Strength analysis of warship hull’s bottom loaded by the pressure wave from a non-contact explosion of sea mine explosion of sea mine

The study was based on the analysis of stamina of steel flat bottom section of transport warships, burdened by the spherical pressure wave from the non-contact explosion of TNT at a distance of 20 m under the keel. This study aims to determine the TNT mass required to break the hull. The task was solved by finite element method (FEM) explicite using CAE program [1], in which the hull’s bottom was modelled as thin shell space. The hull’s burden with pressure wave was modelled as a pressure impulse specified by the formula introduced by T.L. Geers, K.S. Hunter and R.S. Price [2]. To describe the material properties, considering high-speed strain, the Johnson-Cook model was used [3]. Therefore, the main goal of the hereby paper is to present how to correctly model the impact of large, concentrated masses of the ship’s equipment on its hull. The study presents the results of the calculated stress and strain states of the analysed section of the construction of the hull.

Investigation of the Stability of Axially Moving Beams With Discrete Masses

The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

DYNAMIC STABILITY OF PIPELINE WITH CONCENTRATED DAMPERS

The article indicates that pipes with a liquid fl owing through them are one of the most common elements in various fields of industry. Pipelines in oil and gas and a number of other industries have valves and connections that can be modeled as concentrated masses. It is very important to consider their impact when investigating the dynamic behavior of pipelines. Developing fluctuations are the subject of research by many scientists. The article investigates a pipe with a static scheme of a beam freely lying on the supports with concentrated dampers. The stability of the system consisting of a pipe with concentrated dampers and a liquid fl owing through it is investigated. The spectral Galerkin method is used to determine the critical fl uid velocity. On the basis of theoretical studies, it has been established that a pipeline system with dampers loses its stability at 1.26 times lower fl uid fl ow rate (Vav = 122. 67, m/s) than in the case without dampers (Vav = 155 m/s).

Vibrations of a geometrically nonlinear viscoelastic shallow shell with concentrated masses

Shell structures are widely used in various fields of technology and construction. Often, they play the role of a bearing surface with assemblies, overlays, and aggregates installed on them. At the same time, in solving various problems, such attached elements are considered as the elements concentrated at the points and rigidly connected. Vibrations of an orthotropic viscoelastic shallow shell with concentrated masses in a geometrically nonlinear setting are considered. The equation of motion for a shallow shell is derived based on the Kirchhoff-Love theory. The traditional Boltzmann-Volterra theory is used to describe the viscoelastic properties of a shallow shell. The effect of concentrated masses is taken into account using the Dirac delta function. Using the polynomial approximation of the deflections of the Bubnov-Galerkin method, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations with variable coefficients. In the calculations, the three-parameter Koltunov-Rzhanitsyn kernel was used as a weakly singular relaxation kernel. A numerical method was used to solve the resulting system that eliminates the singularity in the relaxation kernel. The problem of nonlinear vibrations of an orthotropic viscoelastic shallow shell with concentrated masses is solved. The influence of concentrated masses and location, properties of the shell material, and other parameters on the amplitude-frequency response of the shallow shell vibrations is investigated.

CONSTRUCTION OF DYNAMIC INSTABILITY ZONES FOR HIGH STUCTURES UNDER SEISMIC IMPACT

Seismic impacts create the possibility of parametric resonances, i.e. the possibility of the appearance of intense transverse vibrations of structure elements (in particular, of high-rise structures) from the action of periodic longitudinal forces. As a design model of a high-rise structure, a model is used which adopted in the calculation of high-rise structures for seismic effects, - a weightless vertical rod (column) rigidly restrained at the base with a system of concentrated masses (loads) located on it (Fig. 1). By solving the differential equation of the curved axis influence function for a rod is constructed by means of which influence coefficients are determined for the rod points, in which the concentrated masses are situated. These coefficients are elements of the compliance matrix . Next, the elements of the stiffness matrix are determined by inverting the matrix . Using a diagonal matrix of the load masses and matrix a system of differential equations of free vibrations of a mechanical system, consisting of concentrated masses, is constructed, and the frequencies and forms of these vibrations are determined. From the vertical component of the seismic impact, its most significant part is picked out in the form of harmonic vibrations with the predominant frequency of the impact. Column vibrations are considered in a moving coordinate system, the origin of which is at the base of the column. The forces acting on the points of the mechanical system (concentrated masses) are added by the forces of inertia of their masses associated with the translational motion of the coordinate system. The forces of the load weights and forces of inertia create longitudinal forces in the column, periodically depending on time. Further, the integro-differential equation of the dynamic stability of the rod, proposed by V. V. Bolotin in [8], is written. The solution to this equation is sought in the form of a linear combination of free vibration forms with time-dependent factors. Substitution of this solution into the integro-differential equation of dynamic stability allows it to be reduced to a system of differential equations with respect to the mentioned above factors with coefficients that periodically depend on time. For some values of the vertical component parameters of the seismic action, namely the frequency and amplitude, the solutions of these equations are infinitely increasing functions, i.e. at these values of the indicated parameters, a parametric resonance arises. These values form regions in the parameter plane called regions of dynamic instability. Next, these regions are being constructed. A concrete example is considered.