Using the results of a previous study, we reconstructed the structure of the wedge actuator, to develop its finite-element (FE) model, and a modal analysis was carried out that revealed the most intense natural vibration modes and their eigenfrequencies within the frequency range used. Both experimental and numerical studies of the generation, propagation, directivity and attenuation of waves in the orthotropic composite panel under study revealed the influence of the angular orientation of the actuator on the formation of wave patterns and allowed to determine the capabilities of the wave’s directivity control.