单向变厚度Levy 型薄板的自由振动分析 - 中南大学学报.PDF

42 5 () Vol.42 No.5 2011 5 Journal of Central South University (Science and Technology) May 2011 Levy 1, 2 1 3 (1. 410083 2. 410004 3. 266100) Levy Volterra Levy 3 Levy Levy Levy TU311.1 A 1672−7207(2011)05−1413−06 Free vibration of Levy-plate with uni-directionally varying thickness 1, 2 1 3 SU Shu-lan , RAO Qiu-hua , WANG Yin-bang (1. School of Civil Engineering and Architecture, Central South University, Changsha 410075, China; 2. College of Civil Engineering and Mechanics, Central South University of Forestry and Technology, Changsha 410004, China; 3. College of Engineering, Ocean University of China, Qingdao 266100, China) Abstract: Based on vibration theory, a new solution method for natural frequency of free vibration of Levy-plate with uni-directionally varying thickness was established by substituting an unknown function into the four-order partial differential equation of vibration with variable coefficients, and then the second Volterra integral equation was solved with quadratic spline function. The results show that the new method has the lowest natural frequency of three Levy-plates with different boundary conditions, verifying that this new solution method is reliable and simple with sufficient accuracy and can be applied for analyzing free vibration of Levy-plate with uni-directionally varying rigidity. Key words: Levy-plate;