The problem of determining the optimum shape of a homogeneous Euler-Bernoulli beam of a circular cross-section, in which the coupled axial and bending vibrations arose due to complex boundary conditions, is considered. The beam mass is minimized at prescribed fundamental frequency. The problem is solved applying Pontryagin's maximum principle, with the beam cross-sectional diameter derivative with respect to longitudinal coordinate taken for control variable. This problem involves first-order singular optimal control, the calculations of which allowed the application of the Poisson bracket formalism and the fulfillment of the Kelley necessary condition on singular segments. Numerical solution of the two-point boundary value problem is obtai...
The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam car...
AbstractThe quenching of the vibration of an Euler–Bernoulli beam under tension with general linear ...
In this paper an analytical approach is used to optimize a beam surrounded by a Winkler's medium and...
In this study, optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the l...
In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analyti...
Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional area, with a ...
Optimum vibrating shapes of beams and circular plates, having piecewise linear variation in thicknes...
The stiffness maximization of elastic straight Euler-Bernoulli beams under the action of linearly di...
International audienceStudying structural elements undergoing transverse vibration is crucial for sc...
In the present paper the Green's function is utilized to provide a simple, exact and direct analytic...
In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse pro...
The minimisation of both the mass and deflection of a beam in bending is addressed in the paper. To ...
The second strain gradient theory is a non-classical continuum theory that captures the behavior of ...
This paper aims to extend earlier optimum design results for transversely vibrating Bernoulli-Euler ...
summary:A design optimization problem for an elastic beam with a unilateral elastic foundation is an...
The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam car...
AbstractThe quenching of the vibration of an Euler–Bernoulli beam under tension with general linear ...
In this paper an analytical approach is used to optimize a beam surrounded by a Winkler's medium and...
In this study, optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the l...
In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analyti...
Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional area, with a ...
Optimum vibrating shapes of beams and circular plates, having piecewise linear variation in thicknes...
The stiffness maximization of elastic straight Euler-Bernoulli beams under the action of linearly di...
International audienceStudying structural elements undergoing transverse vibration is crucial for sc...
In the present paper the Green's function is utilized to provide a simple, exact and direct analytic...
In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse pro...
The minimisation of both the mass and deflection of a beam in bending is addressed in the paper. To ...
The second strain gradient theory is a non-classical continuum theory that captures the behavior of ...
This paper aims to extend earlier optimum design results for transversely vibrating Bernoulli-Euler ...
summary:A design optimization problem for an elastic beam with a unilateral elastic foundation is an...
The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam car...
AbstractThe quenching of the vibration of an Euler–Bernoulli beam under tension with general linear ...
In this paper an analytical approach is used to optimize a beam surrounded by a Winkler's medium and...