Homogeneous Wave Load Effects on the Connections of Main Parts of Side-Anchored Straight Floating Bridge

In this paper, a numerical study is presented to investigate wave force on the connections of main parts of a side-anchored straight floating bridge concept for the Bjørnafjorden fjord crossing. The floating bridge is supported by 18 pontoons, and three groups of mooring lines are employed to restrain the bridge against horizontal loads and increase its transverse stiffness. The created wave forces at the connections of pontoon-column and column-girder of the floating bridge considering the effects of short-crested and long-crested waves, varying wave direction, hydrodynamic interaction between pontoons, and mooring system are analyzed. It is found that short-crested and long-crested waves depending on their direction decrease or increase the wave forces on the joints. Considering that the effect of hydrodynamic interaction between pontoons can increase or reduce the wave forces and moments created in the joints, which means the neglect of the hydrodynamic interaction effects between the pontoons to simplify the modeling of this type of floating bridge, may be unacceptable. Moreover, the results showed that the bridge mooring system does not merely reduce the wave forces and moments at joints along the bridge.

Well-posedness results for the wave equation generated by the Bessel operator

In this paper, we consider the non-homogeneous wave equation generated by the Bessel operator. We prove the existence and uniqueness of the solution of the non-homogeneous wave equation generated by the Bessel operator. The representation of the solution is given. We obtained a priori estimates in Sobolev type space. This problem was firstly considered in the work of M. Assal [1] in the setting of Bessel-Kingman hypergroups. The technique used in [1] is based on the convolution theorem and related estimates. Here, we use a different approach. We study the problem from the point of the Sobolev spaces. Namely, the conventional Hankel transform and Parseval formula are widely applied by taking into account that between the Hankel transformation and the Bessel differential operator there is a commutation formula [2].

A minimization approach to the wave equation on time-dependent domains

We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

Wave-like spatially homogeneous models of Stäckel spacetimes (2.1) type in the scalar-tensor theory of gravity

Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like spacetime models allow the existence of privileged coordinate systems where the eikonal equation and the Hamilton–Jacobi equation of test particles can be integrated by the method of complete separation of variables with the separation of isotropic (wave) variables on which the space metric depends (non-ignored variables). An explicit form of the scalar field and two functions of the scalar field that are part of the general scalar-tensor theory of gravity are found. The explicit form of the eikonal function and the action function for test particles in the considered models is given. The obtained solutions are of type III according to the Bianchi classification and type N according to the Petrov classification. Wave-like spatially homogeneous spacetime models can describe primordial gravitational waves of the Universe.

DETERMINATION OF DEFECTS SIZES AND THEIR POSITION DURING ULTRASONIC CONTROL BY METHODS OF MATHEMATICAL AND COMPUTER SIMULATION

The use of sound waves to study the integrity of various metal structures is the most relevant method. The relevance is traced, in particular, in the ease of conducting such experiments, as well as its cheapness. The design of various parts requires the use of modern computer technology, which, using a mathematical apparatus that describes the process, allows you to determine the actual characteristics of the material to determine durability. This approach makes it possible to effectively create design solutions in order to create new parts and upgrade existing materials to extend their service life. The purpose of this work is to build mathematical models of homogeneous wave processes and their analysis in the form of computational experiments to control the passage of sound signals through the surface of the studied materials of objects. This approach is used to determine the influence of geometric parameters of defects in the form of cracks through which the signal passes, on its characteristics, which it describes after passing through these defects to the signal receiver, in particular, is the amplitude and frequency. For computational experiments, a point exciter of harmonic oscillations and a point receiver were chosen, which are located on different sides relative to the defect of a simple geometric shape. It should be noted that even minor defects affect the amplitude of the received signal, which passed through such defects. When a signal passes through defects of a simple geometric shape, the amplitude of such a signal decreases by 5–8 times and the average frequency decreases by 2–3 times.

Soliton Turbulence in Approximate and Exact Models for Deep Water Waves

We investigate and compare soliton turbulence appearing as a result of modulational instability of the homogeneous wave train in three nonlinear models for surface gravity waves: the nonlinear Schrödinger equation, the super compact Zakharov equation, and the fully nonlinear equations written in conformal variables. We show that even at a low level of energy and average wave steepness, the wave dynamics in the nonlinear Schrödinger equation fundamentally differ from the dynamics in more accurate models. We study energy losses of wind waves due to their breaking for large values of total energy in the super compact Zakharov equation and in the exact equations and show that in both models, the wave system loses 50% of energy very slowly, during few days.

Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity and a Summable Potential

For a mixed problem defined by a wave equation with a summable potential equal-order boundary conditions with a derivative and a zero initial position, the properties of the formal solution by the Fourier method are investigated depending on the smoothness of the initial velocity u′t(x, 0) = ψ(x). The research is based on the idea of A. N. Krylov on accelerating the convergence of Fourier series and on the method of contour integrating the resolvent of the operator of the corresponding spectral problem. The classical solution is obtained for ψ(x) ∈ W1p (1 < p ≤ 2), and it is also shown that if ψ(x) ∈ Lp[0, 1] (1 ≤ p ≤ 2), the formal solution is a generalized solution of the mixed problem.