## 1 Introduction  
In recent years, because of the sustainability goals identified at a public policy level, composites with natural fibers, alongside synthetic fibers, have gained an increased use in both structural and non-structural applications. Some of these applications, which include a large variety of products, are in furniture manufacturing. Thus, the challenge for producers resides in designing, characterizing, and testing new composite materials in a robust and reliable manner. While the general approach in determining the viscoelastic mechanical properties of composite materials has been to perform destructive tests on a relatively large number of samples, novel non-destructive testing (NDT) methods have been developed in order to reduce the time needed to characterize them and to improve the quality assurance of fabrication [1, 2, 3]. Non-destructive testing is the process of testing and inspecting materials that causes no physical damage to the testing object, keeping it in its current state [4]. Various NDT methods built upon different principles for quality assurance during the whole lifecycle of the composite products are presented in papers [5, 6]. As the composite materials with natural fibers are usually non-homogeneous and anisotropic, their elasticity constants should be viewed as global parameters of the tested samples or structures. The evolution of the defects and damages, which can occur within numerous locations at various levels of scale (from nano to macro), is difficult to track by performing only destructive testing. A very efficient method for testing the structural degradation and fatigue behavior of composite materials and structures is the vibration resonance method [7]. Damage altersthe modal properties such as natural frequencies, mode shapes, and damping ratios [8; 9; 10]. Various optimized inverse methods have been developed for damage identification in structures based on the stiffness separation method for reducing calculation time [11; 12; 13]. The elastic modulus is a key parameter in engineering design of structures and material development. The bending vibration frequencies are primarily controlled by the Young's modulus of the tested specimen, being practically independent of any material anisotropy. The dynamic determination of the flexural elastic modulus \(E\) of strawboards using NDT methods based on the free plate modal or transient excitation test is presented in paper [14]. The impulse excitation technique is a non-destructive material characterization method used to determine the elastic properties and internal friction of a material of interest [15]. The test can be carried out by using material samples (light beams or plates) with or without small additional masses (i.e., accelerometers for measuring the transient response). These masses should be placed such as to enhance the load stress in tested specimens, produced by free vibration modes, excited by force impact or initially imposed displacements [16; 17]. Using the free vibration excitation by imposing an initial deformation (potential energy) at the free end of tested sample, followed by a sudden release, is very convenient for both testing (easy to control) and modeling (introduced as initial condition for the equation of motion). In correlation with this, many papers explore numerical methods for determining the eigenfrequencies of composite material samples with simple geometries, based on the elastic constants of the materials treated as homogenized and macroscopically uniform [18; 19; 20; 21]. Nonetheless, some of the limitations of the referenced studies include complex material definitions, a lack of experimental validation, cumbersome analytical expressions, or imply highly specialized personnel in a potential production compliany sector. The objective of this work is to determine the values of the material constant \(E\) for composite materials (polymer reinforced with natural fibers), without taking into account the material constants of neither the constituent elements nor their proportions [22].