Presentation of a Novel Method in the realm of Non-classical Continuum Mechanics Under the Vibration of Nano-scaled Structures
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اصل مقاله (1009.86 K)
کد مقاله : 1001-ISAV (R1)
نویسندگان
1دانشکده مهندسی هوافضا، دانشگاه صنعتی شریف، تهران، ایران
2دانشکده مهندسی هوافضا. دانشگاه صنعتی شریفو تهرانو ایران
چکیده
The following paper contains a presentation of a novel method to derive the lattice constitutive equation based on lattice basics. The lattice is assumed to be made of point masses and springs. In this method, a self-containing differential equation is presented, in which lattice parameter derivation, despite previous non-classical theories, is no longer difficult. The equation represents the displacement field of the lattice which is derived using the Taylor series. The order of the equation is determined by the number of terms in the Taylor series. Also, to compare the results, dispersion relation for a flexural beam in Eringen’s non-local theory, Lattice model and the new method has been derived then the effect of lattice parameter- the distance between the point masses- on the dispersion curve has been investigated. Finally, the first three frequencies for the mentioned beam in these three methods in different boundary conditions have been derived and the error in each mode has been calculated.
کلیدواژه ها
موضوعات
مراجع
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