一类多孔固体的等效偶应力动力学梁模型

发布时间：2019-03-18 17:43

【摘要】：一维多孔固体结构可采用等效连续介质梁模型来研究其动力学行为.当类梁结构的高度尺寸和多孔固体单胞结构尺寸相近时,等效模型的力学行为会产生尺寸效应现象.等效经典模型由于不包含尺度参数而无法描述尺寸相关特点,而广义连续介质力学模型则可以准确地考虑尺寸效应的影响.基于偶应力理论,对一类单胞含有圆形孔洞的周期性多孔固体类梁结构,给出了分析其横向自由振动的等效连续介质铁木辛柯梁模型.通过对单胞分析,在应变能等价和几何平均的意义下,定义了等效偶应力介质的材料常数.利用已有的材料常数,推导了等效铁木辛柯梁的动力学微分方程.将实际多孔固体结构进行完全的动力学有限元离散计算,所获得的解作为精确解以检验等效梁模型所获得的频率和振型的精度.振型的比较借助于模态置信准则矩阵方法.大量算例表明,等效偶应力铁木辛柯梁模型在频率和振型两方面均具有较高的计算精度.重点研究了单胞孔径的相对大小、类梁结构高度与单胞尺寸比以及类梁结构长高比对等效梁模型精度的影响.在此基础上,偏保守地建议了多孔固体类梁结构自振分析方法.
[Abstract]:The equivalent continuum beam model can be used to study the dynamic behavior of one-dimensional porous solid structure. When the height size of the beam-like structure is similar to that of the porous solid cell structure, the mechanical behavior of the equivalent model will produce the size effect phenomenon. The equivalent classical model can not describe the dimension-dependent characteristics because it does not contain the scale parameters, while the generalized continuum mechanics model can accurately consider the influence of the size effect. Based on the coupled stress theory, an equivalent continuous medium Ferroxinko beam model is presented for a class of periodic porous solid beam structures with circular holes in a single cell, which can be used to analyze the transverse free vibration of the beam. In the sense of equivalent strain energy and geometric average, the material constants of equivalent couple stress medium are defined by means of unit cell analysis. Using the existing material constants, the dynamic differential equation of the equivalent iron-wood-sinker beam is derived. The complete dynamic finite element discretization calculation of the actual porous solid structure is carried out. The obtained solution is used as the exact solution to verify the accuracy of the frequency and mode shape obtained by the equivalent beam model. The comparison of mode shapes is based on the modal confidence criterion matrix method. A large number of examples show that the equivalent dual stress Ferroxinkko beam model has high accuracy both in frequency and mode shape. The effects of the relative size of the cell aperture, the ratio of the beam-like structure height to the unit cell size and the equivalent beam-like structure length-height ratio on the accuracy of the equivalent beam model are studied. On the basis of this, the self-vibration analysis method of porous solid beam structure is proposed conservatively.
【作者单位】：大连交通大学土木与安全工程学院;大连理工大学工业装备结构分析国家重点实验室/工程力学系;
【基金】：国家自然科学基金(11002031) 国家重点基础研究计划(973计划)课题(2011CB610304) 辽宁省高校优秀人才支持计划(LJQ2012040)资助项目
【分类号】：O33

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