Asymptotic frequencies of various damped nonlocal beams and plates

作者：Lei, Y; Adhikari, S; Murmu, T^*; Friswell, M I

来源：Mechanics Research Communications, 2014, 62: 94-101.

DOI：10.1016/j.mechrescom.2014.08.002

• Asymptotic frequencies
• Viscoelastic Non local elasticity
• Euler Bernoulli beam
• Timoshenko beam
• Kirchhoff plate
• Mindlin plate
• Damping

A striking difference between the conventional local and nonlocal dynamical systems is that the later possess finite asymptotic frequencies. The asymptotic frequencies of four kinds of nonlocal viscoelastic damped structures are derived, including an Euler Bernoulli beam with rotary inertia, a Timoshenko beam, a Kirchhoff plate with rotary inertia and a Mindlin plate. For these undamped and damped nonlocal beam and plate models, the analytical expressions for the asymptotic frequencies, also called the maximum or escape frequencies, are obtained. For the damped nonlocal beams or plates, the asymptotic critical damping factors are also obtained. These quantities are independent of the boundary conditions and hence simply supported boundary conditions are used. Taking a carbon nanotube as a numerical example and using the Euler Bernoulli beam model, the natural frequencies of the carbon nanotubes with typical boundary conditions are computed and the asymptotic characteristics of natural frequencies are shown.

• 出版日期2014-12
• 单位中国人民解放军国防科学技术大学