International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013) 155 Study on the Effect of Position of the Dampers in Systems with 3 Degrees of Freedom J.O.Kiran 1 , D. Shivalingappa 2 1 Dept. of Mechanical Engg., S.T.J Institute of Technology, Ranebennur, Karnataka, India 2 Dept. of Mechanical Engg., Adhiyamaan College of Engineering, Hosur, Tamilnadu, India Abstract- In this work, the behaviour of systems with three degrees of freedom is modelled for a fixed loss factor. The loss factor used in this work is 0.075. Four models are studied and the displacements as well as the energies stored in the systems are computed using the simulations. The governing equations are numerically solved using MATLAB. The dampers are varied in position and in numbers to derive four models. The simulation results show that among the four models with three degrees of freedom, the model with four dampers added to the system yields the lowest displacement, while the model with no dampers has the largest displacement for oscillator on which the force is acting. The models with dampers attached at different positions yield the displacements in between these two cases. The energy stored in the oscillator becomes large after the attached dampers are removed. Most of the energy is absorbed by the damper attached to the oscillator on which the force is acting. The magnitudes of displacements, velocities and energies for models with different positions of dampers are presented in this paper. Keywords-- Vibration, 3 degrees of freedom, dampers, loss factor. I. INTRODUCTION Vibration or oscillation may be defined as any structural deformation that repeats itself periodically [1, 2]. Engineered structures are made out of individual components and they possess finite mass and finite levels of stiffness and dissipative energy transfer characteristics due to the presence damping that is present inside the structure known as inherent damping. When external loads are applied on the structures which are alternating in nature, it can result in very high amplitude vibrations at various distinct resonant frequencies [3]. Any structure that is subjected to vibration stores energy both in the forms of kinetic energy and potential energy and also has a means to dissipate energy [2]. The kinetic energy is stored due to the mass of the structure, potential energy is stored due stiffness and the energy is dissipated due to damping. If the damping is insufficient, the structure that is vibrating at a resonant frequency tends to result in high amplitudes which radiates sound and might ultimately lead to structural failure. Hence it is essential to calculate or predict these resonant frequencies and prevent the structure from high amplitude vibrations by providing sufficient structural damping [3] inside the structure. Any effect that can reduce the amplitude of oscillation or vibration may be treated as damping in a structure. There are two types of damping that are inherently present in any structure [4], namely, internal damping of the structure and structural damping at the joints in the structure. For cases of those structures which have got low inherent damping it is required to provide additional damping in the form of active damping and passive damping. Active damping can be provided by actuators which control the motion of the structure. The passive damping can be achieved by adding a layer of visco-elastic material is covered by a layer of constraining material to the structure. Due to the presence of dynamic loads, the visco-elastic material dissipates energy in the form of heat energy by disrupting the bonds of its long-chain molecules [5]. The loss factor is an important factor to estimate the loss of energy in a vibrating system and it may be defined as the ratio of the dissipated power per radian to the total energy of the structure [6]. The stored energy in a structure is constant for the steady state conditions and the power that is fed to the structure as input is dissipated by the structure itself. Hence the dissipated power can be replaced with power input to estimate or assess the loss factors This can also be written as