基于行波法的有限加肋板耦合运动研究

Coupled Motion Analysis of Finite Ribbed Plate Based on Traveling Wave Approach

为研究板与加肋条的耦合运动特征,采用行波法和模态叠加法,根据板与加肋条的不同耦合连续性假设,建立3种耦合模型,即板-附加质量模型、板-欧拉梁模型和板-板-欧拉梁模型,此时3种耦合模型对应的加肋条分别为阻振质量、扁钢和T型材。根据行波法推导有限加肋板耦合结构的动力响应表达式,并自编Matlab程序进行振动响应计算,通过对比有限元数值计算结果与行波法半解析计算结果,验证该行波法解法是计算耦合结构振动响应的有效方法。对3种耦合力学模型的对比研究,根据耦合连续性假设分析结构刚度项对响应的影响,说明在低频范围内,结构刚度项对结构的动力响应影响较小,但随着频率的增大,结构刚度项对结构动力响应影响增大。对板厚和损耗因子进行参数分析,计算结果表明:随着板厚增加,板的模态数变少;在共振频率附近,随着损耗因子的增加,结构输入功率流和传递功率流的峰值降低;损耗因子的改变对结构的固有频率影响不大。

Traveling wave method and modal superposition method are used to study the coupled motion characteristics of plate and added ribs. According to the coupled continuity hypothesis of plate and rib,three kinds of coupling model,i. e.,plate-additional mass model,plate-Euler beam model and plateplate-Euler beam model,are established. The three coupling models correspond to blocking mass,flat steel and T-shaped plate,respectively. The dynamic response of finite plate is derived based on the traveling wave method. A self-compiled Matlab program is applied to calculate the vibratory response. The traveling wave method is verified to be an effective approach to calculate the coupled structure by comparing the numerical result of the finite element method with the calculated result of the traveling wave method. The coupling models with three different ribs are compared and analyzed. According coupled continuity assumption,the effect of structural rigidity on response is investigated. In low frequency range,the structural stiffness has less effect on dynamic response. As frequency increases,the impact of structural stiffness on dynamic response increases. The impacts of thickness and loss factor on vibration are analyzed. The results show that,with the increase in plate thickness,the modal number of plate is re-duced. In the nearby regions of the resonant frequencies,the peaks of input power and transmission power are decreased with the increase in loss factor. The loss factor has less effect on the natural frequency of structure.