TEMPLATE DESIGN © Introduction Vibration absorber reduces vibrations of the primary system by channelling energy to the absorber itself. mass. The use of vibration absorbers includes architectural structure (tall buildings, windmills, bridges); consumer goods (refrigerators, vehicles) and in rotational equipment such as pumps, generators etc. extracted stored Energy harvesting is the process by which energy is extracted from external sources and stored in the other form of energy. Representation Representation of the concept of a piezoelectric energy harvesting system Applications Proposed Model-1 Analysis of a Hybrid Vibration Absorber with piezoelectric actuator Proposed Model-2 Result and Discussions for Model-1 Analyzing the proposed model-1 Result and Discussion for Model-2 Conclusions References Analysis of hybrid vibration absorbers are carried out by considering acceleration and displacement feedback of the primary system. It is proposed to reduce the vibration of the system by attaching piezoelectric stack actuator as dynamic vibration absorbers. It is shown that, the control based on the acceleration feedback of the primary mass is more effective comparing with the displacement feedback of the primary system. The HVA with acceleration feedback shows around 82% of amplitude reduction with the controlling force equal to 0.9. In the proposed model as a spring of stiffness is used in series with the actuator so one can increase the controlling force without much increasing the piezoelectric stiffness or the voltage parameter to mitigate the vibration effectively. Present applications of vibration absorber and piezoelectric energy harvester Engineering structure/ machine vibration Vibration reduction method Vibration isolation Vibration absorption Force isolation Base isolation Passive vibration absorber Semi-active vibration absorber Active vibration absorber Hybrid vibration absorber Ambient Vibration Energy Piezoelectric Energy Harvester AC-DC converter and regulator circuit with a storage component Low-power Electronic device a b (a)634 m tall Tokyo skytree, Sumida, Japan made in the year (b) 2010 (b) closed view of the tower at top two TMDs of weight 100 tonne is used (a)Boeing vertol ch-47 chinook where five active vibration absorber are used one in nose, two under (b) the cockpit floor and two inside the aft pylon, (d) F-18 fighter plane wing with piezoelectric actuators for (c) buffeting ( shock wave oscillations) control. a b Technical Cooperation Program: USA, Canada and Australia Slabs were installed at the London Olympic games Pavegen systems piezoelectric generators for road, rail and runway Innowattech, Israel flexible piezoelectric energy harvesters KAIST, Republic of Korea 200 vibration amplitude University of Michigan Biomechanical E.H. Simon Fraser University, Canada Healthcare Military Bridges and Buildings sensors Pavements, Roads, railroads Toys and gadgets Fig.1. Piezoelectric stack actuator based Hybrid vibration absorber. Fig.2. Schematic representation of the model (a) un-deformed position at time t = 0 (b) deformed position at time t (c) a small element of beam at a distance s from the base at time t. (a) (b) (c ) The equations of motion of the system in the Fig.1, can be written as (1) (2) The actuating force from the Fig.1. can be written as (3) Recasting Eq.(1) and Eq.(2) into respective non-dimensional forms one writes, The non-dimensional parameters are,,,,,, x 0 and v 0 are reference displacement and voltage quantity and the ‘dot’ denotes differentiation with respect to the non-dimensional time Providing a negative feedback to the primary system with controller gain is given by Acceleration feedback of the primary mass Block diagram for acceleration feedback of the primary mass Using Routh’s criteria the system is shown to be stable for The transfer function of the primary mass is obtained as where the coefficients and are expressed as kinetic energy potential energy dissipation energy Total kinetic energy ( T ), Total potential energy ( U ), dissipation energy ( D ) and work done (W) By the moment of the system can be written as Momentvoltage Moment about the beam neutral axis produced by a voltage across the piezoelectric layers the governing equation of motion Using Lagrange’s principle and generalized Galerkin’s method the governing equation of motion of the system can be given by Nondimensionalize Nondimensionalize the governing equation of motion method of multiple scales The temporal equation is solved using method of multiple scales Where steady state For steady state voltage frequency response voltage frequency response as power Peak power of the system can be expressed as Fig. Frequency-response plots of the primary system with acceleration feedback of the primary mass for different values of  (b) Variation of area under the frequency response curve with  Fig. Frequency response for primary mass with (a) Frequency-response plots of the primary system with displacement feedback of the primary mass for different values of (b) Variation of area under the frequency response curve and with optimum damping ratio Fig. Frequency-response plots of the primary system with acceleration feedback of the primary mass for different values of . without torsional spring for different values of tip mass. Fig (a) Displacement and (b) voltage frequency response curves without torsional spring for different values of tip mass. (a) (b) with torsional spring for different values of tip mass. Fig. (a) Displacement and (b) voltage frequency response curves with torsional spring for different values of tip mass. output power with resistance for different values of the tip mass Fig. Variation of the output power with resistance for different values of the tip mass (a) without torsional spring and (b) with torsional spring. different values of the load resistance. Fig (a) Displacement and (b) voltage frequency response curves for different values of the load resistance. The nonlinear governing equation of motion is derived and primary resonance case have been studied. Effects of the tip mass, excitation amplitude and load resistance on displacement and output voltage have been studied. Inclusion of torsional spring enhanced the output power of the system. By increasing tip mass the frequency band width and output voltage increases. Proposed harvester can harvest energy even at low excitation frequency. 1.FalAlujević, N., Zhao G., Depraetere, Sas P., Pluymers B. and Desmet W.,. "H2 optimal vibration control using inertial actuators and a comparison with tuned mass dampers." Journal of Sound and Vibration (2014): M. I. Friswell, S. F. Ali, O. Bilgen, S. Adhiari, A. W. Lees, G. Litak, “Non-linear piezoelectric vibration energy harvester from a vertical cantilever beam with tip mass,” Journal of Intelligent Material Systems and Structures. 23, pp , Acar M. A. and Yilmaz. C., "Design of an adaptive–passive dynamic vibration absorber composed of a string–mass system equipped with negative stiffness tension adjusting mechanism." Journal of Sound and Vibration (2013): A. Erturk, D. J. Inman, Piezoelectric Energy Harvesting, A John Wiley and Sons, Chichester, U.K., and where the coefficients and are expressed as and The optimum tuning ratio and damping ratio are obtained by optimization as and using the Routh’s stability criterion, Providing a negative feedback to the primary system with controller gain is given by Displacement feedback of the primary mass Using this optimal tuning ratio, damping ratio by Routh’s stability criterion the system is stable for