Model of a bistable jump membrane as an element of a control system

Abstract

In the article the mathematical model of the dependence of the deformation effort of the membrane on the structural parameters and material characteristics is considered. The membrane is executed in the form of a pinched tape at the ends of the appropriate width and thickness of the elastic material and given free deflection. The diagram of the membrane is presented in three basic positions, depending on the value of the deflection. The effect of forces and bending moments is given. The equilibrium equation of the membrane is made according to the load forces and the analytical dependence of the meltdown deflection effort on its constructional parameters and material characteristics is generated. Proposed dependence for determining the longitudinal membrane response. An example is given of the simulation of the Fр effort, which creates a membrane depending on its deflection f and structural parameters, thickness, width and distance between the edges of fixing the membrane tape. The maximum deflection of the membrane is determined by fixing the membrane and the absence of resistance force. Material of the membrane - manganese bronze, ribbon rolled.The modeling of the Fр effort, which will create the membrane depending on the deflection f, was carried out according to the following parameters: membrane material - manganese bronze, ribbon rolled; membrane thickness h = 0,1 mm; membrane width b = 1,2 mm; the distance between the edges of the membrane fixing 2L = 32 mm; maximum deflection of the membrane f0 = 4 mm. The dependence of the effort created by the membrane at its deflection from the distance between the edges of its fastening and the cross-sectional area is given. For modeling a tape of bronze manganese ribbon rolled with a thickness of h = 0,4 mm and a width of b = 0,4-2 mm was used. The distance between the edges of fastening the membrane was taken from 20 to 38 mm, and the maximum deflection of the membrane was f0 = 2 mm.The analysis of the simulation results showed that with increasing free deflection f0 of the membrane and decreasing the distance 2L between the clamped edges, the forging effort increases linearly. The membrane has two stable diametrically opposite states and one unstable state in which the membrane's effort, at its deflection near the neutral, is equal to zero, and the transition from one position to a diametrically opposite position occurs when passing through an unstable position with a leap. Increasing the free deflection of the membrane leads to an increase in the resistance of the membrane. The growth pattern is linear. The maximum membrane effort corresponds to half of its free deflection.