Review of an Effective Dynamic Vibration Absorber for a Simply Supported Beam and Parametric Optimization to Reduce Vibration Amplitude

Abstract

In this work theoretical natural frequencies and mode shape of the simply supported beam type main vibrating system ie used in many areas like bridges and double-beam structures is determined. Dynamic vibration absorber is designed and developed at one of the resonant frequencies of the main vibrating system. Natural frequencies and mode shapes of main vibrating system obtained theoretically and also by using FEA analysis. The system considered is essentially a modification of the conventional damped vibration absorber and consists of adding, in parallel, a subsidiary undamped absorber mass in addition to the damped absorber mass. Uses MATLAB to find optimize parameter to reduce the vibration amplitude. Also use ANSYS for FEA analysis of simply supported beam type main vibrating system. Development to test the performance of a damped and undamped vibration absorber for the simply supported beam type main system. The analysis clearly shows that it is possible to obtain an undamped antiresonance in a dynamic absorber system which exhibits a well-damped resonance. While the bandwidth of frequencies between the damped peaks is not significantly increased, the amplitudes of the main mass are considerably smaller within the operational range of the absorber. A total of 4 models are taken for consideration for the damped vibration absorber. By comparing in between those models, we came to know that model (C) gives better vibration suppression and also required less damping ratio for anti resonance. LIST OF SYMBOLS Most of the symbols are defined as they occur in the thesis. Some of the most common symbols, which are repeatedly used, are listed below. E = Young's modulus of elasticity of the beam I = M I of the beam ρ= density of the beam í µí±¥= distance from one of the ends of beam X = amplitude of vibration A = c/s area of the beam í µí±¡ = time independent variable í µí¼” í µí±› = natural frequency of the system í µí±˜ = stiffness of the spring í µí±‹í µí±†í µí±¡ = í µí°¹ 0 / í µí±˜ 1 = Frequency deflection of first mass í µí¼” 1 = í µí±˜ 1 / í µí±š 1 = natural frequency of main system alone í µí¼” 2 = í µí±˜ 2 / í µí±š 2 = natural frequency of the absorber system alone í µí¼‡ = í µí±š 2 / í µí±š 1 = ratio of absorber mass to the main mass í µí±‹ í µí± í µí±¡ = F 0 /k 1 = Static deflection of the system í µí¼” í µí±Ž 2 = k 2 /m 2 = Square of natural frequency of the absorber í µí¼” í µí±› 2 = k 1 /m 1 = Square of natural frequency of main mass f = í µí¼” a /í µí¼” n = Ratio of natural frequencies g = í µí¼”/í µí¼” n = Forced frequency ratio C = damping constant C C = 2m 2 í µí¼” n = Critical damping constant RESEARCH ARTICLE OPEN ACCESS