In this study, the free vibration analysis of a functionally graded rotating double tapered BEAM is performed. The analysis is based on Euler-BERNOULLI BEAM THEORY. The Material properties of the BEAM vary continuously in the thickness direction according to the power-law function. The governing differential equation of motion is derived using the Hamilton’s principle. Natural frequencies are obtained using differential transformation (DTM) technique. The effects of the taper ratios, no dimensional rotational speed, no dimensional hub radius and material volume fraction index on the natural frequencies are discussed. Numerical results are tabulated in several tables and figures. To verify the present analysis, the results of this study are compared with the available results from the existing literature. It is shown that the natural frequencies of a functionally graded rotating double tapered Euler-BERNOULLI BEAM can be obtained with high accuracy by using DTM. It was observed that no dimensional rotational speed, height taper ratio and power-law exponent significantly affect the natural frequency. The effects of hub radius and breadth taper ratio on the natural frequencies are negligible.

In this paper, a size-dependent formulation for the BERNOULLI-Euler BEAM is developed based on a new model of couple stress THEORY presented by Hadjesfandiari and Dargush. The constitutive equation obtained in this new model, consists of only one length scale parameter that is capable of capturing the micro-structural size effect in predicting the mechanical behavior of the structure. Having one length scale parameter is claimed to be an advantage of the model in comparison with the classical couple stress THEORY. The governing equations and boundary conditions of the BERNOULLI-Euler BEAM are developed using the variational formulation and the Hamilton principle. The static bending and free vibration problems of a BERNOULLI-Euler BEAM with various boundary conditions are solved. Numerical results demonstrate that the value of deflection predicted by the new model is lower than that of the classical THEORY. It is also found that natural frequencies obtained by the present couple stress model are higher than those predicted by the classical THEORY. The differences between results obtained by the present model and the classical THEORY become significant as the thickness of the BEAM gets close to the length scale parameter of the BEAM material.

This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane's methods. Euler-BERNOULLI BEAM THEORY is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method THEORY, the governing differential equations of motion are derived and solved using both Runge-Kutta-Fehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg4, 5th leads to same results. The mode frequency and the effects of geometry of flexure hinges on intermediate links vibration are investigated and the mode frequency, calculated using Fast Fourier Transform and the results are discussed.

The body freedom flutter phenomenon is one of the aeroelastic instabilities that occurs due to the coupling of the aeroelastic bending mode of the wing with the short-period mode in the flight dynamics of the aircraft. By using the aeroservoelastic model and applying closed loop control, this phenomenon can be suppressed in the operating conditions of the aircraft and the velocity of this event can be increased. The simplest model aircraft capable of displaying this instability includes the flexible wing and the planar flight dynamics model. For this purpose, the wing structure is modeled using the Euler-BERNOULLI BEAM and, the THEORY of minimum variable state is used to model unstable aerodynamics to make the conditions suitable for modeling the system in state space. In the control section, the elevator is used as the control surface and LQR THEORY with Kalman filter is used to body freedom flutter suppression. Finally, the effect of adding a closed loop control to increase the body freedom flutter velocity and the limitations of this work are studied.

In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and EulerBERNOULLI BEAM models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge-Kutta method is employed for the time response integration method. A comparative study is made between the EulerBERNOULLI and Timoshenko BEAM models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a remarkable difference between the models, considering the foreshortening effect and un-stiffened models. It is obvious that for high precisions applications, the stiffened Timoshenko model is recommended. It is interesting to note that joint torques for the entire range of slenderness ratios are the same.

In recent years, impedance measurement method by piezoelectric (PZT) wafer active sensor (PWAS) has been widely adopted for non-destructive evaluation (NDE). In this method, the electrical impedance of a bonded PWAS is used to detect a structural defect. The electro-mechanical coupling of PZT materials constructs the original principle of this method. Accordingly, the electrical impedance of PWAS can sense any change in the mechanical impedance of the structure. A thermal stress on a structure, which was generated by environmental temperature, could change the electrical impedance of PWAS. The thermal stress which affects the output impedance of PWAS is also developed. A temperature-dependent model, the temperature dependency of PWAS, and structure material properties are investigated for a PWAS bonded to an Euler BERNOULLI clamped-clamped BEAM. The Rayleigh-Ritz and spectral element methods are studied and, then, verified by 3D finite element method (FEM).

According to the wide presence of BEAMs in engineering structures, it is very useful to understand how the BEAMs vibrate nonlinearly in conditions where they oscillate with a large amplitude. In this paper, the nonlinear vibrations of an Euler-BERNOULLI BEAM under finite deformation are investigated. In this study, unlike other papers, in order to obtain the governing equations of the BEAM, the field-displacement relationship has been done without approximation. Based on this, the strain-displacement relations are calculated using the Green Lagrange strain, and the nonlinear form of the equations is obtained by using the Hamilton method. In order to solve the partial differential equation, using the Galerkin method, the equation has been converted to an ordinary differential equation and finally solved using the multiple scale method and compared with the Rung-Kutta numerical method. To evaluate the accuracy of the method and the validity of the modelling, the obtained results are compared with the Euler–BERNOULLI BEAM THEORY and the Von-Karman nonlinear model. The results show that the present method in low vibration amplitudes is consistent with the model of Euler-BERNOULLI and Von-Karman, but with increasing amplitude of oscillations, the results of these models will be significantly different from each other, which is as expected.

The issue of the new elastic terms discovered in the nonlinear dynamic model of an enhanced nonlinear 3D Euler-BERNOULLI BEAM is discussed. While the elastic orientation is negligible, the nonlinear dynamic model governing tension-compression, torsion and two spatial bendings is presented. Considering this model, some new elastic terms can be identified in the variation of elastic potential energy in each bending motion equation, and in each transverse shear force. Due to the new terms, each term of a bending equation and a transverse shear force, finds a counterpart in the other bending equation and transverse shear force, but the equations remain asymmetric. The new terms have arisen, since variation of strains and variation of elastic potential energy are derived from exact strains and exact deformations regarding considerable elastic orientation, then the elastic orientation is neglected. The new terms perish in the nonlinear 3D Euler-BERNOULLI BEAM THEORY, since elastic orientation is neglected first, then variation of strains and variation of elastic potential energy are derived from the approximated strains.

Euler-BERNOULLI BEAM model based non-local elasticity THEORY is developed for the static and buckling analysis of cantilever carbon nanotubes (CNTs). The size effect is taken into consideration using the Eringen’s non-local elasticity THEORY. The derivation of governing equation of bending and buckling from the shear and moment resultants of the BEAM and stress-strain relationship of the one-dimensional non-local elasticity model is presented. Buckling and deflection values of CNTs are obtained and presented in graphical form. Numerical results are presented to show the small-scale effect on bending of CNTs.