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| 梯度多孔金属材料梁的屈曲和屈曲基础上的振动 |
| Buckling of Beams made of Graded Porous Metal Materials and Vibration on the Basis of Buckling |
| 投稿时间：2022-10-26 修订日期：2022-12-15 |
| DOI： |
| 中文关键词: 梯度多孔材料 孔隙率 随从载荷 临界载荷 频率 |
| 英文关键词:graded porous material porosity follower force critical load frequency |
| 基金项目:国家自然科学(12062010) |
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| 中文摘要: |
| 为研究梯度多孔金属材料梁的屈曲以及屈曲附近的振动特性,首先建立了随从分布压力下梯度多孔材料梁的动力学控制方程,然后将控制方程的解分解为静态解和谐振动形式的动态解,得到了描述过屈曲的静态控制微分方程和描述屈曲前后振动响应的控制方程。通过数值求解两组强非线性方程,获得了简支-固支梯度多孔梁的屈曲临界载荷以及屈曲前后振动频率与载荷之间的关系曲线。分析了孔隙率系数和孔隙率分布方式对屈曲临界载荷和屈曲前后振动频率的影响。结果表明：随着孔隙率系数 的增加,发生屈曲时的临界载荷减小；各阶固有频率也减小。屈曲前,各阶振动频率随载荷增大而减小,屈曲后,除三阶频率外,一阶和二阶频率随载荷增大而增大。 |
| 英文摘要: |
| In order to study the buckling of the graded porous metal beam and the vibration characteristics before and after buckling, the dynamic control equation of the graded porous metal beam under the follower distributed pressure was first established, and then the solution of the control equation is decomposed into the static solution and the dynamic solution in the form of vibration. The static control differential equation of the problem and the control equation of the vibration before and after post buckling under the assumption of small amplitude vibration were obtained. By numerically solving two sets of strongly nonlinear equations, the critical load of simply supported and fixed supported graded porous beams during buckling and the relationship between vibration frequency and load before and after buckling were obtained. The effects of porosity coefficient and porosity distribution on critical buckling load and vibration frequency near buckling were analyzed. The results show that the critical load decreases with the increase of porosity coefficient; The natural frequencies of each order also decrease. Before buckling, the vibration frequency of each order decreases with the increase of load. After buckling, the first and second order frequencies increase with the increase of load, except for the third order frequencies. |
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