Free Vibration Analysis of Curved Stiffened Plates

Background Curved stiffened plates are most widely used in engineering struc- tures such as ships, aerospace vehicles, and bridges. These plates are frequently under the impact of dynamic loadings during their service life. Therefore, this paper's main objective is to investigate the free vibration of the stiffened plates with curved bound- aries using the finite element method. Purpose The plates' strength is improved by placement of the stiffeners either con- centrically or eccentrically, depending on the use. The stiffeners' orientation, such as radial and circumferential, for the plates with curved boundaries such as annular sector, circular and elliptical plates is inevitable because of their contribution to the plate in that direction. The stiffeners' size and shape play an important role in strengthening the plates, keeping the structure's weight low. All these parameters contribute effectively to the vibration of the stiffened plates significantly. Hence, in this paper, an attempt has been made to present a parametric study for the free vibration characteristics of stiff- ened plates having various boundary conditions and considering the above parameters Methods An in-house finite element MATLAB code is developed for the study of bare plates and plates with stiffeners. An isoparametric quadratic plate bending ele- ment with shear deformation is considered to accomplish this. The plate and stiffener elements' stiffness and mass matrices have been obtained separately and assembled to form the entire structure's global matrices. Some of the example results have been verified with previously published results and the FEAST (Finite Element Analysis of STructures) software to show the method's efficacy. Results Non-dimensional frequency results of plates with various types of stiffen- ers for different boundary conditions and diverse sector angles for bare and stiffened annular plates are reported. Parametric study of the vibration characteristics of stiff- ened plates of various shapes (annular sector, circular and elliptical) with different sizes, shapes, orientations (radial and circumferential), and dispositions (concentri- cally, eccentrically, and floating) of stiffeners have also been presented. Conclusions The non-dimensional frequencies are more significant for the I-beam eccentric stiffener than that of the R-beam and T-beam stiffener for the clamped condi- tions. The results are also higher with the increase of inner-to-outer radii ratios and the decrease of sector angles. The radially attached stiffeners show more pronounced non- dimensional frequencies than the circumferential ones for the circular and elliptical plate cases.

Automated summary

This study investigates the free vibration characteristics of curved plates and the influence of stiffeners on the vibration, as well as the effects of stiffener types, shapes, and orientations on vibration frequencies. Results show that the I-beam eccentric stiffener has higher non-dimensional frequencies under clamped conditions, while radially attached stiffeners have a more pronounced impact on the vibration frequencies of circular and elliptical plates.