Thermo-Mechanical Buckling and Non-Linear Free Oscillation of Functionally Graded Fiber-Reinforced Composite Laminated (FG-FRCL) Beams

We investigated the thermal buckling temperature and nonlinear free vibration of functionally graded fiber-reinforced composite laminated (FG-FRCL) beams. The governing nonlinear partial differential equations were derived from the Euler-Bernoulli beam theory, accounting for the von Karman geometrical nonlinearity. Such equations were then reduced to a single equation by neglecting the axial inertia. Thus, the Galerkin method was applied to discretize the governing nonlinear partial differential equation in the form of a nonlinear ordinary differential equation, which was then solved analytically according to the He's variational method. Three different boundary conditions were selected, namely simply, clamped and clamped-free supports. We also investigated the effect of power-index, lay-ups, and uniform temperature rise on the nonlinear natural frequency, phase trajectory and thermal buckling of FG-FRCL beams. The results showed that FG-FRCL beams featured the highest fundamental frequency, whereas composite laminated beams were characterized by the lowest fundamental frequency. Such nonlinear frequencies increase for an increased power index and a decreased temperature. Finally, it was found that FG-FRCL beams with [0/0/0] lay-ups featured the highest nonlinear natural frequency and the highest thermal buckling temperature, followed by [0/90/0] and [90/0/90] lay-ups, while a [90/90/90] lay-up featured the lowest nonlinear natural frequency and critical buckling temperature

Finite Strain-Based Theory for the Superharmonic and Subharmonic Resonance of Beams Resting on a Nonlinear Viscoelastic Foundation in Thermal Conditions, and Subjected to a Moving Mass Loading

We address the nonlinear free vibration, superharmonic and subharmonic resonance response of homogeneous Euler–Bernoulli beams resting on nonlinear viscoelastic foundations, under a moving mass and an abrupt uniform temperature rise. The nonlinear differential equation of motion stemming from the Hamiltonian principle and Finite Strain Theory is discretized according to a Galerkin decomposition method, and is solved by means of a multiple time scale method. A comparison between the Finite Strain theory and the Von-Karman approach is discussed, accounting for the effect of temperature rise, linear and nonlinear coefficients of the elastic foundation on the nonlinear vibration history and phase trajectory. At the same time, we check for the sensitivity of the frequency response of the system in superharmonic and subharmonic resonance for different input parameters, namely, location, velocity, and magnitude of the moving load, temperature rise and elastic foundation

Nonlinear Dynamic Study of Non-Uniform Microscale CNTR Composite Beams Based on a Modified Couple Stress Theory

This study aims at investigating the nonlinear dynamic behavior of microscale carbon nanotube reinforced (CNTR) composite Euler-Bernoulli beams with a non-uniform cross-section, based on a modified couple stress theory (MCST). The nonlinear partial differential equations (PDEs) of motion are established based on the Von-Karman nonlinear strain-displacement relationship and Hamiltonian principle. The coupled PDEs are reduced to a single PDE, by neglecting the effects of the axial inertia and considering two different types of boundary conditions (i.e. clamped-clamped and clamped-free). At the same time, the single PDE is reverted to a nonlinear ordinary differential equation (ODE) by means of the Galerkin approach, and it is solved by using a semi-inverse method and the method of multiple time scales (MTS) for a free and forced vibration analysis, respectively. A large systematic numerical analysis is here performed to check for the sensitivity of the nonlinear response of CNTR composite beams to different boundary conditions and reinforcement parameters, with useful scientific insights for further computational investigations on the topic