The Effect of Continuous Suspension Constraint on the Free Vibration and Buckling of a Beam

In this paper, the free vibration and the buckling of a continuously suspended simply-supported beam are analyzed. A semi-analytical approach is used to calculate the natural circular frequencies and the critical forces of the beam. The length of the suspension is used as a parameter, and the natural circular frequencies and the critical forces are presented in a frequency map or a buckling map. The maps are analyzed in view of the trivial solutions, and the frequency map is compared to the map of discrete cable-stayed beams. Finally, for the validation of the results a numerical, finite element analysis is performed

Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings

The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity (UD-convexity), we increase this mileage even further. Additionally, with the help of definitions of lower UD-concave (lower UD-concave) and upper UD-convex (concave) fuzzy number valued mappings (FNVMs), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued UD-convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study