考虑长程力,非局部弹性直梁内参考点的应力与直梁占据区域内所有点的应变都有关系.基于Eringen的非局部弹性理论积分型本构关系和采用幂指数型参模空间推导了Euler-Bernoulli直梁的积分型方程和4阶偏微分型方程,采用Laplace变换得到了直梁自然频率、振型的通解.给出了简支直梁、固定直梁、自由直梁、悬臂直梁的自然频率和振型.实例结果表明除悬臂直梁的第1阶自然频率随Eringen参数的增加而略微增加外,直梁自然频率随Eringen参数的增加而减小.固定直梁、自由直梁、悬臂直梁振型的振幅大体上随Eringen参数的增加而减小.但Eringen参数对简支直梁的振型没有影响.当Eringen参数为零时,非局部弹性理论与局部弹性理论的自然频率、振型一致.%The stress at a reference point in the nonlocal elasticity straight beam depends on the strains at all points of the region occupied by the straight beam by taking long range force into consideration.Based on integral constitutive relation of Eringen's nonlocal elasticity theory and adopting exponential modulus,the integral equation and four order partial differential equation of Euler-Bernoulli straight beam were obtained.The general solutions of natural frequency and vibration mode of straight beam were derived with Laplace transform.For the simply supported straight beam,clamped-clamped straight beam,free-free straight beam and cantilever straight beam,natural frequency and vibration mode were given.The example results show that the natural frequencies of straight beam are seen decreasing with the increase of Eringen parameter when exception is the first order frequency of a cantilever beam,which is shown to be slightly increasing with the increase of Eringen parameter.In addition,it is observed that when Eringen parameter is increased,the amplitudes of vibration modes of the clamped-clamped straight beam,free-free straight beam and cantilever straight beam are decreased in general.However,it is interesting to note that Eringen parameter has no influence on the vibration modes of the simply supported straight beam.The natural frequency and vibration mode of nonlocal elasticity theory are the same as those of local elasticity theory when Eringen parameter becomes zero.
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