## 4 Conclusions  
This study investigates the influence of various factors--including the modulus of elasticity, height, lower and upper inner diameters, and lower and upper outer diameters--on the dynamic properties of electric poles. To conduct the numerical analysis, finite element models of 3240 distinct electric poles were developed. It was assumed that these poleswere made of reinforced concrete and that a specific area was firmly anchored to the ground. Modal analyses were performed, and the poles were evaluated based on their natural frequencies and mode shapes. A prediction model was developed using ridge regression based on the analytically determined frequencies as dependent variables and Elastic modulus, Height, Bottom inner diameter (Bid), Top inner diameter (Tid), Bottom outer diameter (Bod), and Top outer diameter (Tod) as independent variables. To minimize bias and enhance prediction accuracy, 10-fold cross-validation was implemented during the ridge regression analysis. According to the results, the frequency predictions achieved acceptable accuracy with an approximate error rate of 5% and an R\({}^{2}\) value of approximately 0.90. The other results of this investigation are summarized below:  
* The increase in the modulus of elasticity in all frequency types increased the frequency. * It has been determined that as the height of the electricity poles increases, the natural frequency values decrease. * It was determined that all frequency values increased as the Lower Inner Diameter and Upper Outer Diameter values increased. * When the upper inner diameter value increases, the F3, F4, F5, F6, F7, F9, and F10 frequency values increase, but the F1, F2, and F8 frequencies decrease. * When the lower outer diameter value increases, the F8 frequency decreases and the frequencies outside of these increase. * When the regression analysis results are evaluated, it is seen that the R2 values of all frequencies are approximately above 90%. In addition, predictions were made with an error rate of approximately 6% at all frequencies. * One of the primary limitations of this study is the absence of direct experimental or field validation of the developed regression model. The model was constructed solely on the basis of simulation data, a factor that must be acknowledged as a constraint. Nonetheless, the simulation dataset was meticulously generated through systematically controlled parametric analyses and was designed to encompass a comprehensive range of reinforcement configurations. The model demonstrated robust statistical performance, evidenced by an R\({}^{2}\) value exceeding 0.95, along with minimal values for RMSE, MAE, and MAPE, thereby indicating a high level of predictive accuracy within the specified input domain. Future work is planned to validate the model through experimental pullout tests, which will further substantiate its applicability in real-world contexts. * Moreover, the natural frequencies of electric poles can be efficiently calculated using the aforementioned formulas, even in the absence of finite element (FE) analysis, albeit with varying degrees of error. It is crucial to recognize that these equations are contingent upon the specific material and geometric characteristics of the selected electric poles. In subsequent research endeavors, this methodology may be expanded beyond electric poles to encompass a diverse array of pre-production components, facilitating swift frequency estimations without the complexities typically associated with FE analysis. Conceptualization, H.E., D.R., E.C.R. and S.T.G. ; Methodology, H.E. and I.K. ; Software, H.E. and I.K. ; Investigation, D.R. and E.C.R. ; Resources, D.R., E.C.R. and S.T.G. ; Data curation, I.K. ; Writing--original draft, H.E., I.K. and E.C.R. ; Writing--review & editing, D.R. and S.T.G. ; Visualization, H.E., I.K. and E.C.R. ; Project administration, S.T.G. All authors have read and agreed to the published version of the manuscript.