Compensatory bellows oscillations as a corrugated shell with liquid inside

The paper deals with a relevant problem of shipbuilding, i.e. calculation of free and forced vibrations of pipeline compensatory bellows. These devices are used to reduce the vibration load caused by ship power machines. When analyzing the vibrations of the compensatory bellows, it is necessary to take into account the liquid contained in the bellows. In this work, the design model of the bellows is represented by a corrugated elastic shell as a material surface with five degrees of freedom. A variant of the classical theory of shells, built on the basis of Lagrangian mechanics, is used. The influence of the liquid is taken into account by two models. First, the liquid is considered to be ideal and incompressible and is considered through the attached mass to the shell. The shell is replaced by a cylindrical surface with a radius in the middle line of the corrugation. To account for the influence of the frequency of bellows oscillations on the attached inertia of the liquid in the calculation we also used the acoustic approximation; and derived a formula for a generalized attached mass of the ideal compressible liquid. The equations of the bellows oscillations under the periodic loading are obtained. The problem has been solved by the finite difference method. The values of natural frequencies of free vibrations are obtained for the compensatory bellows from the corrosion-resistant heat-resistant steel. It is shown that by taking account of the liquid, we significantly change the natural frequencies of the bellows. With high-frequency vibrations it is necessary to take into account the compressibility of the liquid. The problem of the forced vibrations of the bellows caused by a displacement of its end face by the harmonic law is solved. The internal forces and moments are determined, as well as occurring stresses by Mises criterion in the bellows. We found the critical value of the end face displacement at a frequency of 50 Hz, at which the bellows goes into a plastic state.

DEPENDENCE OF THE FREQUENCY SPECTRUM OF MICRO- AND NANO- RESONATORS ON PRESSURE AND ATTACHED MASS

An elastic rod of circular or rectangular section is rigidly fixed on both ends. The applicability of classical equations for the deformation of thin elements like rods, plates and shells to describe the stated problem is assessed using such integral characteristics, as eigenfrequencies. The assembly pressure is uniform, specifically atmospheric, and acts also on the areas of strip edges. It is assumed that there are no strains in this case. Excess pressures act only on the strip’s surface. The self-weight of the strip is neglected. Accounting for the attached mass of the surrounding medium and radiation penetrating into it shows that pressures in the upper and lower parts of the rod differ. But these factors are not taken into account, which can be justified in case of light gases. Since the relative axial lengthening at the boundaries equals zero in case of rigid clamping, it will also equal zero along the entire length in the absence of external axial forces. Frequency equations have been derived in case of the action of the surrounding pressure and also uniformly distributed and attached point masses. The influence of the excess pressure of the surrounding medium on the frequency spectrum of the rod oscillations is determined by the non-dimensional parameter that increases with an increase in pressure and the rod length and decreases with an increase of bending rigidity. At the negative excess pressure (vacuuming) this parameter reverses its sign, and the frequencies become lower. With an increase in both distributed and attached point mass the eigenfrequencies of oscillations decrease due to the rod invariable bending rigidity. The displacement of the point mass towards the center results in a decrease in odd eigenfrequencies, while even eigenfrequencies remain the same. Using the first frequency measured we can determine the excess pressure acting on the rod’s surface. Using two frequencies of bending oscillations we can determine the attached point mass and its coordinate. These results can be used when simulating the performance of resonators, including micro and nano ones.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

On attached masses of panels oscillating in incompressible medium

The paper discusses small oscillations of a panel in an incompressible medium. Air can be considered an incompressible medium during modal tests of solar array panels for spacecraft deployed on the ground in a lab environment. A panel is represented as a two-sided boundary surface. Conditions are determined for applicability of the potential motion of the medium. Calculation of the attached mass is reduced to the solution of the Neumann boundary value problem. To solve the boundary value problem, the method of boundary elements is used in the piecewise constant approximation variant, which provides a solution of the hypersingular boundary integral equation. Numerical solutions are obtained for the three fundamental modes of rectangular panels. The obtained numerical values are refined using non-linear Shanks transformation. Dependence of attached mass on panel elongation and the amount of the gap between its fragments is studied. For any in-plane oscillation mode of a panel fragment, the attached mass is determined using the principle of linear superposition. An estimate is given of the effect of the distance from the panel to the wall on the attached mass value. Key words: oscillations, incompressible medium, air, attached mass, rectangular panels, boundary elements method.

ON ATTACHED MASSES OF PANELS OSCILLATING IN INCOMPRESSIBLE MEDIUM

The paper discusses small oscillations of a panel in an incompressible medium. Air can be considered an incompressible medium during modal tests of solar array panels for spacecraft deployed on the ground in a lab environment. A panel is represented as a two-sided boundary surface. Conditions are determined for applicability of the potential motion of the medium. Calculation of the attached mass is reduced to the solution of the Neumann boundary value problem. To solve the boundary value problem, the method of boundary elements is used in the piecewise constant approximation variant, which provides a solution of the hypersingular boundary integral equation. Numerical solutions are obtained for the three fundamental modes of rectangular panels. The obtained numerical values are refined using non-linear Shanks transformation. Dependence of attached mass on panel elongation and the amount of the gap between its fragments is studied. For any in-plane oscillation mode of a panel fragment, the attached mass is determined using the principle of linear superposition. An estimate is given of the effect of the distance from the panel to the wall on the attached mass value. Key words: oscillations, incompressible medium, air, attached mass, rectangular panels, boundary elements method.

CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

Modal damping ratio of symmetric laminate composite under the effect of attached mass using experimental design

Nowadays, the use of composite materials has taken a large place in civilian industries as well as in military and aerospace industries. Therefore, significant investigations about their mechanical and physical properties are needed. The present study addresses the effect of attached mass on damping ratio of symmetric angle ply laminate composite. Furthermore, factor influencing the effect of attached mass on damping ratio of laminate composite are studied using Taguchi method. The considered factors parameters are: attached mass locations from the clamped edge, stacking sequences and boundary conditions. The results of this study indicate that the damping ratio of the laminate composite plates is sensitive to the attached mass, where the damping ratio is found to be proportional to the locations of the attached mass. The findings of this study indicate that the attached mass decreases frequency parameter and increase the damping ratio of the composite plate, if it is inserted at a point other than a nodal line. In addition, the paper presents a good correlation between the numerical results of the fundamental frequency obtained by the ANSYS software and those obtained experimentally.