In this paper, two kinds of vibrations are considered for a composite Timoshenko rotor: longitudinal-torsional vibration and two plane transverse one. The kinetic and potential energies and virtual work due to the gyroscopic effects are calculated and the set of six governing equations and boundary conditions are derived using Hamilton principle. Differential quadrature method (DQM) is used as ...

In this paper, free vibration analysis of a polymer-based nano-composite beam reinforced by boron-nitride nanotubes and subjected on elastic foundation, is studied. Smooth and defect-free nanotubes with uniform and directly- orientated in matrix are intended. Also, nanotubes’ distribution in the thickness direction of beam is regarded as a uniform distribution of the three different targeted on...

In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...

we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set ...

A rotor dynamic analysis method for the complex three-dimensional design blade was developed and applied to analyzing its aeroelastic stability. Based on medium-size deformation beam theory Hamilton principle, joint transfer matrix used in kinematic compatibility principle assembled finite element develop structural dynamics model. The BO105 validate this characteristic of analyzed detail. resu...

In this paper, the influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based functionally graded materials (FGM) cylindrical shells under combined loadings is investigated. The equations of motion are obtained by using the principle of Hamilton and Maxwell's equations and the Navier's type solution used to solve these equations. Material propertie...

In this paper free vibration analysis of two rectangular isotropic plates, which are connected to each other by two translational and rotational springs along the edges, are investigated. The equation of motion and associated boundary and continuity conditions are derived using the extended Hamilton principle. To solve the eigenvalue problem, the Ritz method is utilized. Numerical investigation...

Dynamic behavior of a circular shaft with geometrical nonlinearity and constant spin, subjected to periodic axial load is investigated. The case of parametric combination resonance is studied. Extension of shaft center line is the source of nonlinearity. The shaft has gyroscopic effect and rotary inertia but shear deformation is neglected. The equations of motion are derived by extended Hamilto...

The concept of the geometrical solution of Hamilton-Jacobi equations in arbitrary space dimension is introduced. The characterization of such solution is based on the intersection of several invariant hyper-surfaces in the space of 1-jets. This solution notion allows not only for the smooth evolution beyond the usual singularity formation but also for superposition of underlying geometrical sol...