• Advances in nano research
• /
• 제15권5호
• /
• pp.401-410
• /
• 2023

Vibration investigation of fluid-filled three layered cylindrical shells is studied here. A cylindrical shell is immersed in a fluid which is a non-viscous one. Shell motion equations are framed first order shell theory due to Love. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the wave propagation approach procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped (C-C), simply supported-simply supported (SS-SS) frequency curves are higher than that of clamped-simply (C-S) curves. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Computer software MATLAB codes are used to solve the frequency equation for extracting vibrations of fluid-filled.

• Journal of Mechanical Science and Technology
• /
• 제16권8호
• /
• pp.1072-1078
• /
• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• 한국산업융합학회 논문집
• /
• 제20권4호
• /
• pp.299-305
• /
• 2017

This study proposes a new technique to design and control of robot hand gripper for assembling and disassembling of a machine parts. The motion equation describing dynamics of the manipulators and object together with geometric constraint is formulated by Lagrange-Euler's equation. And the problems of controlling both the grasping force and the rotation angle of the grasped object under the constraints are analyzed. The effect of geometric constraints and a method of computer simulation for overall system is verified. Finally, it is illustrated that even in case of there exists a sensory feedback from sensing data of the rotational angle of the object to command inputs control of joint and this feedback connection from sensing data to control grasping of machinery parts.

• 한국소음진동공학회논문집
• /
• 제13권8호
• /
• pp.605-611
• /
• 2003

A simply supported pipe conveying fluid and two moving masses upon it constitute this nitration system. The equation of motion is derived by using Lagrange's equation. The influence of the velocities of two moving masses, the distance between two moving masses, and the velocities of fluid flow in the pipe have been studied on the dynamic behavior of a simply supported pipe by numerical method. The velocities of fluid flow are considered with in its critical values of a simply supported pipe without moving masses upon It. Their coupling effects on the transverse vibration of a simply supported pipe are inspected too. As the velocity of two moving masses increases, the deflection of a simply supported pipe is increased and the frequency of transverse vibration of a simply supported pipe is not varied. In case of small distance between two masses, the maximum deflection of the pipe occur when the front mass arrive at midspan. Otherwise as the distance get larger, the position of the front masses where midspan deflection is maximum moves beyond the midpoint of a simply supported pipe. The deflection of a simply supported pipe is increased by coupling of the velocities of moving masses and fluid flow.

• 한국소음진동공학회논문집
• /
• 제14권3호
• /
• pp.236-243
• /
• 2004

In this paper a dynamic behavior of a simply supported cracked pipe conveying fluid with the moving mass is presented. Based on the Timoshenko beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. And the crack is assumed to be in th first mode of fracture. As the depth of the crack and velocity of fluid are increased the mid-span deflection of the pipe conveying fluid with the moving mass is increased. As depth of the crack is increased, the effect of the velocity of the fluid on the mid-span deflection appears more greatly.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제8권2호
• /
• pp.117-126
• /
• 2016

In this paper, a numerical procedure for the natural vibration analysis of plates with openings and carlings based on the assumed mode method is extended to assess their forced response. Firstly, natural response of plates with openings and carlings is calculated from the eigenvalue equation derived by using Lagrange's equation of motion. Secondly, the mode superposition method is applied to determine frequency response. Mindlin theory is adopted for plate modelling and the effect of openings is taken into account by subtracting their potential and kinetic energies from the corresponding plate energies. Natural and frequency response of plates with openings and carlings subjected to point excitation force and enforced acceleration at boundaries, respectively, is analysed by using developed in-house code. For the validation of the developed method and the code, extensive numerical results, related to plates with different opening shape, carlings and boundary conditions, are compared with numerical data from the relevant literature and with finite element solutions obtained by general finite element tool.

• 한국소음진동공학회논문집
• /
• 제13권7호
• /
• pp.562-569
• /
• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion Is derived by using Lagrange’s equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results In higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally. as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid Is Increased. The time which produce the maximum dynamic deflection of the simply supported pipe Is delayed according to the increment of the crack severity.

• 대한기계학회논문집A
• /
• 제27권11호
• /
• pp.1815-1823
• /
• 2003

The vibrational system of this study consists of a cantilever pipe conveying fluid, the moving masses upon it and having an attached tip mass. The equation of motion is derived by using Lagrange's equation. The influences of the velocity and the inertia force of the moving mass and the velocities of fluid flow in the pipe have been studied on the dynamic behavior and the natural frequency of a cantilever pipe by numerical method. The deflection of the cantilever pipe conveying fluid is increased due to the tip mass and rotary Inertia. After the moving mass passed upon the cantilever pipe, the amplitude of pipe is influenced by energy variation when the moving mass fall from the cantilever pipe. As the moving mass increase, the frequency of the cantilever pipe conveying fluid is increased. The rotary inertia of the tip mass influences much on the higher frequencies and vibration mode.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 추계학술대회논문집A
• /
• pp.387-394
• /
• 2000

Theoretical and experimental study is conducted on the contact pressure distribution of a radial tire in motion under various camber angles. Tire construction is modelled by a spring bedded elastic ring, consisted of sidewall springs and a composite belt ring. The contact area is assumed to be a trapezoidal shape varying with camber angles and weighted load. The basic equation in a quasi-static form is derived for the deformation of a running belt with a constant velocity by the aid of Lagrange-Euler transformation. Galerkin's method and stepwise calculation are applied for solving the basic equation and the mechanical boundary condition along both sides of the contact belt part subjected to shearing forces transmitted from the sidewall spring. Experimental results on the contact pressure, measured by pressure sensors embedded in the surface of the drum tester, correspond well with the calculated ones for the test tire under various camber angles, running velocities and weighted loads. These results indicate that a buckling phenomenon of the contact belt in the widthwise direction occurs due to the effect of camber angle.

• 한국소음진동공학회논문집
• /
• 제13권1호
• /
• pp.26-32
• /
• 2003

The vibrational system of this study is consisted of a rotating cantilever pipe and the flow in the pipe. The equation of motion is derived by using Lagrange equation. The influences of the rotating angular velocity and the velocities of fluid flow in the pipe have been studied on the dynamic characteristics of a rotating cantilever pipe by numerical method. The tip-amplitude of axial vibration and maximum tip-deflection of axial direction of cantilever pipe are directly proportional to the velocity of fluid and rotating angular velocity of pipe In the steady state. respectively The bending tip-amplitude of cantilever pipe is inversely proportional to the velocity of fluid in the steady state. When the rotating angular velocity is 5 rad/s, the velocity of fluid increase with increasing the natural frequency of axial vibration at second mode and third mode, but the natural frequency axial direction of first mode is decreased. The natural frequency of lateral direction is decreased due to increase of the rotating angular velocity. It identifies that the Influence of velocity of fluid give much variation lower mode of vibration in lateral direction. And the Influence of velocity of fluid give much variation higher mode of vibration in axial direction.