Nonlinear analysis of flexible beams undergoing large rotations via symbolic computations.
Nonlinear elastic membranes involving the -Laplacian operator.
Nonlinear feedback stabilization of a rotating body-beam without damping
Nonlinear feedback stabilization of a rotating body-beam without damping
This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear...
Nonlinear flexural excitations and drill-string dynamics.
Nonlinear free vibration for viscoelastic moderately thick laminated composite plates with damage evolution.
Nonlinear modeling of cables with flexural stiffness.
Nonlinear models of suspension bridges: discussion of the results
In this paper we present several nonlinear models of suspension bridges; most of them have been introduced by Lazer and McKenna. We discuss some results which were obtained by the authors and other mathematicians for the boundary value problems and initial boundary value problems. Our intention is to point out the character of these results and to show which mathematical methods were used to prove them instead of giving precise proofs and statements.
Nonlinear normal modes and their application in structural dynamics.
Nonlinear Variational Inequalities Depending on a Parameter
This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.
Nonsmooth optimal design problems for the Kirchhoff plate with unilateral conditions
Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case
We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.
Nontrivial solutions of the asymmetric beam system with jumping nonlinear terms.
Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions : slow oscillations of beams on elastic bearings
Novel procedure to compute a contact zone magnitude of vibrations of two-layered uncoupled plates.
Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle
In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.
Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle
In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.
Numerical experiments for mathematical models of railway track oscillations
Two mathematical models of railway track oscillations are compared on the basis of numerical experiments.
Numerical implementation of coherence for the example of the "Swiss Cross".
Numerical minimization of eigenmodes of a membrane with respect to the domain
In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.