初应力状态下夹芯复合材料曲梁面板的局部振动的理论分析

在船舶领域,以复合材料层合面板及泡沫芯材组成的夹芯复合材料板梁结构已大量应用在游艇及复合材料高速艇上.文章研究了受初始静载荷作用下夹芯复合材料曲梁的面板的局部自由振动问题,并给出一种相应的理论分析方法.文中通过将芯材简化为Winkler弹性地基,将面板简化为一复合材料曲梁,从而使所研究问题蜕化为有初始静载荷作用下弹性地基上任意曲梁的固有振动问题.在局部振动位移是基于初始静载平衡位置并与初始位移相比是小量的假定的基础上,根据能量原理推导出面板的运动方程.研究的结果表明,该面板的局部振动不只取决于面板的弯曲刚度和长度,以及芯材的弹性刚度,也在很大程度上取决于梁的曲率及面板所受到的初始轴向压力.

Theoretical Analysis of Local Vibration of the Skin in an Initially Stressed Curved Sandwich Beam

Sandwich structures with composite laminate face and foam core are widely used in yachts and high speed crafts in ship area.A theoretical approach is provided to investigate the problem of local free vibration of an initially stressed curved sandwich beam in this paper. The equation of motion of the skin is derived from energy principles and based upon small displacements away from an initial,loaded equilibrium state.The core material is simplified as an elastic foundation and the skins are considered as composite beams on an elastic foundation.The investigation shows that the vibration frequencies and modes are dependent not only on the flexural rigidity and length of beam and foundation modulus, but also on geometry of curvature and axial compressive/tensile force.