PSI - Issue 81

Andrejs Kovalovs et al. / Procedia Structural Integrity 81 (2026) 388–395

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determination and accurate characterization of their elastic constants. Conventional destructive testing methods – such as tensile, shear, and bending experiments – necessitate the preparation of multiple specimens cut along different fiber orientations. These procedures are time-consuming, expensive, and often impractical when dealing with thin laminates or fully manufactured components, where specimen extraction or machining is not feasible without compromising structural integrity. To overcome these limitations, non-destructive approaches have emerged as viable alternatives, substantially reducing experimental costs and preserving the integrity of valuable components (Akishin et al., 2014; Kovalovs et al., 2024). Such methods are typically categorized as either static or vibrational. In static testing, a quasi-static load is applied to the specimen, and its elastic strain field is analyzed. Vibration-based methods, in contrast, employ experimental modal analysis to identify key modal parameters such as natural frequencies and vibration modes. Because the modal characteristics depend directly on the structure’s mass and stiffness distribution, and the mass density can be measured independently, variations in modal frequencies primarily reflect stiffness properties. The identification of elastic constants from modal characteristics does not require large deformation amplitudes. Therefore, the obtained data describe the linear material properties and do not introduce any significant damage. Consequently, comparing experimentally measured frequencies with numerically simulated ones allows the identification of the unknown elastic constants of the laminate. Vibration-based identification belongs to the class of inverse problems, where material parameters are iteratively adjusted to make the numerical model reproduce the measured modal behavior. The process typically includes construction of a numerical finite-element (FE) model, experimental modal testing of a specimen, and optimization of material parameters to minimize the residuals between experimental and simulated frequencies and mode shapes. The error functional quantifying this residual is used as the criterion for parameter estimation. Early implementations of such techniques were computationally demanding because each optimization iteration required a complete FE analysis (Rikards, 2003). To reduce computational cost, Rikards and Auzins (2004) introduced the Response Surface Methodology (RSM), which replaces direct iterative FE analysis by low-order polynomial approximations linking modal frequencies to material constants. This approach allows rapid optimization while maintaining accuracy. Rikards (2003) successfully applied this methodology to laminated composites, identifying the orthotropic elastic constants of carbon-fiber layers from measured modal frequencies. Subsequent studies have demonstrated that RSM-based inverse methods require far less computational power than traditional iterative algorithms, enabling routine laboratory application. Furthermore, vibration-based inverse analysis can retrieve not only elastic parameters but also damping-related characteristics, such as the loss modulus (Barkanov et al., 2009; Matter et al., 2009). Recent research efforts have been directed toward enhancing the accuracy, robustness, and automation of vibration-based identification techniques for composite materials. Acosta- Flores and Eraña - Díaz (2024) experimentally determined the in-plane elastic moduli of orthotropic laminates by combining resonance testing with analytical modeling, demonstrating high repeatability of the identified parameters. Liu and Kam (2025) proposed a multi-level, sensitivity-based optimization framework capable of simultaneously identifying multiple elastic constants with improved numerical stability. Niutta et al. (2021) developed a vibro acoustic methodology for the nondestructive assessment of local stiffness variations in heterogeneous composites, highlighting its high sensitivity to manufacturing defects and damage. Huang and Chen (2025) introduced a modal-data inversion approach confirming the reliability and practical applicability of vibration-based inversion for elastic property extraction. Similarly, Li et al. (2018) employed a vibration-based identification strategy for stitched sandwich panels, successfully correlating measured eigenfrequencies with orthotropic stiffness parameters. Building on these advances, recent studies have further confirmed the feasibility of integrating vibration testing with inverse numerical modeling for the identification of composite material properties. In particular, Akishin et al. (2014) and Kovalovs et al. (2024, 2025) applied this approach to carbon- and glass-fiber composites, demonstrating that the combination of experimental modal analysis with response-surface-based optimization enables a reliable and accurate determination of in-plane stiffness characteristics and anisotropy-related effects. The present study builds upon this foundation and refines the RSM-based inverse approach by integrating modern design-of experiments strategies, statistical sensitivity analysis, and global optimization routines. The methodology is validated for two representative CFRP laminates – unidirectional and twill-weave monolayer – which differ in anisotropy. This comparison enables assessment of the robustness of the identification procedure across material architectures. The principal objective is to evaluate the accuracy of the numerical-experimental method for identifying the elastic constants of composite laminates from measured natural frequencies and mode shapes, using the framework originally proposed by Rikards (2003) and further developed by Kovalovs et al. (2025). 2. Methodology The procedure for determining the elastic properties of a layered composite material is formulated as an inverse problem, in which the elastic constants of a composite monolayer are recovered from the measured natural frequencies of a rectangular plate. The complete solution involves several consecutive stages, as schematically illustrated in Fig. 1. A brief description of each stage of the identification procedure is provided below. The identified elastic constants are constrained within prescribed bounds representing admissible material variability. The physical basis of vibration-based identification is that the modal frequencies f of a structure depend on its stiffness and mass distribution according to the generalized eigenvalue problem: