开孔功能梯度板的自由振动

Free vibration of functional gradient orifice plates

开孔板在机械工程中有重要应用.应用Kirchhoff薄板理论和虚功原理建立开孔功能梯度板的动力学有限元方程,弹性支承布置在方形开孔的4个角点处,以系统势能的形式将弹性支承引入有限元方程.在固支边界条件下,当梯度指数取极限值时对比了本文解和ANSYS解,证明本文所建模型有效,随后重点探讨了梯度指数和支承刚度对前两阶固有频率的影响.结果表明梯度指数增大固有频率降低,频率降低的趋势逐渐放缓.第一阶频率受弹性支承的影响远大于第二阶频率.

Orifice plate has important applications in mechanical engineering.Kirchhoff thin plate theory and virtual work principle are used to establish the dynamic finite element equation of functionally gradient orifice plate.The elastic supports are arranged at the four corners of the square hole,and the elastic supports are introduced into the finite element equation in the form of system potential energy.Under the boundary condition of four edges simply supported,when the gradient exponent is taken as the limit value,the proposed solution is compared with the ANSYS solution,which proves that the proposed model is effective.Then,the influence of gradient exponent and elastic stiffness on the first two natural frequencies is discussed.The results show that the natural frequency decreases with the increase of gradient exponent and the trend slows down gradually.The first order frequency is much more affected by the elastic support than the second order frequency.