VIBRATION OF THE CIRCULAR ANNULAR PLATE WITH AN INTERNAL FREE EDGE

Abstract

Whole and with opening elliptic membranes meet as elements of machines of devices: diaphragms, winders. Results of calculations of frequency parameter for the symmetric vibrations of such membranes at the different values of excentricity are presented in background literature and based on one of works. In scientific literature there are not experimental information on determination of frequencies of vibrations of such plates, which would enable to estimate exactness of the presented results. Absent calculations of frequency parameter of asymmetrical vibrations, and also results of calculation frequency the parameter of elliptic membrane with opening. A whole elliptic membrane is stretched by equipartition forces. Worked out an equation of eigentones in the rectangular system of coordinates. The formulas of transformation of rectangular co-ordinates are entered to elliptic and equalization of eigentones is determined in the set elliptic system of coordinates. The decision of this system is given through the ordinary and modified Mathieu function of the first family. Worked out a frequency equation and his decision is found for symmetric vibrations and asymmetrical vibrations at different. For an elliptic membrane with opening to the decision the Mathieu function of the second family is added on the basis of Floquet theorem. Resulted decisions of frequency equalization at the different values of excentricity of internal and external ellipse it is Necessary to conduct experimental researches of tasks on determination of frequency parameter of symmetric and asymmetrical whole with opening of membranes. .