报告主题：複合樑自然頻率的上界理論近似方法
报告人：刘进贤 教授 (河海大学)
报告时间：2017年5月5日（周五）13:00
报告地点：校本部G507
邀请人：刘东杰
报告摘要：For the free vibration of composite beams and non-uniform beams we propose a new upper bound theory to approximate the first few natural frequencies. The Rayleigh quotient is expressed in terms of boundary functions, instead of that in terms of eigenfunctions. The boundary function satisfies all boundary conditions of the given beam, and is at least the fourth-order polynomial with leading coefficient to be one. We prove that the maximality of the Rayleigh quotient in the space of the kth order boundary functions is equivalent to the orthogonality of the kth order boundary function to lower order optimal boundary functions. Hence, we can easily find the kth order natural frequency through an orthogonalization technique provided. When the first three natural frequencies are compared with the exact or numerically found ones, good results are obtained, which confirm the applicability of the present upper bound theory.
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