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In the present study, the nonlinear aeroelastic and sensitivity analysis of high aspect ratio wings subjected to a transverse follower force are discussed. A nonlinear structural model of wings is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations of motions are obtained via Hamilton’s principle and Galerkin method. Utilizing the method of multiple-scales, analytical approximate flutter response of the system is obtained. For validation, the analytical solution is compared with numerical solution and good agreement is observed. The time history of the tip displacement and tip twist solution are plotted for different airspeeds. Effects of follower force and its spanwise location and also the wing geometric characteristics on the flutter margin are discussed. Moreover, flutter margin sensitivity to different design parameters is analyzed. Results indicate that increasing the wing chord makes the system unstable. Furthermore, according to the analytical solution, effects of the wing chord and mass per unit length on the flutter margins are more important than the other system parameters.

In this paper, the aeroelastic response of a wing containing a propeller system with rotating unbalanced mass is presented. Nonlinear structural model of the wing carrying a propeller system is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations and boundary conditions are determined via Hamilton's variational principle. Galerkin's approach is used to transfer the resulting partial differential equation into ordinary nonlinear differential equations. Using the method of multiple scales, frequency response function of the system in different primary resonance cases is obtained analytically and the flutter occurrence possibility in each case is investigated. According to the results, jump phenomenon can be observed in each two primary resonance cases. Also, for the case of non-resonant excitation, the stability of the system is independent of the rotating unbalanced mass parameter.

In the present study, transverse vibrations of nanobeams with manifold concentrated masses, resting on Winkler elastic foundations, are investigated. The model is based on the theory of nonlocal elasticity in presence of concentrated masses applied to Euler-Bernoulli beams. A closed-form expression for the transverse vibration modes of Euler-Bernoulli beams is presented. The proposed expressions are provided explicitly as the function of two integrated constants which are determined by the standard boundary conditions. The utilization of the boundary conditions leads to definite terms of natural frequency equations. The natural frequencies and vibration modes of the concerned nanobeams with different numbers of concentrated masses in different positions under some typical boundary conditions (Simply Supported, Cantilevered and Clamped-Clamped) have been analyzed by means of the proposed closed-form expressions in order to show their efficiency. It's worth mentioning that the effect of Downloaded by [University of Nebraska, Lincoln] at 03:53 11 June 2016 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 various nonlocal length parameters and Winkler modulus on natural frequencies and vibration modes are also discussed. Finally the results are compared with those corresponding to classical local model.

Analysis of transverse vibration of beams is presented in this paper. Unfortunately, complexities which appear in solving differential equation of transverse vibration of non-uniform beams, limit analytical solution to some special cases, so that the numerical method is presented. DTM is a numerical method for solving linear and some non-linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of transverse vibration of conical Euler-Bernoulli beam. Natural circular frequencies and mode shapes have been calculated. Comparing results with the cases which exact solution have been presented, shows that DTM is a strong method especially for solving quasi-linear differential equations.