PSI - Issue 17

H. Lopes et al. / Procedia Structural Integrity 17 (2019) 971–978 Lopes et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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destructive tests. However, considering that composite materials are heterogeneous in nature, numerous tests are usually necessary to determine all the material properties. In most cases the composite materials used in aircraft, aerospace and automotive structures have layered internal structure, which makes them belonging into the category of laminated composites. Such laminated structures are usually characterized by transversely isotropic or orthotropic material models, requiring the identification of four or nine independent material constants, respectively, to fully describe the material behavior. This can only be accomplished by experimental tests, performed according to appropriate and specific standards, which are demanding and time consuming. In some cases, however, due to significant difficulties to prepare testing specimens of a given material, performing such tests can be very changeling. In order to avoid such difficulties, numerous methods of non-destructive identification of material properties were developed (Tam et al. (2016)). In particular, there are vibration-based (Araujo et al. (1996)), acoustics-based (Lago et al (2014)) and ultrasonic-based (Wooh and Daniel (1991)) non-destructive methods. One of these non-destructive methods for determination of material properties, which is proven to be very efficient, is based on the use of experimental vibration data (Araujo et al. (1996). The approach presented in this paper is based on measurement of natural frequencies and modal rotations of a polymer reinforced composite plate using non-destructive and non-contact full-field optical measurement techniques. The experimental studies were performed on a transversely isotropic glass fiber-reinforced polymeric plate. In order to identify the four independent material constants, an optimization problem is formulated and solved, which has an objective function relating experimental and numerical natural frequencies. Three optimization algorithms were applied in this study for comparison purposes: (1) particle swarm, (2) genetic, and (3) pattern search algorithms. The identified material constants were validated by comparing modal rotations measured with shearography with those computed by finite element analysis. The obtained results of non-destructive determination of material properties were finally compared with the results obtained from destructive quasi-static testing in previous studies (Katunin and Gnatowski (2012)). 2.1. Laminated composite plate The laminated composite plate analyzed has the length of ʹͻͻǤʹ͸ mm, the width of ͻ͵Ǥ͹ͳ mm and the thickness of 2.3 mm, with a mass of ͳʹ͹Ǥ͸ g, corresponding to the volumetric mass density of ͳͻ͹ͺǤ͵ kg/m 3 . According to Katunin and Gnatowski (2012), this plate is made with polymeric laminated specimen with symbol EP GC 201 and were manufactured and supplied by Izo-Erg S.A. The matrix of the laminate constitutes a mixture of commercial compounds: bisphenol A and tetrabrombisphenol A. The plain weave E-glass fibre cloth with weight of ʹͲͲ g m -2 . Laminate sheets with dimensions of ͳͲͲͲšͳͲͲͲ mm with ͳͶ unidirectional layers and resulting thickness of ʹǤͷേͲǤʹ mm were fabricated using an hydraulic press. The specimens were cut from the prepared sheets. The average flexural modulus of elasticity for the same plate in the three-point bending test was ʹͶǡʹͲ͵Ǥ͸ͳ MPa. 2.2. Experimental modal analysis The natural frequencies of the plate in free-free condition are extracted from the analysis of the peaks of experimental Frequency Response Functions (FRF). A small impact hammer from PCB Piezotronics model:086E80 was used to generate a transient excitation to the structure and response was measured using a laser vibrometer from MetroLaser model: VibroMet 500V, allowing the measurement without contact of the response. Both signals were recorded and processed using the multichannel analyzer from OROS model: OR35. The laminated plate was suspended by two flexible wires and mounted on top of an optical table to minimize the effect of external perturbations during the measurements. The analysis was performed in the band [ Ͳ – ͳǤ͸ kHz] with a frequency resolution of ʹͷͲ mHz. This bandwidth was selected in order to capture bending modes in both directions, thus allowing to get a better identification of material properties. The experimental setup is shown in next the Figure 1. The magnitude of four mobility functions, using the estimator H 1 , are presented in the next Figure 2. Although the FRS present some noise in the antiresonances due to the poor-quality signal captured by the laser vibrometer, it is possible to clearly identify 2. Natural frequencies and identification of properties