六参数一般弹性约束FGM夹层梁的自由振动和屈曲特性

FREE VIBRATION AND BUCKLING CHARACTERISTICS OF FUNCTIONALLY GRADED SANDWICH BEAMS UNDER GENERALLY ELASTIC BOUNDARY CONDITIONS WITH SIX-PARAMETER

应用微分求积法(DQM)数值研究了六参数一般弹性约束边界下Winkler-Pasternak弹性地基上功能梯度材料(FGM)夹层梁的自由振动和屈曲特性。考虑夹层梁由3层组成,中间芯层分别为陶瓷单相(硬芯)、陶瓷-金属复合(FGM芯)、金属单相(软芯)材料这三类夹芯,采用Voigt混合幂率模型来表征FGM层的材料属性沿梁厚的梯度连续变化,梁两端的一般弹性约束边界由3组线性弹簧模拟。基于Timoshenko梁理论,在Hamilton体系下统一建立该系统静动态力学分析模型的控制方程并导出边界条件。通过编写DQM计算程序获得FGM夹层梁的自由振动响应,基于屈曲和振动这两种静动态力学行为之间的二元耦联性解耦求解临界屈曲载荷。通过算例主要探究了梁边界弹簧刚度、层厚比、夹芯类型、材料组分梯度指标、跨高比、弹性地基刚度等因素对FGM夹层梁自由振动和屈曲特性的影响。结果表明:该文分析方法行之有效,数值结果可靠精确;静力屈曲解耦求解过程极大简化;与各种典型边界梁相比,该六参数力学模型具有明显的普适优越性。

The free vibration and buckling characteristics of functionally graded material(FGM)sandwich beams resting on Winkler-Pasternak foundation and under general elastic boundary condition of six-parameter model are investigated by using differential quadrature method(DQM).Sandwich beams are composed of three layers with cores of ceramic material(hardcore),ceramic-metal composites(FGM core)or fully metal material,respectively.Voigt model is employed to describe the effective material properties of FGM layer across the depth of sandwich beams according to mixture power-law distributions.The general elastic boundary conditions at both ends of the beam is simulated by three sets of linear springs.Based on the Timoshenko beam theory,the governing equations and boundary conditions of the static and dynamic model of the system are derived from Hamilton’s principle as a unity.The free vibration responses of FGM sandwich beams are obtained by DQM programming.Based on the duality between the static and dynamic behaviors of the structure,the critical buckling loads are also obtained.The significant influences of stiffness coefficients of boundary spring,ratio of thickness of each layer,sandwich types,material graded index,slenderness ratios and foundation parameters on the free vibration and buckling characteristics of the structure are taken into investigation.Several numerical examples are presented to demonstrate the convergence,reliability and accuracy by using DQM.The decoupling process for static buckling analysis of FGM sandwich beams is distinctly simplified.Moreover,the superiority and universality of the sixparameter beam model are indicated through a comparison with various classical boundary ones.