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基于Euler-Bernoulli梁理论,建立了钢板加固含单裂纹RC梁的自由振动微分控制方程。提出一种简单的数值方法,即将位移函数直接以Chebyshev正交多项式展开,进而得到钢板加固含裂纹RC简支梁自由振动特征方程。通过数值分析,探讨了该数值方法在求解RC梁自由振动特征值问题上的可行性,并研究了裂纹深度以及粘钢板加固对RC梁固有振动特性的影响。研究表明,本文提出的数值方法具有精确度高、快速收敛的优点;且由分析可知,裂纹的扩展将使RC梁的固有频率降低,进行粘钢加固将有效提高含裂纹RC梁的自由振动特性。
Based on the Euler-Bernoulli beam theory, a free-vibration differential governing equation of a steel plate strengthened single cracked RC beam is established. A simple numerical method is proposed, in which the displacement function is expanded directly by the Chebyshev orthogonal polynomial, and then the free vibration characteristic equation of steel plate reinforced cracked RC beam is obtained. Through numerical analysis, the feasibility of the numerical method for solving the eigenvalue of free vibration of RC beams is discussed, and the influence of crack depth and inherent strengthening of RC beams on the inherent vibration characteristics of RC beams is studied. The results show that the numerical method proposed in this paper has the advantages of high accuracy and fast convergence. The analysis shows that the crack propagation will reduce the natural frequency of RC beams and the bonding steel reinforcement will effectively improve the free vibration characteristics of cracked RC beams. .