针对粘结型组合梁, 考虑粘结层的滑移效应, 在Euler-Bernoulli 梁弯曲变形假定下, 以挠度和轴向位移为基本未知量, 研究了简支组合梁在均布荷载作用下的弯曲响应, 得到了问题的解析解, 考察了不同梁长下组合梁中点挠度、梁端粘结层滑移位移和剪切应力等随粘结层剪切模量和厚度的响应. 同时, 研究了简支组合梁的固有频率, 利用分离变量法得到了固有频率表达式, 考察了粘结层剪切模量和厚度等对组合梁第一固有频率的影响. 研究结果表明: 粘结层厚度和剪切模量对组合梁挠度和粘结层滑移位移有较为显著的影响, 对粘结层剪力的影响很小; 相比于粘结层厚度, 剪切模量对其固有频率的影响较大.
For composite beam with adhesive layers, taking slip displacement of the adhesive layer into account and assuming bending of an Euler-Bernoulli beam, the bending of simple-supported composite beam with a uniform load is studied. With fundamental unknowns of deflection and axial displacement, an analytical solution is obtained. Responses of deflection at the beam’s mid-point, slip displacement and shear force of the adhesive layer at the beam end versus the shear modulus and thickness of the adhesive layer are examined for different beam lengths. Further, the natural frequency of a simple-supported composite beam is studied. The expression is obtained with separation of variables. Influences of shear modulus and thickness of the adhesive layer on the first natural frequency are examined. It is revealed that the thickness and shear modulus have a great influence on the deflection of the composite beam and slip displacement of the adhesive layer. They have a little influence on the shear force of the adhesive layer. The shear modulus of the adhesive layer has a reater influence than that of the thickness on the first natural frequency of the composite beam.
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