Free Vibration Of Beams Considering Cross-section Warpage

The space curved beam structure plays an important role in civil and transportation,mechanical engineering,and aerospace engineering because of its streamlined shape,good stress characteristics,and adaptability to various terrains and features.In addition to the common fields mentioned above,in recent years,the application of curved beam structures with non-circular cross sections has become more diverse.Many scholars have done a lot of research on the static characteristics of beams,and put forward many theories and calculation formulas.In engineering practice,beams are inevitably subject to dynamic loads,and research on their vibration characteristics is necessary.At present,most studies have only considered one or more of the moment of inertia,axial and transverse shear deformation,and rarely take into account the effect of warpage and deformation of the cross section in the differential equation of motion of the beam.This paper mainly studies three types of beams with non-circular cross-sections,which are: straight beams,plane curved beams and space curved beams made of isotropic materials.A new differential equation of motion was theoretically derived.For the first time,the cross-section warpage deformation was considered in the equation,and a variety of parameters(such as the shape of the cross-section,the aspect ratio of the cross-section,and the height-span ratio of the beam were systematically studied.,Curvature and torsion of the beam axis,material properties)on the natural frequency of the beam and the variation of the warping effect with various parameters,some meaningful results were obtained.The work of this paper has certain guiding significance for the designers of curved beams in engineering.The main work of this article is as follows:1.Based on the traditional beam theory,the differential equations of motion for beams with multiple axis forms and multiple cross-sectional shapes are derived theoretically.It consists of 14 mutually coupled differential equations,and after adding two variables,generalized warping coordinates and generalized warping moments,the equation appears very rigid and difficult to solve.2.This paper adopts the improved Riccati transfer matrix method to solve the above-mentioned motion differential equations,and finds out that the natural frequency of various forms of beams varies with various design parameters.3.Numerical examples show that: for some parameters,the warping deformation of the cross section has a great influence on the natural frequency of the curved beam;for other parameters,the effect of the warping effect is not obvious.Through the comparative study of various parameters in this paper,the variation law of warping effect with different parameters is revealed.The main innovations of this paper are: 1.The effect of warpage deformation on the free vibration characteristics is considered in the differential equations of motion of 3 types of beams with non-circular cross-sections,and the natural frequency is modified by the improved Riccati transfer matrix Solve the problem;2.It is planned to answer the case where the warpage effect must be considered...