A Study On Damage Identification Of Functionally Graded Timoshenko Beam Structures Based On Modal Strain Energy Change Ratio Method

Functionally graded materials (FGMs) are a novel type of heterogeneous composite materials that properties and functions of materials vary continuously in space, and materials inner is no obvious interface. Due to these unique advantages, functionally graded materials have been widely used in many fields of aerospace, civil engineering, mechanical engineering, chemical engineering etc. Due to various factors lead to structure damage, even the disasters occured because of loss of stability, and life safety is endangered or loss the property, so it is very important to identify the damage of function graded materials structure.Based on functionally graded Euler-Bernoulli beam theory, firstly the modal strain energy expression of the beam element with two node six degrees of freedom is derived, then damage identification of Euler-Bernoulli beam structure is carried out by modal strain energy change ratio method. In the process of damage identification, modal shapes are calculated by finite element method and are joined in gaussian noise to simulate the actual measurement error. The anti-noise properties of modal strain energy change ratio method is studied and analyzed by numerical examples, and these preparatory works set the foundation for the damage identification of Timoshenko beam.For functionally graded Timoshenko beam structure, modal strain energy change ratio method is adopted for structural damage identification. Based on functionally graded Timoshenko beam theory, the modal strain energy expression of the beam element with two node six degrees of freedom is derived, and the expression of element stiffness matrix of explicit integral is given. By using finite element method of functionally graded Timoshenko beam, modal modes are calculated, and on this basis, damage identification method of functionally graded Timoshenko beam structure is constructed. In the process of damage identification, by the large commercial finite element analysis software ABAQUS, modal modes are obtained and added to the noise of Gauss distribution to simulate the actual measurement error, then the influence of measurement error for damage identification result is discussed. Numerical example results show that structural damage location can be well identified based on modal strain energy change ratio method and the method has good anti-noise performance.For functionally graded beam structure, respectively based on Euler-Bernoulli beam theory and Timoshenko beam theory of the finite element method for vibration analysis, and the differences of the two models of vibration mode are compared, then the influence of these differences on the results of damage identification are discussed, furthermore, measurement error of modal mode is considered. The results show that the error of two models is the smallest when the span-depth ratio is about 20, and moreover, the existence of measurement error makes most of the damage identification index decrease.