摘要
为了研究加强筋对阶梯板振动和能量传递的影响,基于Kirchhoff薄板理论,采用有限积分变换法,建立了简支边界条件下加筋阶梯矩形板的自由与强迫振动分析的动力学模型,获得了加筋阶梯矩形板的自由与强迫振动的解析解,并且结合多目标粒子群算法,提出了通过加强筋的设置来控制阶梯板振动能量传递的策略。首先,提出了加筋阶梯变厚度板动力学模型的构建方法,对动力学模型的振动响应进行了基于有限元分析方法的计算与验证;然后,分析了加强筋的插入对激励板和接收板振动能量损失的影响,开展了加强筋的物理参数和插入位置对两板之间振动能量传递影响的研究;最后,提供了一种寻找最佳加强筋插入位置的优化算法,对加强筋的插入位置进行了优化分析。研究结果表明:通过在激励板和接收板上各插入一根加强筋,将获得较好的插入损失效果;加强筋的弯曲刚度增加,在低频段传递到接收板上的振动能量明显下降,而加强筋的质量对高频段的能量传递影响较大;激励板上加强筋的位置对能量传递的影响较小,而通过改变接收板上加强筋的位置,会使得接收板振动能量分布产生差异,对振动能量传递具有一定的影响;采用多目标粒子群优化算法寻得加强筋最佳插入位置,可使阶梯板总振动能量损失最大。可见采用有限积分变换法对加筋阶梯板进行动力学建模与振动控制分析是可行的。
In order to study the influence of stiffeners on the vibration and energy transfer of stepped plates,a dynamic model for free and forced vibration analysis of simply supported rectangular ribbed stepped plates was established based on Kirchhoff thin plate theory using the finite integral transform method.The analytical solutions of free and forced vibration of stiffened stepped rectangular plates were obtained,and a strategy of controlling vibration energy transfer of stepped plates by setting stiffeners was proposed in combination with multi-objective particle swarm optimization.Firstly,an analytical solution for the dynamic model of the ribbed stepped variable-thickness plate was proposed.The results obtained from finite element method calculations were employed for validation.Then,the influence of stiffening configurations on the vibration energy of the excitation and receiving plates was analyzed,and studies were conducted on the effects of the physical parameters and locations of the ribs on the vibration energy transfer.Finally,an optimization algorithm was proposed to determine the optimal insertion positions of the stiffeners,and a detailed optimization analysis of their insertion positions was conducted.The research results show that inserting one rib on each of the excitation and receiving plates yields effective vibration reduction.An increase in the bending stiffness of the ribs significantly reduces the vibration energy transferred to the receiving plate at low frequencies,while the mass of the ribs has a more pronounced effect on energy transfer at high frequencies.The position of the rib on the excitation plate has a minimal impact on energy transfer,whereas altering the position of the rib on the receiving plate results in differences in the vibration energy distribution of the receiving plate,thereby affecting vibration energy transfer to a certain extent.Multi-objective particle swarm optimization algorithm is used to find the best insertion position of stiffeners to maximize the total vibration energy loss of stepped plates.It indicates that the finite integral transform method is effective for dynamic modeling and vibration control analysis of stiffened stepped plates.
作者
郭慧
孙义
张凯
GUO Hui;SUN Yi;ZHANG Kai(School of Intelligent Manufacturing,Qingdao Huanghai University,Qingdao 266427,China;School of Mechanical and Automotive Engineering,Qingdao University of Technology,Qingdao 266520,China)
出处
《机电工程》
北大核心
2025年第8期1533-1542,共10页
Journal of Mechanical & Electrical Engineering
基金
山东省高等学校青创科技支持计划项目(2023KJ293)
青岛黄海学院博士科研启动基金资助项目(2023boshi07)。
关键词
加筋阶梯板
机械振动
能量传递
插入损失
Kirchhoff薄板理论
有限积分变换
粒子群优化算法
ribbed stepped plate
mechanical vibration
energy transmission
insertion loss
Kirchhoff thin plate theory
finite integral transform
particle swarm optimization algorithm
