Vibration of Euler–Bernoulli and Timoshenko beams in large overall motion on flying support using finite element method

High precise analysis of lateral vibration of quintic nonlinear beam

“…In the PEM, an artificial perturbation equation is constructed by embedding an artificial parameter which is used as an expanding parameter. According to PEM the solution of equation (7) is expanded into a series of in the form (11) The coefficients 1 and in the equation (7) are expanded in a similar way (12) where are to be determined. When , equation (7) becomes a linear differential equation for which an exact solution can be calculated for .…”

“…Non-linear modal analysis of a rotating beams studied by [11,12]. When the vibration amplitudes are moderate or large, the geometric nonlinearity must be included.…”

“…From the engineering outlook, structures like helicopter rotor blades, space craft antennae, flexible satellites, airplane wings, robot arms, high-rise buildings, long-span bridges, drill strings and vibratory drilling can be modelled as a beam-like member. The problem of the transversely vibrating beam was recently formulated in terms of the partial differential equation of motion by many researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] with different boundary conditions. Sedighi et al [1] presented the advantages of recent modern analytical approaches applied on the governing equation of transversely vibrating cantilever beams.…”

A New Fourier series solution for free vibration of non-uniform beams, resting on variable elastic foundation

“…This is comprised of such as those like parabolic thickness variation [10], bilinearly varying thickness [11], linearly variable depth [12] and those with exponentially varying width [13]. In addition to analytical solutions, some numerical and approximation methods including Finite Element Method [14][15][16][17], Variational Iteration Method [18][19] and approximate fundamental solution [20] has been developed in order to treat the vibration analysis of beams. The underlying elastic foundation modeled usually as the Winkler or Pasternak foundation [21][22] has also been a subject of interest in many studies.…”

Application of Recent Powerful Analytical Approaches on the Non-Linear Vibration of Cantilever Beams

“…Structures like helicopter rotor blades, space craft antennae, flexible satellites, airplane wings, robot arms, highrise buildings, long-span bridges and drill strings can be modeled as a beam-like member. The problem of the vibrating beams was recently formulated in terms of the partial differential equation of motion by many researchers [10][11][12][13][14][15][16][17][18][19] with different boundary conditions. A comprehensive study on the analytical investigation of vibrating tapered beams has been conducted by Bayat et al [2].…”