A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.

the existence of an $\omega$-periodic solution of the equation $\frac{{\partial }^{2}u}{\partial t^2}+\alpha \frac{{\partial }^{4}u}{\partial x^4}+\gamma \frac{{\partial }^{5}u}{\partial x^4\partial t}-\tilde{\gamma }\frac{{\partial }^{3}u}{\partial x^2\partial t}+\delta \frac{\partial u}{\partial t}-\left[\beta +\aleph {\int }_0^n{\left(\frac{\partial u}{\partial x}\right)}^2(·,\xi )d\xi +\sigma {\int }_0^n\frac{{\partial }^{2}u}{\partial x\partial t}(·,\xi )\frac{\partial u}{\partial x}(·,\xi )d\xi \right]\frac{{\partial }^{2}u}{\partial x^2}=f$ sarisfying the boundary conditions $u(t,0)=u(t,\pi )=\frac{{\partial }^{2}u}{\partial x^2}\left(t,0\right)=\frac{{\partial }^{2}u}{\partial x^2}\left(t,\pi \right)=0$ is proved for every $\omega$-periodic function $f\in C\left(\left[0,\omega \right],L_2\right)$.

The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...

For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the...

We study the 3-D elasticity problem in the case of a non-symmetric heterogeneous rod. The asymptotic expansion of the solution is constructed. The coercitivity of the homogenized equation is proved. Estimates are derived for the difference between the truncated series and the exact solution.