CAJ | 학술논문

提出一种考虑水平阻尼的双参数地基模型，推导了此地基模型上多层矩形板的中性面位置表达式，建立水平动载荷与垂向动载荷联合作用下多层地基板内力平衡方程，并在此基础上给出了板的运动微分方程。采用级数分解和 Laplace 积分变换相结合的方法，求解了圆形刚性承载板载荷作用下多层地基板的挠度解析表达式。在 MATLAB 软件中编写计算程序，以三层地基板为例深入分析了水平阻尼系数、摩擦系数、运动方向对板动力响应的影响。研究表明，随着水平阻尼系数的增大，板的挠度逐步减小，摩擦系数和运动方向对载荷作用面圆心处的动力响应几乎没有影响，而对远离圆心处点的挠度影响较大。
제출일충고필수평조니적쌍삼수지기모형，추도료차지기모형상다층구형판적중성면위치표체식，건립수평동재하여수향동재하연합작용하다층지기판내력평형방정，병재차기출상급출료판적운동미분방정。채용급수분해화 Laplace 적분변환상결합적방법，구해료원형강성승재판재하작용하다층지기판적뇨도해석표체식。재 MATLAB 연건중편사계산정서，이삼층지기판위례심입분석료수평조니계수、마찰계수、운동방향대판동력향응적영향。연구표명，수착수평조니계수적증대，판적뇨도축보감소，마찰계수화운동방향대재하작용면원심처적동력향응궤호몰유영향，이대원리원심처점적뇨도영향교대。
A two-parameter foundation model was proposed considering horizontal damping.Then the displacement expressions of neutral layer plane of a multi-layer rectangular plate on the foundation model were deduced.In order to get the motion differential equation of the plate,its internal force equilibrium equations were built under the combined action of horizontal dynamic load and vertical dynamic one.Then the analytical expression of the plate deflection under a circular rigid bearing plate's load was solved with the combination of Laplace integral transformation and the triangular series methods.The influences of horizontal damping coefficient,friction coefficient and motion direction on the dynamic response of the plate were analyzed by using MATLAB software and taking a three-layer plate as an example.Results indicated that the deflection of the plate decreases gradually with increase in horizontal damping coefficient;the friction coefficient and motion direction have a greater influence on the deflection of the point far from the circuar plate center,but their effects on the dynamic response of the circular plate center can be ignored.