Effect Of Concentrated Mass Research Articles

Effects of Concentrated Mass on the In-Plane Dynamic Behaviors of Two-Cable Networks with a Cross-Tie

This study proposes a two-cable network model, which includes a cross-tie and two concentrated masses installed at the connection points of cross-tie and cable. The characteristic equation of such a cable network system is formulated via the complex modal analysis method. Then, dynamics of a twin-cable network is discussed in details, and the effect of concentrated mass on the system modal frequencies, damping and mode shapes is investigated. Furthermore, a general two-cable network system is analyzed. Results show that the concentrated mass always reduces the modal frequency, as it causes an increase in the modal mass of the system. When installing a concentrated mass in a twin-cable network, the difference of vibration modes between the cables can be increased in the in-phase modes, thereby achieving the damping effect of the damping type cross-tie on these modes. For a twin-cable network with a viscous damper, a small concentrated mass can significantly increase the modal damping of the in-phase modes as long as the damping coefficient of the damper is properly set. Meanwhile, when there is a two-cable network with unequal length cables, the presence of concentrated masses may reduce differences in vibration modes between cables, thus leading to decreased damping of some modes.

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.

Semi-analytical Solution for Nonlinear Transverse Vibration Analysis of an Euler–Bernoulli Beam with Multiple Concentrated Masses Using Variational Iteration Method

In this article, linear and nonlinear transverse vibration of Euler–Bernoulli beams with multiple concentrated masses have been investigated using variational iteration method (VIM), and the effects of concentrated mass on natural frequencies and mode shapes have been taken into account as well. VIM is a powerful method with high convergence which gives analytical solution to linear problems and is capable of being extended to present semi-analytical solutions to nonlinear ones. The proper choice of Lagrange’s multiplier and Initial Function can increase the convergence speed. In this study, along with presenting the suitable trend for determining these two functions, the obtained frequencies in linear and nonlinear states are compared with those calculated from other methods, and the accuracy and convergence speed of this procedure are examined. It is concluded that with increasing the intensity of concentrated mass, linear natural frequency and the ratio of nonlinear frequency to linear one will decline.

Nonlinear vibration analysis of a Timoshenko beam with concentrated mass using variational iteration method

Complicated structures used in a wide variety of engineering fields consist of simple structural elements like beams which in some cases include one discontinuity such as a crack or mass and are more likely to vibrate with larger amplitude. In this article, considering shear deformation and rotatory inertia, transverse vibration of nonlinear Timoshenko beam carrying a concentrated mass oscillating with large amplitude is investigated using VIM. This method is a very powerful method with suitable convergence speed in which by choosing the proper Lagrange’s multiplier and Initial Function, the convergence speed could increase even more. This method would be able to present analytical solutions for linear equations and semi-analytical solutions for non-linear ones. One of the greatest advantages of this method is that its calculations are not dependent on the number of masses located on the beam. In this paper, along with presenting the suitable trend for determining the Lagrange’s multiplier, the effects of concentrated mass on natural frequencies in linear and non-linear states are taken into account. The obtained results, moreover, are compared with the results gained through other procedures and the accuracy and speed convergence are studied as well.

Transverse vibration of free–free beams carrying two unequal end masses

Transverse vibration of free–free slender beams carrying two tip masses is studied. An exact frequency equation is derived and the natural frequencies are calculated. An alternative Fredholm integral equation approach is presented to determine resonant frequencies of a vibrating mass–beam system. Simple approximate expressions for fundamental frequencies with high accuracy are obtained. Analytical and approximate results of the frequencies are computed and compared. The effects of concentrated masses at two ends on the natural frequencies and mode shapes are discussed. The results are helpful to design micromechanical sensors and energy harvesters.

Exact closed form solution for the analysis of the transverse vibration modes of a Timoshenko beam with multiple concentrated masses

Concentrated masses on the beams have many industrial applications such as gears on a gearbox shafts, blades and disks on gas and steam turbine shafts, and mounting engines and motors on structures. Transverse vibration of the beam carrying a point mass was studied in many cases by both Euler–Bernoulli and Timoshenko beam theory for a limited number of concentrated masses mounted on a specific place on the beam. This was also investigated for a beam carrying multiple concentrated masses, yet they were solved by numerical methods such as Differential Quadrature (DQ) method. The present study investigated an exact solution for free transverse vibrations of a Timoshenko beam carrying multiple arbitrary concentrated masses anywhere on the beam with various boundary conditions. Using Dirac’s delta in governing equations, the effects of concentrated masses were imposed. After extracting a closed form solution, basic functions were used to reduce the amount of computations. Standard symmetric and asymmetric boundary conditions were enforced for beam; in addition, the effects of value, position, and number of concentrated masses were examined. Generally, while the existence of concentrated masses reduces the natural frequencies, the reduction depends on the parameters of concentrated masses. Finally, there were acquired mode shapes for different boundary conditions and different value, position, and number of concentrated masses.

Nonlinear flutter of viscoelastic rectangular plates and cylindrical panels of a composite with a concentrated masses

The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δ-Dirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov-Galerkin method. The resulting system with a weakly singular Koltunov-Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters.

크랙을 가진 밸브 배관계의 강제진동 특성

The forced vibration response characteristics of a cracked pipe conveying fluid with a concentrated mass are investigated in this paper. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Hamilton's principle. The effects of concentrated mass and fluid velocity on the forced vibration characteristics of a cracked pipe conveying fluid are studied. The deflection response is the mid-span deflection of a cracked pipe conveying fluid. As fluid velocity and crack depth are increased, the resonance frequency of the system is decreased. This study will contribute to the decision of optimum fluid velocity and crack detection for the valve-pipe systems.

The effect of concentrated masses on the response of a plate under a turbulent boundary layer excitation

This work is aimed at the numerical analysis of the vibration response of a plate, carrying one or more concentrated masses, under a stochastic, and convective load. The pressure load is a typical turbulent boundary layer excitation (TBL) and the structural configurations reproduce common experimental situations because the concentrated masses can be considered similar to accelerometer sensors.The models adopt the Corcos TBL model and the concentrated masses are simulated with the Dirac singularity function. The approximations, introduced with the above assumptions on the concentrated masses, and the necessary numerical accuracy, in calculating the structural responses, are discussed.The added masses do not lead to a relevant modification of the global structural response but, on the contrary, the results show that the local effects can be relevant: the paper highlights the differences of the vibration responses from the analogous structural configurations under a stochastic load without convective characteristics.

Effect of concentrated masses with rotary inertia on vibrations of rectangular plates

The effect of attached masses on free vibrations of rectangular plates is studied by considering rotary inertia of concentrated masses and geometric imperfections of the plate. Experiments are performed to understand the changes in natural frequencies and mode shapes. In order to validate and better understand the experiments, numerical results are also presented. Boundary conditions at the plate edges are those of simply supported plate with additional rotational springs at the plate edges. By tuning the stiffness of these springs, any boundary conditions comprised between simply supported and clamped edges can be simulated. Numerical results are successfully compared to experiments performed on a stainless-steel plate with an attached mass of different translational and rotary inertia. In particular, it is shown that a small mass placed on the diagonal of a square thin plate is enough to transform the shape of modes with one nodal line parallel to the edge, into diagonal modes, i.e. modes with diagonal nodal lines. Rotary inertia of concentrated masses reduces significantly natural frequencies. Moreover, additional modes due to the presence of large rotary inertia of concentrated masses arise, which do not appear if rotary inertia is neglected. Finally it is shown that masses placed only on one side of the plate or symmetrically (with respect to the mid-plane) placed on both sides give similar results.

Calculation of natural frequencies of beam structures including concentrated mass effects by the dynamic stiffness matrix method

In this paper, the dynamic stiffness matrix method for a 2-node and 6-DOF (Degree Of Freedom) per node beam element is presented along with a numerical method to include the effect of concentrated masses. We treat as examples the case of free vibrations of beam structures with and without the concentrated masses effect. By means of a parametric study, we assess the quantitative effect of concentrated masses to the natural frequencies of the structure.

Effect of concentrated mass on stability of cantilevers under rocket thrust

The paper describes the effect of an intermediate concentrated mass on the dynamic stability of cantilevered columns subjected to a rocket thrust. It is assumed that the rocket thrust is produced by the installation of a solid rocket motor at the tip end of the cantilevered columns having the intermediate mass. The rocket motor is assumed to be a rigid body having finite sizes but not a mass point. The importance of the magnitude and size of the intermediate mass is demonstrated by theory and experiment. The experimental results are compared with theoretical predictions made by taking into account the mass and size of the rocket motor as well as intermediate mass effect. The internal damping was neglected in the theoretical predictions. It is shown that theoretical stability predictions and experimental flutter limits agreed well.

A note on vibrations of a circumferential arch with thickness varying in a discontinuous fashion

This paper deals with the determination of the fundamental frequency of in-plane vibration of arcs of non-uniform thickness for three types of boundary conditions, hinged, clamped, and clamped-free. The effect of concentrated masses is considered. The fundamental mode shape is approximated by means of a polynomial co-ordinate function in the angular co-ordinate which includes an exponential optimization parameter. The frequency equation is generated by means of the Rayleigh-Ritz method and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter. Results of an independent finite element solution are also presented and, in general, good agreement with the analytical solution is shown to exist.

Vibration analysis of elastically restrained rectangular plates with concentrated mass

A numerical method developed earlier for determining natural frequencies of rectangular plates has been extended to include edges elastically restrained in translation and also to consider the effects of concentrated masses inside the plate. Many of the results are presented for the first time. Comparison of the results with those available showed good agreement.