Vibration Characteristics Analysis Of Cracked Thin Plate Based On Improved Fourier Transform

Due to the use environment and use time and other reasons,the plate structure inevitably crack,these cracks also affect the use of the performance of the plate structure,and in industry,the impact of crack on the vibration of the plate structure is not to be ignored.However,due to the existence of cracks,the structural characteristics of the plate are affected,and its vibration characteristics change accordingly.This paper mainly discusses the vibration analysis of rectangular plate and laminated plate with cracks,and analyzes the influence of cracks on the vibration characteristics of the plate by analyzing the natural frequencies of each order.In order to establish the rectangular plate model with cracks,the crack term is firstly established based on fracture mechanics.In order to be suitable for arbitrary elastic boundary conditions,the displacement admissible function is established by using the improved Fourier series.At the same time,the mathematical model of the rectangular plate with cracks is established by combining the Rayleigh Ritz method.On this basis,a mathematical model of laminated plates with cracks is established based on the theory of laminated plates.For the establishment of the model and the corresponding analysis and verification,this paper will be carried out from the following three perspectives.1.In the process of theoretical derivation,the vibration model of rectangular thin plate and laminated plate with cracks under arbitrary elastic boundary conditions is established by combining fracture mechanics,improved Fourier series method and Rayleigh-Ritz method under global marking.By using the improved Fourier series method to express the crack term and the vibration displacement function of the rectangular thin plate,the discontinuity of the traditional Fourier series method on the boundary conditions is overcome,and the method can be applied to any elastic boundary conditions.And then use the Rayleigh Ritz method to establish the vibration of the cracked plate containing matrix equation,the free vibration can be calculated under the condition of natural frequency and modal vibration mode,through the contrast with references,finite element simulation results,which proved the accuracy of this method and accuracy,and on the size and location of the crack and boundary conditions for the parametric analysis.2.Parameterized analysis was carried out on the vibration characteristics of the cracked plate,and the natural frequency and high-order mode mode were analyzed from the perspective of the size and position parameters of the crack,boundary constraints,and the ratio of length to width of the plate.In order to analyze the root cause of the crack's influence on the vibration characteristics,the static analysis of the crack was carried out,and the local stress and strain caused by the crack and the influence on the vibration characteristics were demonstrated through the explanation and verification of the stress concentration phenomenon of the crack and the comparison of the stress field distribution in the plate.Based on the model of the cracked plate,the crack fatigue propagation formula is obtained,and the influence of damping and excitation loading position on the fatigue life of the cracked plate is analyzed.3.Designed and carried on the modal experiments of rectangular thin plates with cracks under free boundary conditions and fixed boundary conditions.Data are collected by single point vibration method,and processed by DHDAS software to obtain the natural frequency and modal pattern of the plate with cracks.Compared with the numerical results,the correctness and reliability of the modeling method proposed in this paper are verified,and the scientific experimental method used to collect and analyze the mode shapes is also mastered.