###### Abstract
Meanwhile, extensive research has been conducted on the properties of metallic materials when exposed to dynamic forces, including deformation, strengthening due to strain rate, and fracture mechanisms. However, the effects of size on these dynamic mechanical properties at the micro and mesoscale have not been thoroughly explored. To investigate the impact of size on these properties, experiments were conducted on oxygen-free, high-conductivity (OFHC) copper using both quasi-static compression and split Hopkinson pressure bar (SHPB) testing with varying geometrical and grain sizes. The effects of changing geometrical and grain sizes on dynamic forces were reported by [PERSON] et al. [19]  
A valuable method for detecting cracks and notch location is through vibration-based techniques. These methods analyze changes in dynamic properties to determine the presence of cracks. [PERSON] et al. [20] found that the natural frequencies of a cantilever beam with a notch shift primarily when the damage is near the end. Additionally, the depth of the damage is inversely proportional to the natural frequency. According to research conducted by [PERSON] et al. [21] and [PERSON] et al. [22], the presence and location of cracks can have an impact on vibration amplitude. [PERSON] et al. used linear finite element analysis and the local flexibility method to determine the relationship between normalized stiffness and notch locations. They identified crack locations by finding the intersection points of normalized stiffness at the first two natural frequencies of the beam. [PERSON] et al. utilized wavelet finite element methods to detect the location and depth of cracks in a free\(-\)free beam. The frequency contour lines were used to identify the gaps with an error rate of 26.5% and 26.1% for location and depth, respectively, without Young modulus correction. The correction reduced the error rate to 9.9% and 15.0%. Numerous studies have been carried out to identify cracks present in beam-type structures. [PERSON] et al. employed a frequency-based approach and achieved an accuracy of 4% in detecting surface cracks [23]. Meanwhile, [PERSON] et al. [24] utilized contour graphs of the first three normalized natural frequencies to locate and determine the size of the damage. [PERSON] and [PERSON] used the measurement of natural frequencies and solved nonlinear equations to calculate crack locations and depths. However, their method has limited accuracy in detecting tiny cracks, specifically those with a crack depth ratio of less than 0.1 [25]. [PERSON] et al. [26] developed a new method that utilizes a rotational spring model to calculate the natural frequencies of beams with multiple cracks. [PERSON] and [PERSON] [24] investigated the impact of notch location on the modal parameters of a cantilever beam subjected to vibration. Lastly, [PERSON] and [PERSON] [27] studied the effect of natural frequencies for two types of single-sided and double-sided notch locations. [PERSON] et al. [26] also developed a modified approach to detect cracks' location via notch shape in beams, which can be seen as a significant contribution to the field. Extensive research has been conducted in the literature regarding the free vibration of thin-walled beams. [PERSON] [28] utilized a wave propagation approach to solving the triply coupled vibrations of beams, employing a Fourier transform for the displacement components and a Laplace transform for the time factor. [PERSON] et al. [29] compared the natural frequencies and buckling loads of aluminum non-symmetric thin-walled beams under axial forces through experimental and numerical methods. Their experimental approach involved a vibration testing apparatus, while their numerical analysis utilized a finite element method. The development of the finite element method (FEM) to analyze the free vibration behavior of thin-walled beams based on the Timoshenko beam theory and including a substructuring technique for the efficient analysis of complex structures that agree well with R. [PERSON] et al.