Stability result of a suspension bridge Problem with time-varying delay and time-varying weight

In this paper, we study a plate equation as a model for a suspension bridge with time-varying delay and time-varying weights. Under some conditions on the delay and weight functions, we establish a stability result for the associated energy functional. The present work extends and generalizes some similar results in the case of wave or plate equations.

An $$L^2$$ approach to viscous flow in the half space with free elastic surface

We consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in the half space $${\mathbb {R}}^n_+$$ R + n such that on the lower boundary a function h satisfying an undamped Kirchhoff-type plate equation is coupled to the flow field. Originally, h describes the height of an underlying nonlinear free surface problem. Since the plate equation contains no damping term, this article uses $$L^2$$ L 2 -theory yielding the existence of strong solutions on finite time intervals in the framework of homogeneous Bessel potential spaces. The proof is based on $$L^2$$ L 2 -Fourier analysis and also deals with inhomogeneous boundary data of the velocity field on the “free boundary” $$x_n=0$$ x n = 0 .

Transient processes in a gas/plate structure in the case of light loading

The problem of a pulse excitation in an acoustic half-space with a flexible wall described by a thin plate equation is studied. The solution is written as a double Fourier integral. A novel technique of estimation of this integral is developed. The surface of integration is deformed in such a way that the integrand is exponentially small everywhere except the neighbourhoods of several ‘special points’ that provide field components. Special attention is paid to the pulse associated with the coincidence point of the branches of the dispersion diagram of the acoustic medium and the plate. This pulse is shown to be a harmonic wave of a finite duration.

Existence, Nonexistence, and Stability of Solutions for a Delayed Plate Equation with the Logarithmic Source

In this work, we study a plate equation with time delay in the velocity, frictional damping, and logarithmic source term. Firstly, we obtain the local and global existence of solutions by the logarithmic Sobolev inequality and the Faedo-Galerkin method. Moreover, we prove the stability and nonexistence results by the perturbed energy and potential well methods.