f. kakavand

The optimal position and minimum support stiffness of a vibrating Timoshenko beam are investigated to maximize the fundamental frequency. The Finite element method is employed. The intermediate support's ideal position and minimal stiffness for a wide variety of slenderness proportions were achieved after validating the finite element model with the Euler-Bernoulli and Timoshenko model's analytical solution. It was observed that the ideal position of intermediate support and its minimum stiffness are sensitive to the slenderness ratio. According to the maximum-minimum theorem of Courant, the optimum position is at the zero of the second mode shape function (ZSMS). Also, it was observed that for thick cantilever beams with intermediate support at the optimal location, the minimum support stiffness is less than 266.9, which was reported in the literature for the Euler-Bernoulli beam. The minimum stiffness of familiar end conditions of an optimally located beam is presented for a wide range of slenderness ratios. Since, in many practical applications, it is impossible to locate support at the optimal position, the minimum support stiffness for a beam in which its intermediate support is not located at the optimal position is obtained for various boundary conditions and slenderness ratios.

Emerging contaminants of nanoparticles in aquatic ecosystems cause stress response in aquatic animals and decrease their immune function. Therefore, use of immune stimuli such as prebiotics is very necessary. The aim of this study was to investigate the effect of different levels of prebiotic Pleurotus ostreatus on hematological indices of tilapia (Oreochromis niloticus) exposed to silver nanoparticles.

120 fish were distributed for 42 days in 4 treatments (3 replicates): control (1), no prebiotic fungi, treatment (2) food containing 0.05, treatment (3) food containing 0.1 and treatment (4) food contained 0.2% prebiotic. Then, 0.5 ppm of silver nanoparticles was exposed to each group for 16 days and blood parameters were examined.

Prebiotic alone had no significant effect on erythrocyte count, mean cell volume (MCV), mean cell hemoglobin (MCH), mean erythrocyte hemoglobin concentration (MCHC), hematocrit, hemoglobin, white blood cell (P <0.05) but exposure to silver nanoparticles and prebiotic in combination increased the mentioned factors compared to the control and prebiotic treatments alone. However, the levels of white blood cells and erythrocytes, hemoglobin, hematocrit, and MCH were higher than the other treatments in the combination of 0.2 prebiotic and silver nanoparticles.

Oral probiotics stimulate non-specific immunity in tilapia, the combined use of nano-silver and prebiotic mushrooms increase the amount of blood indices and reduce the destructive effects of nano-silver on blood indices. It is concluded that the 0.2% prebiotic level could have the best effect on the blood indices of tilapia.