Nonlinear Dynamic Analysis Of Multi-crack Structure

It is well known that a crack in the structure induces a drop in its natural frequencies and affects its mode shapes. This paper is a theoretical investigation of the geometrically non-linear free vibrations of multi-cracked structure containing an open crack under large vibration amplitudes and a semi-analytical solution about the beam of non-linear vibrations is established. Using the combined mode functions of line model to express the mode functions based on the Rayleigh method. The first mode explicit expression of non-linear vibrations is established. Besides, by numerical simulation method various crack location and crack depth, as well as assigned different first non-linear function contribution make the effect on maximum displacements of the crack structure. An explicit solution is simple and ready to use for engineering applications.(1) The establishment of a crack model is combined of linear elastic fracture mechanics, by which is introduced the rotational flexibility coefficient. The establishment of cracked beam functions are considered crack as a flexible hinge without mass which satisfy the boundary conditions and continuity conditions, as well as compatibility conditions. The approach uses a semi-analytical model based on the extension of the Rayleigh method to non-linear vibrations by choice of the admissible crack beam functions.(2) The use of semi-analytical method of a single-cracked beam with different boundary the numerical analysis, the single-cracked beam dimensionless natural frequencies and the cracked beam functions. Using the solved cracked beam functions, it is obtained by analysis of non-linear geometric parameters. An explicit solution of the first non-linear is established by neglecting minor items for the single-cracked beam.(3) By analysing the clamped-clamped beam with different crack location and depth, it is obtained the different changes of non-dimensional natural frequencies of cracked beam for various location and depth and the trends to crack beam functions. (4) The use of semi-analytical method with two crack clamped-clamped beam geometric non-linear dynamic analysis.