基于高阶变形理论的夹层板的弯曲与振动

考虑面板和夹芯的面内刚度和横向剪切刚度以及抗弯刚度，考虑了高阶剪切变形，根据横向剪应变分布情况给出横向剪切转角的位移函数，基于哈密尔顿原理，推导了基于高阶变形理论、适用于软、硬夹芯情况夹层板的基本方程。作为算例，以四边简支条件下的夹层板的弯曲与振动，在不同的面板与芯层的弹性模量比和厚度比下进行了计算，并与Reissner理论、Hoff理论以及邓宗白基于Reissner理论的修正模型的计算结果进行了对比。与前述理论与方法相比，本文方法考虑因素更为全面，对夹层板的适用范围更为广泛，计算结果更为精确。针对Nastran软件计算夹层板的振动问题，对其适用范围作了简要分析。

Bending and Vibration of Sandwich Plates with High-Order Deformation Theory

Sandwich structures, due to their outstanding properties, such as high stiffness and relatively low weight, have found wide applications in aircraft, aerospace, naval/marine, construction, transportation, and wind energy systems. There are a good number of outstanding works studies devoted to the modeling and analysis of sandwich structures. Most of these works studies are based on the First-order Shear Deformation Theory (FSDT), in which the transverse shear stresses are assumed to be uniformly distributed across the thickness of sandwich plate. The FSDT is simple and accurate for thin sandwich plates, but needs a shear correction factor in order to satisfy the zero transverse shear stress boundary conditions at the top and bottom surfaces of the plate. Besides, the errors in deflection and stresses predicted by FSDT are not negligible when the plates are not sufficiently thin enough. Therefore, the Higher-order Shear Deformation Theory (HSDT) was proposed by several researchers to overcome the shortcomings of FSDT. In this paper, a special HSDT model is developed to investigate the bending and vibration behaviors of sandwich plates. In the HSDT model, the in-plane stiffness, bending stiffness, and transverse stiffness are considered in for both the surfaces and the core; the rotational displacement function associated with transverse shear effect is given based on the transverse strain distribution; the governing equations of the sandwich plates are derived by using Hamilton’s variational principle. Parameter studies are conducted to demonstrate the influences of the core elastic modulus and the surface thickness of surfaces on the bending and vibration behaviors of simply supported sandwich plates. The results calculated by using the present model are compared with those given by Reissner, Hoff and Deng. The comparison shows that the present model has a better accuracy and a wider application scope. Also, the modal solutions obtained by from the present model are compared with those obtained by using Nastran software to show the suitable application scope of each model in dealing with the vibration behavior of sandwich plates.