Duality based a posteriori error estimates for higher order variational inequalities with power growth functionals.
Duality in the obstacle and unilateral problem for the biharmonic operator
The paper presents a problem of duality for the obstacle and unilateral biharmonic problem (the equilibrium of a thin plate with an obstacle inside the domain or on the boundary). The dual variational inequality is derived by introducing polar functions.
Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity.
Dynamic crack propagation between two bonded orthotropic plates.
Dynamic stability of functionally graded plate under in-plane compression.
Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions
In the paper, time-periodic solutions to dynamic von Kármán equations are investigated. Assuming that there is a damping term in the equations we are able to show the existence of at least one solution to the problem. The Faedo-Galerkin method is used together with some basic ideas concerning monotone operators on Orlicz spaces.
Dynamics of flexible shells and Sharkovskiy's periodicity.
Effect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells.
Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting
In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions Δ₂ and...
Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting
In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type...
Effects of In-plane Elastic Stress and Normal External Stress on Viscoelastic Thin Film Stability
Motivated by recent experiments on the electro-hydrodynamic instability of spin-cast polymer films, we study the undulation instability of a thin viscoelastic polymer film under in-plane stress and in the presence of either a close by contactor or an electric field, both inducing a normal stress on the film surface. We find that the in-plane stress affects both the typical timescale of the instability and the unstable wavelengths. The film stability...
Effects of variations in nonlinear damping coefficients on the parametric vibration of a cantilever beam with a lumped mass.
Eigenfrequencies of generally restrained beams.
Eigenvalue problem and unbounded connected branch of positive solutions to a class of singular elastic beam equations.
Elastic buckling behaviour of a four-lobed cross section cylindrical shell with variable thickness under non-uniform axial loads.
Elastic membrane equation in bounded and unbounded domains.
Elastic-plastic torsion problem over multiply connected domains
Electronic properties of superconductor-semiconductor mesoscopic device.
Eliciting harmonics on strings
One may produce the qth harmonic of a string of length π by applying the 'correct touch' at the node during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude b concentrated at . The 'correct touch' is that b for which the modes, that do not vanish at , are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree ....
Energy Convergence Results for Strongly Damped Nonlinear Wave Equations.