Forced Vibration Analysis of Functionally Graded Nanobeams

Abstract

In this paper, forced vibration responses of functionally graded (FG) nanobeams are presented for modified couple stress theory (MCST) with damping effect. The FG nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. Mechanical properties of FG beam depends on the position. The Kelvin–Voigt model is considered in the damping effect. In solution of the dynamic problem, finite element method is used within Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Influences of the geometry and material parameters on forced vibration responses of FG nanobeams are examined and discussed.

Phân tích phi tuyến ứng xử uốn của tấm bằng vật liệu FGM xốp đặt trên nền đàn hồi Pasternak với các điều kiện biên khác nhau có xét đến vị trí thực của mặt trung hòa

“…[6] phân tích dao động tự do của tấm FGM có bọt rỗng phân bố đều và không đều trên cơ sở lý thuyết tấm với bốn ẩn số chuyển vị. Ảnh hưởng của vi bọt rỗng đến ứng xử uốn và dao động riêng của tấm FGM được Akbas khảo sát trong [7]. Tu và cs.…”

Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

“…Consequently, manufacturing technologies were extended to make functionally graded (FG) layers in micron and submicron dimensions with the desired electrical and mechanical properties at their bottom and top sides. Therefore, many researchers have focused on the thermal [38][39][40] and mechanical [41][42][43][44] behavior of FG micro-and nanostructures. With the rapid advancement of manufacturing technology, CNTs are used as the favorite reinforcements for polymer nanolayers utilized in different engineering applications.…”

Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory

“…Bellifa et al [46] used a theory of simple shear deformation as well as the concept of the position of the neutral surface for the analysis of flexion and free vibration of plates made of functionally graded materials. Akbaş [47,48] studied the vibratory response of viscoelastic beams and wave propagation in a beam made of functionally graded materials in thermal environments. Bellifa et al [49] used the theory of non-local zero-order shear strain for the non-linear post-buckling of nano-beams.…”