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.

The optimal position and minimum stiffness of an intermediate support is implemented to maximize the fundamental natural frequency of a vibrating cantilever Euler-Bernoulli beam with tip mass. According to Courant’ s maximum-minimum theorem, maximum value of the first natural frequency of a beam with a single additional rigid internal support, is equal to the second natural frequency of the unsupported beam. In literature, for a cantilever beam without tip mass, the optimum position of intermediate support was reported as 0. 7834L and minimum dimensionless stuffiness as 266. 9. In this paper, the effect of tip mass ratio on optimum location and minimum stiffness is investigated. The Finite element method is employed. Cross sectional area is uniform and material is homogeneous and isotropic. Numerical results demonstrate that as tip mass ratio increases the optimal position moves toward the tip mass and minimum stiffness increases. For instance, for tip mass ratio 0. 5, optimal position is 0. 92L and minimum dimensionless stiffness is 284. Optimal position and minimum stiffness are presented for various range of mass ratio. In many applications, it is not possible to place intermediate support at optimal position; therefore, the minimum stiffness does not exist. In these cases, a tolerances zone is considered and related design curves are proposed. As a practical example, an agitator shaft is considered and end impeller is modeled as tip mass. The effectiveness of the proposed design curves in order to maximize natural frequency is shown. A design of an intermediate support is presented; in this example the fundamental frequency has increased as much as 300 percent without any change in shaft diameter.

Background: Organophosphate compound (OPC) poisoning with suicidal intent is common in Indian ICUs. These compounds are the organic derivatives of phosphorous containing acids and their effect on neuromuscular junction and autonomic synapses is clinically important. Organophosphate poisoning can present as acute cholinergic syndrome, intermediate syndrome and delayed neuropathy. Case Presentation: Intermediate syndrome secondary to organophosphate poisoning is a serious health problem leading to increased morbidity and mortality. The incidence of problem varies and ranges from 8%-84% of OPC poisoning cases. After initial recovery from cholinergic crisis, some patients have resurgence of respiratory muscle paralysis requiring continued ventilatory support. This is termed intermediate syndrome (IMS). The factors accounting for this difference is the nature of organophosphate compound, severity of poisoning and inadequate oxime therapy. The recognition of this syndrome is important as if this entity is overlooked it can have disastrous effects. Discussion: Our patient had developed respiratory muscle weakness as evidenced by inadequate respiratory efforts, drop in oxygen saturation, retention of CO2 and need for ventilatory support. There was no evidence of weakness in ocular, neck, bulbar muscles but he had weakness in all 4 limbs more pronounced in proximal muscles. Conclusion: We presented this case of OPC poisoning with intermediate syndrome, which remained for a prolonged time and required mechanical ventilation for 16 days. This case highlights how the timely intervention can save the patient’ s life.