Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived based on Hamilton’s principle. The developed nonlocal models have the capability to interpret small scale effects. Winkler and Pasternak types elastic foundation are employed to represent the interaction of the nano FG beam and the surrounding elastic medium. A parametric study is conducted to investigate the influences of the static load factor, temperature change, nonlocal elastic parameter, slenderness ratio, surface effect and springs constant of the elastic medium on the dynamic stability characteristics of the FG beam, with simply-supported boundary conditions. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanobeams with lower aspect ratios. Moreover, it is observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origins of the instability regions to higher excitation frequencies and leads to further stability of the system at lower excitation frequencies, considering surface stress effect shifts the FG beam to higher frequency zone.

In this paper, the continuum model, which is known as Kwan model, has been presented for the analysis of tall buildings that have been as an appropriate approximation of the overall behavior of the structure. Tall building was modeled as a cantilever beam and analyzed with the assumption of flexural behavior based on Euler– Bernoulli beam theory, then the displacement of floors was calculated. o consider the shear lag effects in the overall displacement of the structure, Timoshenko’ s beam model has been considered and related relations were extracted. The lateral displacement formulas obtained and calculated for the framed tube system modeled by Kwan’ s method. To verify the results, numerical models were created in software (ETABS) and statically were analyzed for lateral loading. Finally the results were compared with those obtained by computer analysis and the corresponding diagrams were presented. At the end, the shape factor formula has been developed to improve the results of the Timoshenko’ s theory.

This paper presents a research into the progress of modeling of N-viscoelastic robotic manipulators. The governing equations of the system is obtained by using Gibbs-Appell (G-A) formulation and Assumed Mode Method (AMM). When the beam is short in length direction, shear deformation is a factor that may have substantial effects on the dynamics of the system. So, in modeling the assumption of Timoshenko beam theory (TBT) and its associated mode shapes has been considered. Although considering the effects of damping in continuous systems makes the formulations more complex, two important damping mechanisms, namely, Kelvin-Voigt damping as internal damping and the viscous air damping as external damping have been considered. Finally, to validate the proposed formulation a comparative assessment between the results achieved from experiment and simulation is presented in time domain.

In this paper, the analysis of nonlinear free vibrations of beams made of functionally graded materials with magnetorheological fluid as core is investigated. It is assumed that the beam is made of three layers including constraining layer, magnetorheological fluid and base layer and is located on Simply-Simply, Clamped-Simply and Clamped–, Clamped supports. The governing equations of the beam are derived using the Hamilton’, s principle. To obtain the vibrational frequencies, the theory of Timoshenko beam is used by the Generalized Differential Quadrature method. The effects of magnetic field intensity, power law exponents, core thickness and constraining layer thickness and the length of the beam on natural frequency and modal loss factor related to different frequencies modes for the three boundary conditions have been investigated. The results show the effects of physical and geometrical parameters regarding the natural frequency and modal loss factor of the sandwich beam with different modes. Also, the frequency and loss factor values obtained from Generalized Differential Quadrature method are very close to the results obtained by the Finite Element method. This shows the accuracy and precision of this method.

In the present study, a proper analytical model is developed for investigating nonlinear vibration behavior of asymmetric and symmetric rotors under unbalanced and misalignment induced forces in rotating coordinates. The rotor is connected to a motor through an asymmetric coupling. For a more accurate vibration analysis, Timoshenko's beam theory is applied and for a better modeling of misaligned coupling forces, Gibbons’ equations are used. The equations of motion are discretized by Rayleigh-Ritz method and derived from Hamilton's principle, thereafter. According to this investigation, for asymmetric rotors as opposed to symmetric rotors, a frequency range is detected in which resonance and instability occurs. Also, the dynamic behaviors of the symmetric and asymmetric rotors are analyzed at the same rotational speed to indicate specifically the effects of different parameters on both rotors. For investigating the vibration behaviors of the rotors more accurately, their time-domain vibration responses are plotted and then their Fast Fourier Transform (FFT) are presented to determine the vibration frequencies of the rotors, so the effects of different parameters can be well observed. As a whole, in this study, the effects of each of the defects such as shaft asymmetry, misalignment, mass unbalance and also nonlinear terms are investigated on the dynamic behavior of the rotor system.

In this paper flexural vibration and buckling analysis of the viscoelastic nanotube under electromagnetic force is investigated analytically. In order to consider more realistic assumptions, the linear solid viscoelastic model is used. The differential equations of motion are derived via the nonlocal Timoshenko beam theory. The Lorentz magnetic force is obtained from the Maxwell's relation. The analytical method is used to obtain nonlocal natural frequencies and buckling load of the system. The influence of magnetic field, aspect ratio and nanoscale effects on the natural frequencies and buckling load are studied. Then the results are validated and illustrated with appropriate figures and tables.

In this paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory. The beam material property is separated to shear and bulk effects. It is assumed that the beam is incompressible in bulk and viscoelastic in shear, which obeys the standard linear model with the material time derivative. The axial speed is characterized by a simple harmonic variation about a constant mean speed. The method of multiple scales with the solvability condition is applied to dimensionless form of governing equations in modal analysis and principal parametric resonance. By a parametric study, the effects of velocity, geometry and viscoelastic parameters are investigated on the response.

In this study, a semi analytical method for transverse and axial vibration of single-walled boron nitride nanotube (SWBNNT) under moving a nanoparticle is presented. The surrounding elastic medium as Pasternak foundation and surface stress effect are included in the formulations of the proposed model. Using Timoshenko beam theory (TBT), Hamilton’s principle and nonlocal piezoelasticity theory, the higher order governing equation is derived. The influences of surface stress effects, spring and shear parameters of Pasternak foundation and aspect ratio are also investigated on the free and forced vibration behavior of SWBNNT under moving a nanoparticle. Through an inclusive parametric study, the importance of using surrounding elastic medium in decrease of normalized dynamic deflection is proposed. It is demonstrated that the values of shear modulus have significant role on the vibration behavior of SWBNNT. The influences of surface stresses on the amplitude of normalized dynamic deflection are also discussed. The output result's of this study has significant influences in design and production of micro electro mechanical system (MEMS) and nano electro mechanical system (NEMS) for advanced applications.