Related papers: Cantilever Beam Equation for Almost Arbitrary Defl…
In this work we obtain an approximate solution of the strongly nonlinear second order differential equation $\frac{d^{2}u}{dt^{2}}+\omega ^{2}u+\alpha u^{2}\frac{d^{2}u}{dt^{2}}+\alpha u\left( \frac{du}{dt}\right)^{2}+\beta \omega…
The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order…
In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several…
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming…
In this paper we derive a variational formulation for a linear curved beam which is natively expressed in global Cartesian coordinates. During derivation the beam midline is assumed to be implicitly described by a vector distance function…
The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science…
This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…
Using an analytical expression for an integral involving Bessel and Legendre functions we succeeded to obtain the partial wave decomposition of a general optical beam at an arbitrary location from the origin. We also showed that the solid…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…
We investigate the nonlinear vibration of a fractional viscoelastic cantilever beam, subject to base excitation, where the viscoelasticity takes the general form of a distributed-order fractional model, and the beam curvature introduces…
Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We consider a nonlinear transmission problem for a Bresse beam, which consists of two parts, damped and undamped. The mechanical damping in the damped part is present in the shear angle equation only, and the damped part may be of arbitrary…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
An inadvertent or unwanted angular deviation to a passing beam can be introduced by any single optical component within an optical system. The problem arises due to an imperfect tilt alignment of the optical component or manufacturing…
We consider a system of quasilinear elliptic equations, with indefinite super-linear nonlinearity, depending on two real parameters $\lambda,\mu$. By using the Nehari manifold and the notion of extremal parameter, we extend some results…
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the…