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A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation

机译：Pasternak弹性地基上的梁弯曲和自由振动的混合方法

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摘要

In this paper a mixed method, which combines the state space method and the differential quadrature method, is proposed for bending and free vibration of arbitrarily thick beams resting on a Pasternak elastic foundation. Based on the two-dimensional state equation of elasticity, the domain along the axial direction is discretized according to the principle of differential quadrature (DQ). As a result, the state equations about the variables at discrete points are established. With consideration of the end conditions and the upper and lower boundary conditions in the derived state equations, governing equations for bending and free vibration problems are formulated. Numerical results prove that the present approach is very efficient and reliable. The effects of Poisson's ratio and foundation parameters on the natural frequencies are discussed.
机译：本文提出了一种将状态空间法和微分求积法相结合的混合方法，用于基于Pasternak弹性地基的任意厚梁的弯曲和自由振动。基于二维状态弹性方程，根据微分正交（DQ）原理离散沿轴向的域。结果，建立了关于离散点处的变量的状态方程。考虑到导出状态方程中的结束条件和上下边界条件，制定了弯曲和自由振动问题的控制方程。数值结果证明，该方法是非常有效和可靠的。讨论了泊松比和基础参数对固有频率的影响。

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