Abstract
We present an exact method to model the free vibration of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) beams with arbitrary boundary conditions based on first-order shear deformation elasticity theory. Five types of carbon nanotube (CNT) distributions are considered. The distributions are either uniform or functionally graded and are assumed to be continuous through the thickness of the beams. The displacements and rotational components of the beams are expressed as a linear combination of the standard Fourier series and several supplementary functions. The formulation is derived using the modified Fourier series and solved using the strong-form solution and the weak-form solution (i.e., the Rayleigh–Ritz method). Both solutions are applicable to various combinations of boundary constraints, including classical boundary conditions and elastic-supported boundary conditions. The accuracy, efficiency and validity of the two solutions presented are demonstrated via comparison with published results. A parametric study is conducted on the influence of several key parameters, namely, the L/h ratio, CNT volume fraction, CNT distribution, boundary spring stiffness and shear correction factor, on the free vibration of FG-CNTRC beams.
Highlights
Carbon nanotube (CNT)-reinforced composites have shown outstanding physical, mechanical, thermal and electrical properties over traditional structural materials, drawing interest from numerous researchers
Shen[14] in 2009 first proposed a new distribution form with carbon nanotube (CNT) distributed in an Functionally graded (FG) manner in the matrix; the volume fraction of CNTs was assumed to vary along the thickness direction
The issue of nonlinear bending behaviour of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) plates was investigated in which a transverse uniform or sinusoidal load in thermal environments was taken into consideration
Summary
Γxz γyz (5b) in which εx and γxz denote the normal and shear strain, respectively. εx[0], εy0 and γxy represent the strain at the middle surface; kx, ky and kxy are the bending and twisting curvatures; Nx, Ny and Nxy indicate the force resultants at the middle surface; Mx, My and Mxy are the bending and twisting moment resultants; and Qxy and Qyz represent the shear force resultants. Γxz γyz (5b) in which εx and γxz denote the normal and shear strain, respectively. Εx[0], εy0 and γxy represent the strain at the middle surface; kx, ky and kxy are the bending and twisting curvatures; Nx, Ny and Nxy indicate the force resultants at the middle surface; Mx, My and Mxy are the bending and twisting moment resultants; and Qxy and Qyz represent the shear force resultants. Regarding the CNTRC beam, certain force and moment resultants, namely, Ny, Nxy, Qyz and My, are equal to zero, while the corresponding strains εy[0], γxy and curvature ky are assumed to be non-zero. Eq (5) can be expressed as: Nx Mx Mxy
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
