Equations Of Motion For Beams Research Articles

Beam Motion With Unilateral Contact Constraints and Wear of Contact Sites

In the present paper, a computational algorithm is proposed for the motion of a beam which is constrained by unilateral contact at prescribed contact sites. Special attention is focused on the numerical difficulties arising due to the iteration between the beam equation of motion and the contact algorithm, and a method to overcome these difficulties is suggested. The algorithm also includes wear, and the dynamical properties of the system are allowed to change gradually as the contact sites wear down.

Static and dynamic analysis of composite box beams using large deflection theory

The static and dynamic behavior of composite box beams is investigated using a large deflection beam theory. The finite element equations of motion for beams undergoing arbitrary large displacements and rotations, but small strains, are obtained from Hamilton's principle. The importance of non-classical structural phenomena is systematically investigated for composite box beams. The sectional elastic constants including warping deformations have been determined from the refined cross-sectional finite element method. The effects of fiber orientations and stacking sequences on the static deformation and vibration characteristics have been investigated. Numerical results are compared with the previously published experimental and theoretical results. The present results are proved to be very accurate.

The methods of shuttle-sums and of shuttle-integrals in ion optics

A new recursive technique which is called the shuttle-sums or a generalized analogue of the Gaussian brackets, is proposed and developed. A special form of this technique is continuous generalized analogue to the Gaussian brackets which is called the shuttle-integrals. The shuttle-sums are used for analytical and numerical investigations of ion optical systems. The shuttle-integrals are used to calculate the matrizant (or the transfer matrix function) of the nonlinear equations of beam motion for an arbitrary coefficient matrix. In this method there is rigorous conservation of the phase volume of the beam at each stage of the calculations.

Aeroelastic stability of hingeless rotor blade in hover using large deflection theory

The coupled flap-lag-torsion aeroelastic stability of a hingeless rotor blade in hover is investigated using finite elements based on large deflection beam theory. The finite element equations of motion for beams undergoing arbitrary large displacements and rotations, but small strains, are obtained from Hamilton's principle. The stability boundary is calculated assuming blade motions to be small perturbations about the nonlinear steady equilibrium deflections, which are obtained through an iterative Newton-Raphson method. The p-k- mudal flutter analysis based on coupled rotating natural modes is used. Various unsteady two dimensional strip theories are used to evaluate the aerodynamic loads

Large amplitude beam equations of motion including base rotation and translation

Large amplitude beam equations of motion including base rotation and translation

A continuum theory for viscoelastic composite beams

A dynamical continuum theory is developed for laminated composite beams. Starting with an assumed displacement- and temperature field, the one-dimensional approximate theory is consistently constructed within the frame of the three-dimensional theory of linear, nonisothermal, anisotropic, coupled viscoelasticity. Each constituent of the beam may possess different constant thickness and mechanical properties. All dynamic interactions between the adjacent constituents are included. Further, the effects of transverse shear and normal strains and rotatory inertia as well as those of cross-sectional distortion are all taken into account. The resulting equations consist of the macroscopic beam equations of motion and heat conduction, the kinematical relations, the initial and boundary conditions and the constitutive equations, and they govern the extensional, flexural and torsional motions of laminated composite beams. The special cases of constituents which made of either isotropic thermoviscoelastic or anisotropic thermoelastic materials are discussed briefly.