Abstract. The dynamics of unsteady oscillations of a rectangular membrane with one and two attached masses is studied. Adequate mathematical models are constructed using methods for solving direct problems in the mechanics of an elastically deformable body, namely, the Volterra equations and the Cramer method. It is noted that the obtained solution of the direct problem has an experimental application to the problems of analy-sis of displacements, deflections, deformations and stresses during unsteady vibrations of membranes with at-tached concentrated mass used in switching elements (membrane reed switches) and micromechanical pres-sure sensors. Based on the developed mathematical models, calculations of membrane elastic elements of a patented series of switching elements and pressure sensors are performed.

Keywords: membrane element, attached masses, concentrated mass, loading force, non-stationary oscillations, deflection value, Volterra equations, Cramer method, direct problem solution

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