摘要
A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two oppo- site simply-supported edges. In contrast to the traditional MRRM, numerical stability is achieved by using the present new formulation for high-order frequencies or/and for plates with large span-to-width ratios. The heavy computational cost of storage and memory are also cut down. An improved recursive formulation is further proposed by modifying the iterative formula to reduce the matrix inversion op- erations. Numerical examples are finally given to demonstrate the effectiveness and efficiency of the proposed recursive formulae.
A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two opposite simply-supported edges. In contrast to the traditional MRRM, numerical stability is achieved by using the present new formulation for high-order frequencies or/and for plates with large span-to-width ratios. The heavy computational cost of storage and memory are also cut down. An improved recursive formulation is further proposed by modifying the iterative formula to reduce the matrix inversion operations. Numerical examples are finally given to demonstrate the effectiveness and efficiency of the proposed recursive formulae.
基金
Supported by the National Natural Science Foundation of China (Grant Nos. 10725210, 10832009, and 10432030)
the National Basic Research Program of China (Grant No. 2009CB623204)
the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060335107)
the Program for New Century Excellent Talents in University (Grant No. NCET-05-0510)
