基于改进Chebyshev级数的层合结构振动分析新理论

提出了一种基于改进Chebyshev级数的层合结构高阶分层建模理论.该理论位移场由线性位移场和高阶位移场组成,线性位移场控制位移场的总体分布趋势,高阶位移场进行局部修正.高阶位移场由具有统一表达式的改进Chebyshev级数表示,通过改变高阶截断阶数可实现高阶位移场快速配置,能够满足不同建模精度需求.采用该高阶分层理论和广义谱方法推导了层合结构的自由振动特征方程,研究了一般边界条件下层合梁、板、壳的自由振动特性,并将计算结果与其他文献数据对比.结果表明:基于改进Chebyshev级数的层合结构高阶分层理论具有较高的建模精度和计算效率.

A New Layerwise Theory for Vibration Analysis of Laminated Structures Based on Modified Chebyshev Polynomials

A new layerwise theory for vibration analysis of laminated structures based on modified Chebyshev polynomials was proposed. The displacement field in each discrete layer was composed of a global linear component introduced under the layerwise strategy and a local high order counterpart considered to improve the accuracy of the theory. In each discrete layer, the high order displacement field distribution through the laminate thickness was determined with the modified Chebyshev polynomials. Therefore, the proposed theory offers an easy analysis operation to realize different modeling precision requirements only by changing the truncation order without the need for reprogramming from case to case. The theory also has the ability of achieving arbitrary modeling precision according to practical requirements. Based on the proposed theory, the general spectral method was combined to formulate the vibration equations of laminated beams, plates and shells. To test the efficiency and accuracy of the present theory, dynamic properties of laminated beams, plates and shells with different dimensions, boundary conditions and lamination schemes were studied. The numerical results obtained from the present theory are in good agreement with exact elasticity solutions published previously.