Piezoelectric Based Lamb Waves Generation and Propagation in Orthotropic CFRP Plates: II. Influence of Interfacial Stress Distribution

Abstract

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.

On the Directivity of Lamb Waves Generated by Wedge PZT Actuator in Thin CFRP Panel

“…The sources, which have been used to adequately build the transducer's structure and replicate its dynamics in FE model, were the technical notes about the ultrasonic principles important to wedge transducer application and design, including the scheme and main requirements to the active element, backing, matching layers and the sound path presented by Olympus Co. ® [48], the outer dimensions of the used actuator (see Figure 3), the frequency response functions for the electric current through PZT active plate, and out-of-plane displacement amplitude on the actuator's footprint (see Figure 4a,b), which have been determined experimentally. Only averaged normal displacement amplitudes of the actuator's contact surface were measured experimentally by using the VibroGo single-point vibrometer (Polytec Co. ® , Irvin, Figures 1b and 2b demonstrates that the wavelength of A0 Lamb waves mode is 2-5 time less than the wavelength of SS0 horizontally polarized shear wave, i.e., spatial defects resolution of A0 waves can be significantly better that is fully consistent with the results of the papers [11,20,22,30].…”

“…. The angular distribution of relative dimensionless attenuation coefficient for the anti-symmetric A0 waves propagating from the center of the orthotropic CFRP panel [20].…”

“…This list makes obvious the damping's anisotropy of the multilayered composites with differently oriented layers. The propagation of attenuating waves generated by the omnidirectional circular PZT actuators in a CFRP plate with significant anisotropy of elastic and dissipative properties was studied in Materials 2020, 13, 907 3 of 22 the authors' works [20,21], where the properties of the orthotropic material were previously determined as effective modules in accordance with the methodology considered in [22]. But the dissipative properties of the fiber reinforced composites depend on the many factors, and these dependencies should be taken into account at the estimation of the range of wave advancement to supply the desired parameters of SHM system.…”

“…The angular distribution of relative dimensionless attenuation coefficient for the anti-symmetric A0 waves propagating from the center of the orthotropic CFRP panel[20]. The experimentally studied CFRP panel with schematically shown coordinate systems of orthotropic symmetry ( )2 1 , x x and wedge actuator's (X,Y) rotated relative to the first one by an angle, θ (a); the arrangement of sensors for recording the A0 Lamb waves propagation (b).…”

On the Directivity of Acoustic Waves Generated by the Angle Beam Wedge Actuator in Thin-Walled Structures

“…The particular shapes of the waves intensity angular distributions can be explained by the forms of the actuator's vibration modes. The very large computational complexity of the task did not allow us to reveal the distribution of contact stress on the actuator footprint in the same way as was done in [31]. These stresses sharply increase near the border of the footprint and change around its perimeter.…”