Analysis Of Euler-Bernoulli Beams Research Articles

Hermite Reproducing Kernel Meshfree Thermal Buckling Analysis of Euler-Bernoulli Beams with Elastic Foundation

The Hermite reproducing kernel meshfree method is employed for the stability analysis of Euler-Bernoulli beams with particular reference to the thermal buckling problem. This meshfree approximation employs both the nodal deflectional and rotational variables to construct the deflectional approximant according to the reproducing kernel conditions. In this paper, we apply this HRK meshfree method to the thermal buckling analysis of Euler-Bernoulli beam on elastic foundation. By comparison to the Gauss Integration method, HRK meshfree method shows much better solution accuracy.

Analysis of Euler-Bernoulli Beam with Piecewise Quadratic Hermite Finite Elements

The piecewise quadratic Hermite polynomials are employed in the finite element context to analyze the static and free vibration behaviors of Euler-Bernoulli beam. The desirable C1 continuity is achieved for the piecewise quadratic Hermite element that is required for the numerical solution of the Galerkin weak form of Euler-Bernoulli beam. In contrast to the classical cubic Hermite element, the piecewise quadratic Hermite element has a piecewise constant curvature representation within each element and thus the integration of the stiffness matrix is trivial. Several benchmark problems are shown to demonstrate the convergence properties of the piecewise quadratic Hermite element. The frequency error of the beam free vibration with this quadratic Hermite element is derived as well. Numerical examples consistently verify the analytical convergence rates.

Analysis of Euler-Bernoulli Beam with Piecewise Quadratic Hermite Finite Elements

The piecewise quadratic Hermite polynomials are employed in the finite element context to analyze the static and free vibration behaviors of Euler-Bernoulli beam. The desirable C1 continuity is achieved for the piecewise quadratic Hermite element that is required for the numerical solution of the Galerkin weak form of Euler-Bernoulli beam. In contrast to the classical cubic Hermite element, the piecewise quadratic Hermite element has a piecewise constant curvature representation within each element and thus the integration of the stiffness matrix is trivial. Several benchmark problems are shown to demonstrate the convergence properties of the piecewise quadratic Hermite element. The frequency error of the beam free vibration with this quadratic Hermite element is derived as well. Numerical examples consistently verify the analytical convergence rates.

On the Use of Differential Transformation Method for Free Vibration Analysis of Euler-Bernoulli Beams with General Elastically End Restraints

On the Use of Differential Transformation Method for Free Vibration Analysis of Euler-Bernoulli Beams with General Elastically End Restraints

Transverse Vibration Analysis of Euler-Bernoulli Beams Carrying Concentrated Masses with Rotatory Inertia at Both Ends

Transverse vibration analysis is presented for Euler-Bernoulli beams carrying concentrated masses and taking into account their rotatory inertia at both ends. The dimensionless eigenfunctions for the problems are first obtained using the differential equations of motion and considering translational and rotatory springs at both ends. A numerical technique, the Newton–Raphson algorithm, is then used to solve vibration eigenfunctions of the beams. Finally, the influences of different non-dimensional parameters on frequencies are discussed.

A Semianalytical Method for Nonlinear Vibration of Euler-Bernoulli Beams with General Boundary Conditions

This paper presents a new semianalytical approach for geometrically nonlinear vibration analysis of Euler-Bernoulli beams with different boundary conditions. The method makes use of Linstedt-Poincaré perturbation technique to transform the nonlinear governing equations into a linear differential equation system, whose solutions are then sought through the use of differential quadrature approximation in space domain and an analytical series expansion in time domain. Validation of the present method is conducted in numerical examples through direct comparisons with existing solutions, showing that the proposed semianalytical method has excellent convergence and can give very accurate results at a long time interval.