Nonlinear Vibration Analysis Of Beam With Different Tension-Compression Modulus

Material with nonidentical elastic modulus in tension and compr-ession, which is material that its elastic modulus is changed when stretching and compressing. It is different with the classical theory of elasticity that the material elastic modulus is a fixed value. In fact material’s mechanical property is very complex, and it is nonlinear among most of materials. However, many engineering materials, especially new materials, which are widely developed and applied, Such as pottery, porcelain, glass reinforced plastics, plastic, reinforced concrete, graphite, powder metallurgy materials, polymer materials and composite materials, etc. that have different strength when they are loaded with tension and compression, respectively. Most of them have distinctive mechanical characteristics, and they have different Young’s moduli. So the analysis of nature of materials with different tension and compression modulus is more and more attentive, With the development of science and technology, some research turns into a new study trending to develop new materials and to explore potency of material speciality of itself, this is a new direction of the development of the theory of elasticity.By applying different modulus of elasticity theory to mechanics to analyze the material with different modulus, this method can improve the analysis accuracy. The theory breaks through the assumption that elastic modulus is only related to the properties of material itself. The elastic modulus is related to the material shape, boundary condition and external loadings of structures, so it is a nonlinear problem contributed by many factors. Based on beam’s basic theory of elastic mechanics and different modulus’elasticity theory, we can list the static equilibrium equation for analyzing the tensile stress and compressive stress area, at the same time, corresponding stress calculation formula is given, using Hamilton principle form of vibration control equation. The equation for dimensionless processing is building, using Fortran software to analyze the vibration differential equation of free vibration. Through numerical calculation, the paper analyzes the free vibration of two different boundary conditions, and it is changing with the neutral axis, displacement, vibration amplitude, Analyzing of the frequency of the beam with the different modulus ratio, different uniformly distributed load, different vibration amplitude, parsing the free vibration of the second order frequency and main modes. The different elastic modulus vibration problem’s results are compared With Young’s moduli. Illustrating the impact on the material of different modulus.