状态空间微积分法分析Winkler地基梁的自由振动

针对平面应力问题,提出了利用状态空间法和微分积分法的混合解法(SSDQM).基于二维问题的弹性力学状态方程,在梁的轴向运用微分积分法进行离散,建立了离散点上的状态方程.引入端部支承条件和Winkler地基模型的假设,从状态方程出发推导得到自由振动的频率方程.简支梁的SSDQM计算结果和弹性力学三角函数精确解吻合得很好.数值分析表明,地基梁的频率参数随着地基模量以及梁的跨高比的增大而增大.

Free vibration analysis of beams on Winkler foundation via state-space-based differential quadrature

The state space method coupled with the technique of differential quadrature (SSDQM) was presented for plane stress problems. Based on the two-dimensional state equations of elasticity, the axial domain of a beam was discretized according to the principle of differential quadrature and thus the state equations with respect to the variables at discrete points were established. Application of end conditions and the hypothesis of Winkler foundation model to the state equations yielded the frequency equation governing the free-vibrating beams. The present method was validated as sufficiently proficient by comparison of the numerical results with the exact solutions based on elasticity using trigonometric functions for simply supported beams. Numerical experiments indicate that the natural frequency parameter increases with the growth of foundation modulus and aspect ratio (length/depth) of the beam.