Analysis of flexural natural vibrations of thin‐walled box beams using higher order beam theory. (25th July 2019) - Jiang, Lizhong; Yu, Jian; Zhou, Wangbao; Feng, Yulin; Chai, Xilin
Summary: In order to study the influence of high‐order shear deformations and shear lag on the dynamic characteristics of thin‐walled box beams (TWBBs), this paper takes the Hamilton principle as a basis to consider multiple factors such as high‐order shear deformations, shear lag, and cross section rotary inertia of the TWBBs. The vibration differential equations and natural boundary conditions of TWBBs are deduced. On the basis of eight examples of TWBBs with different boundary conditions and span–width ratios, analytical results of this paper are compared with those of the ANSYS finite element method. Both results are in good agreement with each other, and the validity of the calculation method is verified. The effects of higher order shear deformations and shear lag on natural vibration characteristics of TWBBs are analyzed. And some meaningful conclusions are drawn: This theory shows the capability to accurately describe both higher order deformations and shear lag; when the span–width ratio is small, neglecting higher order web deformations will produce a large calculation error; under the action of shear lag, the natural vibration frequency of TWBBs decreases greatly, which cannot be neglected; and both the high‐order shear deformations and shear lag effect increase with increasing mode order and increase with decreasing span–width ratio.