{"title":"Application of Method of Symmetries at a Calculation and Planning of Circular Plate with Variable Thickness","authors":"Kirill Trapezon, Alexandr Trapezon","volume":124,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":831,"pagesEnd":835,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10007033","abstract":"
A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.<\/p>\r\n","references":"[1]\tB. Radg, V. Radgendran, P. Palanichami, Applications of ultrasound. Moscow, Russia: Technosfera, 2006.\r\n[2]\tL. Bergman, Ultrasound and his application are in science and technique. Moscow, USSR: Nauka, 1957.\r\n[3]\tA. Trapezon, Calculation of resilient elements at resonant fatigue tests. Kyiv, Ukraine: Naukova dumka, 1983.\r\n[4]\tS. Timoshenko, D. Young, Vibration problems in engineering. New York, USA: Van Nostrand, 1955.\r\n[5]\tK. Trapezon, \u201cMethod of symmetries at a calculation and planning of acoustic thickeners,\u201d Acoustic Bulletin, vol. 9, no. 4, pp. 50\u201355, Dec. 2006.\r\n[6]\tK. Trapezon, A. Trapezon, \u201cUltrasonic oscillating system,\u201d in 2016 Proc. RTPSAS-2016 Conf., pp. 69\u201371.\r\n[7]\tA. Kovalenko, Round plates with variable thickness. Moscow, USSR: Phizmatgiz, 1959.\r\n[8]\tK. Trapezon, \u201cMethod of factorization at the decision of tasks on own values,\u201d Electronics and Communications, vol. 68, no. 3, pp. 19\u201323, Sept. 2012.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 124, 2017"}