Analysis Of Warpage Effect On Vibration Of Unidirectional Composite Beam With Rectangular Cross Section

With the increasing application of unidirectional composite beams,it is necessary to study their vibration characteristics systematically.In the existing research,the vibration differential equation generally includes only one or more of the moment of inertia,axial and transverse shear deformation.However,when the beam has a non-circular section,the warping deformation of cross section is mostly ignored in existing research.In this paper,three kinds of unidirectional composite rectangular beams with different axial forms(straight line,plane curve and space curve)are studied.The differential equations of motion for their free vibration are derived,in which the warpage of cross section is specially considered.The natural frequencies of the beam are systematically studied,which varies with various geometric parameters(aspect ratio of cross section,length of beam,curvature and torsion of beam axis,axis form)and material parameter(E₁/E₂?G₁₂/E₂).The work of this paper not only considers the warpage effect of beam cross section for the first time in theory,but also has a certain guiding significance for the designers of composite beams in engineering.The main works of this paper are as follows:1.The naturally curved and twisted beam theory is extended to the vibrations of space rods made of anisotropic materials.Based on the Xu rongqiao's model,explicit analytical expressions of the Saint-Venant's torsion warping function of unidirectional composite bar with rectangular cross-section is obtained.2.Based on the anisotropic natural bending and torsion beam theory,in the third,fourth and fifth chapters of this paper,the free vibration problems of three kinds of unidirectional composite beams are studied systematically.They are:straight beam,plane curved beam and spatial curved beam of unidirectional composite materials with rectangular section.The differential equations of motion of their free vibration are derived,which include warpage deformation.3.The natural frequencies and modes of the above three kinds of rectangular beams are calculated by the improved Riccati transfer matrix method and Mathematica software.Finally,the effects of various parameters(including geometric parameters and material parameters)on the natural frequencies are obtained,and some properties different from those of isotropic beams are found.4.Several groups of comparative design of unidirectional composite rectangular section beams with different geometric and material parameters are carried out to find out the variation of warpage effect with various parameters.