The Researches On Static Performances,Dynamic Characteristics And FRP-Reforcement Of Viscoelastic Cracked Beams

Viscoelastic materials have been widely used in various engineering fields,and researchers have focused on various mechanical properties of viscoelastic materials.However,due to the influences of natural environments,external loads and manufacturing techniques,the imperceptible or obvious cracks can appear easily in the viscoelastic beams,which makes the reduction of the stiffness,bearing capacity and durability of the viscoelastic beam,and leads a serious threat to its normal use.Therefore,it is of important theoretical significance and engineering application for research on the static performances and dynamic characteristics of the viscoelastic cracked beam in order to ensure the safety of the beam components and to avoid the failure and damage of the structure and its members.Based on the constitutive equations of the standard linear solid model and Kelvin-Voigt model of viscoelasticity,the static performances and dynamic characteristics of the viscoelastic cracked beam,as well as the influences of FRP-reinforcement on the bending behaviors of the viscoelastic cracked beam were investigated in this thesis by using the analytical method as main and supplement with the finite element simulation.The main research contents and achievements are given as follows:Regarding the transversal crack in the beam as a massless viscoelastic torsion spring,the equivalent bending stiffness of a viscoelastic cracked beam with open cracks was presented in the Laplace transform domain.Then,some general explicit analytical solutions in the time domain for the deflection and rotational angle of a Timoshenko beam having an arbitrary number of open cracks and the requirement for the standard linear solid constitutive equation of viscoelasticity were derived.The influences of the time,span-height ratio of beam and crack depth on the bending deformation under the simple-supported boundary condition with the different cracked beam models were analyzed numerically.Additionally,the bending behavior of the simple-supported Timoshenko viscoelastic beam with switching cracks was also studied.Based on the equivalent bending stiffness of the viscoelastic beam with open cracks derived in this thesis,the equations of motion of Euler-Bernoulli and Timoshenko viscoelastic cracked beams were presented,respectively,and the corresponding complex frequency characteristic equations of Euler-Bernoulli and Timoshenko viscoelastic cracked beams were obtained by using the method of separation of variables and Laplace transform.Meanwhile,based on the principle of virtual work and the continuity condition of deflection on the crack locations for the beam bending deformation,the analysis framework of finite element method to investigate the dynamic characteristics of the viscoelastic cracked beams was presented.In numerical examples,the accuracy and applicability of the finite element method were verified,the influences of crack location,crack depth and crack number on the dynamic characteristics of the viscoelastic cracked beams were analyzed,and the influences of the transverse shear deformation and moment of inertia of beam on the vibration characteristics of Timoshenko viscoelastic cracked beams were examined.Combining the equivalent viscoelastic torsion spring model of an open crack and the elastic translational spring model of the FRP-sheet reinforcement,the equivalent flexural stiffness expression of the viscoelastic cracked beam strengthened with FRP-sheet was presented,and some general explicit analytical solutions of the bending deflection and rotational angle of a FRP-sheet reinforcement Timoshenko viscoelastic beam with an arbitrary number of open cracks were obtained.Then,the bending behaviors of the simple-supported and continuous viscoelastic cracked beam with FRP-sheet reinforcement symmetrically were analyzed numerically,and the strengthening effects of FRP-sheet were also investigated.