Influence of geometric nonlinearity on static and dynamic response of flexible beam

Abstract

Abstract The flexible beam theory is widely applied in engineering, due to that many engineering structures can be regarded as flexible beam. For the flexible beam under large rotation, researches have shown that consideration of geometric nonlinearity is necessary: beam deflection will be erroneously larger or diverge without consideration of geometric nonlinearity. The reason lies on the dynamic stiffening effect caused by geometric nonlinearity. The dynamic stiffening effect of flexible beam under large rotation is well studied already, however, most studies only focus on flexible beam with constant cross section and rarely considers flexible beam without rotation. In view of this, a flexible beam with variable and twisted cross section is adopted to analyze the influence of geometric nonlinearity, and the response of flexible beam without rotation or static response is also analyzed. The results of dynamic beam deflection with and without consideration of geometric nonlinearity is compared, the results of static beam deflection under different load is also compared. On the basis of result comparison, the influence of geometric nonlinearity on static and dynamic response of flexible beam is then explained.