Mechanics Analysis Of Nonlocal Elastic And Viscoelastic Structural Element

The application study of nonlocal elastic theory is a hot topic in the study of nonlocal theory. In this paper, the basic problems of nonlocal theory are summarized, meanwhile the nonlocal theory is applied into the dynamic analysis of nonlocal elasticity, static and dynamic analysis of nonlocal viscoelasticity. The main works of this paper are summarized as follows1) Basing on Eringen's nonlocal elastic model and adopting exponential kernel function, the control equation of a nonlocal elastic bar is obtained. The dynamic analysis of the straight bar is studied with transfer function method and Ritz method and corresponding natural frequencies and modes are given.2) According to elastic integral constitutive equation, using laplace transformation a four-order partial differential equation is obtained for nonlocal elastic beam problem with exponential kernel function. The dynamic analysis of nonlocal elastic beam is studied with transfer function method and corresponding natural frequencies and modes are illustrated.3) Adopting nonlocal differential constitutive relationship, dynamic equation of nonlocal elastic thin plate is deduced. For two different boundary conditions, the frequency equations and the natural frequencies modes are showed. The relationship between nonlocal parameter lαand frequency is presented.4) Introducing the nonlocal stress-strain relationship into Kelvin viscoelastic model, nonlocal viscoelastic constitutive equation is obtained and the strain response of a bar in tension is studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and Neumann series, the closed form solution of strain field of the bar is obtained. Meanwhile the stable response of viscoelastic bar in tension is illustrated with harmonic excitation.