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Free vibration of sandwich beams using the dynamic stiffness method

机译:使用动力刚度法的夹心梁自由振动

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The free vibration analysis of three-layered symmetric sandwich beams is carried out using the dynamic stiffness method. First the governing partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two partial differential equations that are coupled both in axial and bending deformations. For harmonic oscillation, the two equations are combined into one ordinary differential equation, which applies to both axial and bending displacements. A closed form analytical solution is then sought in its most general form. By applying the boundary conditions the dynamic stiffness matrix is developed. The Wittrick―Williams algorithm is used as a solution technique to compute the natural frequencies and mode shapes of an example sandwich beam. The discussion of results is followed by some concluding remarks.
机译:采用动力刚度法对三层对称夹层梁进行了自由振动分析。首先,使用汉密尔顿原理推导自由自然振动中支配的运动的偏微分方程。该公式导致两个偏微分方程,它们在轴向变形和弯曲变形中都耦合在一起。对于谐波振荡,将两个方程组合为一个常微分方程,该方程适用于轴向位移和弯曲位移。然后寻求一种最一般形式的封闭形式的分析解决方案。通过应用边界条件,建立了动态​​刚度矩阵。 Wittrick-Williams算法被用作一种解决方案技术,用于计算示例夹层梁的固有频率和模式形状。在对结果进行讨论之后,再作一些总结性发言。

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