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In the present article, free vibration behavior of carbon nanotube‐reinforced composite (CNTRC) microbeams is investigated. Carbon nanotubes (CNTs) are distributed in a polymeric matrix with four different patterns of the reinforcement. The material properties of the CNTRC microbeams are predicted by using the rule of mixture. The microstructure‐dependent governing differential equations are derived by applying Hamilton's principle on the basis of couple stress theory and several beam theories. The obtained vibration equation is solved by using Navier's solution method. The effects of length scale parameter, length/thickness ratio, volume fraction and the reinforcement pattern of CNTs on frequencies are examined. It is observed that the biggest frequencies occur in X‐Beam while O‐Beam has the lowest ones. It is also found that the size effect is more prominent when the thickness of the beam is close to the length scale parameter and this effect nearly disappears as the thickness of the beam increases.

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This paper presents the dynamic responses of a fiber-reinforced composite beam under a moving load. The Timoshenko beam theory was employed to analyze the kinematics of the composite beam. The constitutive equations for motion were obtained by utilizing the Lagrange procedure. The Ritz method with polynomial functions was employed to solve the resulting equations in conjunction with the Newmark average acceleration method (NAAM). The influence of fiber orientation angle, volume fraction, and velocity of the moving load on the dynamic responses of the fiber-reinforced nonhomogeneous beam is presented and discussed.

In this study, non-linear static analysis of a cantilever Timoshenko beam composed of functionally graded material (FGM) under a non-follower transversal uniformly distributed load is studied with large displacements and large rotations. Material properties of the beam change in the thickness direction according to a power-law function. In this study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The non-linear problem is solved by using the incremental displacement-based finite element method in conjunction with the Newton-Raphson iteration method. To use the solution procedures of the Newton-Raphson method, there is a need to linearize equilibrium equations, which can be achieved through the linearization of the principle of virtual work. In this study, the effects of large deflections, large rotations and various material distributions on displacements and normal stress and shear stress distributions through the thickness of the beam are investigated in detail. The convergence study is performed for various numbers of finite elements. In addition, some of the particular results of the present study which are obtained for the homogeneous material case are compared with the results of the SAP2000 packet program. Numerical results show that geometrical non-linearity and material distribution play very important roles in the static responses of FGM beams.

In this study, the free vibration analysis of edge cracked cantilever microscale beams composed of functionally graded material (FGM) is investigated based on the modified couple stress theory (MCST). The material properties of the beam are assumed to change in the height direction according to the exponential distribution. The cracked beam is modeled as a modification of the classical cracked-beam theory consisting of two sub-beams connected by a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces to the classical one when the length scale parameter is zero. The problem considered is investigated using the Euler–Bernoulli beam theory by the finite element method. The system of equations of motion is derived by Lagrange’s equations. To verify the accuracy of the present formulation and results, the frequencies obtained are compared with the results available in the literature, for which good agreement is observed. Numerical results are presented to investigate the effect of crack position, beam length, length scale parameter, crack depth, and material distribution on the natural frequencies of the edge cracked FG microbeam. Also, the difference between the classical beam theory (CBT) and MCST is investigated for the vibration characteristics of the beam of concern. It is believed that the results obtained herein serve as a useful reference for research of similar nature.

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.