Classical particle in presence of magnetic field, hyperbolic Lobachevsky and spherical Riemann models.
In this paper it is first shown that the linear evolution equations for a generalized thermoelastic solid generate a C0 semigroup. Next an analysis of the long time evolution behaviour yields the some results known for classical thermoelasticity: generically, the natural state is asymptotically stable.
A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.
We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces for , (localy) Lipschitz continuous in and discontinuous in for arbitrary . Examples show that this result is optimal.
In this paper we present a few results on convergence for the prime integrals equations connected with the bounce problem. This approach allows both to prove uniqueness for the one-dimensional bounce problem for almost all permissible Cauchy data (see also [6]) and to deepen previous results (see [3], [5], [7]).
We consider nonlinearly coupled string-beam equations modelling time-periodic oscillations in suspension bridges. We prove the existence of a unique solution under suitable assumptions on certain parameters of the bridge.
Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by a rigid plate...