Adaptive Electromechanical Tuned Vibration Absorbers and Their Application in Semi-Active Fluid Mounts

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1 roceedgs of th nternational ongress on Acoustics, A 3-7 August, Sydney, Australia Adaptive Electromechanical Tuned Vibration Absorbers and Their Application Semi-Active Fluid Mounts Nader Vahdati (), Somayeh Heidari () () School of Mechanical and Aerospace Engeerg, Nanyang Technological University, Nanyang Avenue, Sgapore AS: 43.4.TM Vibration isolators, attenuators, and dampers ABSTRAT An adaptive electromechanical tuned vibration absorber (ETVA) is developed consistg of a voice coil and a sgle degree of freedom mass sprg system. The natural freuency of the ETVA is varied and tuned by addition of a variable capacitor. n this paper, the design, mathematical model, and experimental data of the ETVA is presented. Experimental data dicates that the natural freuency of the ETVA can be varied by 66% usg capacitive shuntg of the voice coil. Analytical studies have also revealed that if the wires of the voice coil could be replaced with room temperature superconductors, the natural freuency of the ETVA can be changed by a factor of 8 usg a resistive shuntg of the voice coil. The ETVA is then used conjunction with a passive fluid mount to create a variable notch semi active fluid mount. Fally, the mathematical model and simulation results of the ETVA plus the passive fluid mount are described and presented. NTRODUTON An adaptive Electromechanical Tuned Vibration Absorber (ETVA) is a semi-active vibration control device which is tunable and it has the ability of reducg undesired vibration at any desired freuency. Here this paper, an electromechanical tuned vibration absorber (ETVA) is troduced consistg of a voice coil and a sgle degree of freedom mass sprg system. The natural freuency of the ETVA is varied and tuned by addition of an electronic circuit (RL circuit). The design, mathematical model, and experimental data of the ETVA is presented and thereafter, the effect of changg RL parameters varyg natural freuency of the tuned vibration absorber (TVA) is discussed. Fally, the ETVA is used conjunction with a passive sgle pumper fluid mount to create a variable notch freuency semi active fluid mount. The mathematical model and simulation results of the passive sgle pumper fluid mount plus the ETVA is then presented and discussed. ELETROMEHANAL TUNED VBRATON ABSORBER n this section, the developed adaptive electromechanical tuned vibration absorber (ETVA) is explaed details. The ETVA consists of a mass, a sprg, a voice coil, and a RL electrical circuit. The RL circuit is shunted to the voice coil and is used to change the natural freuency of the TVA [,]. A RL circuit consists of a resistor, an ductor, and a capacitor element series. Here this paper, it is not tended to use all the three electrical elements simultaneously but only one at a time. Meang, the coil will be connected to either a variable resistor, or to a variable ductor, or to a variable capacitor. Fig. shows a picture of the developed ETVA which is fixed to a dynamic test mache. Figure. Adaptive Electromechanical Tuned Vibration Absorber (ETVA) HSYAL MODEL The schematic physical model of the ETVA is shown Fig. The math model consists of a mass (M) representg the mass of the movg coil plus the mass of the steel disk, a sprg (K) representg the total sprg rate of the four sprgs, and a damper () representg the overall dampg of the 4 metal sprgs. Fig. dicates that the movg coil can be connected to a variable resistor, or an ductor, or a capacitor to change the natural freuency of the TVA. As is shown, the permanent magnet and one end of the sprgdamper are fixed to a rigid frame. Mass-sprg-voice coil system is stimulated by a susoidal acceleration which is applied to the rigid frame. Two accelerometers are connected, one to the mass (M) and one to the rigid frame. The accelerometer which is connected to the mass (M) measures the output acceleration (a out ) and the other one which is connected to the rigid frame measures the put acceleration (a ). A

2 3-7 August, Sydney, Australia roceedgs of th nternational ongress on Acoustics, A lkage variable (λ ) which is eual to time tegral of the duced voltage the voice coil. By takg Laplace transform of Es. to 4, the ratio of mass acceleration (a out ) over the put acceleration (a ) is derived as E. : Figure. hysical model of the ETVA Voice coils consist of a wire wdg (coil) and a magnet. The coil can be modeled as an ductor and a resistor, so when a RL circuit is added to the coil, the model of the coil plus the RL circuit can be as follows, see Fig. 3: sx aout ( sr4 + )( s + R3s + ) + s α a ( s + R4s + )( s + R3s + ) + s To simulate the design of Fig. MATLAB, the followg parameters were chosen: K sp Stiffness of the sprg, ( / K sp ), N/m α R sp Dampg of the sprg, (R 4 R sp ), 7 N.s/m M+M coil Disk Mass (M) plus oil mass ( M+M coil ), Kg α Voice coil force sensitivity (GY - α ),. N/Amp Figure 3. oil Model plus the RL circuit Sce the ETVA volves multiple energy doma system (electrical, mechanical and magnetic), bond graph modelg techniue is used to derive the constitutive euations of the system [3]. Fig. 4 shows the bond graph model of Fig.. Figure 4. Bond graph model of Fig. The followg state-space euations are derived from the bond graph model of Fig. 4: Sf ( Sf ) R α( Sf ) 4 + R 3 + α n the above state-space euations, and are the generalized displacement variables; p and p are the momentum variables. defes the relative displacement between the rigid frame ( shown as MTS frame) and the mass (M). represents the duced electrical charge the voice coil-rl circuit. p defes mass momentum and p shows the flux () () (3) (4) coil v R coil R v Voice oil nductance, 7. mh Variable nductance, < v < mh Voice oil Resistance, ohms Variable Resistance, < R v < ohms v Shunted apacitance ( ), < v <33 μ f A parametric study was done to evaluate the effect of changg resistance, ductance and capacitance of the RL circuit on a a out ratio. The parametric study defes how the variation the electrical components affects the natural freuency of the TVA, and which one is the most viable to use as a variable component to change TVA natural freuency. The followg sections describe the simulation results. EFFET OF A VARABLE RESSTANE (R V ) ON NATURAL FREQUENY OF THE ETVA First, it is assumed that a variable resistance is connected to the coil. Therefore, the coil model plus the electrical circuit (Fig. 3) cludes the coil resistance (R coil ), coil ductance ( coil ), and a variable resistance (R v ). n the bond graph model of Fig. 4, R 3 represents the combation of the coil resistance plus the variable resistance (R coil+ R v ). defes the coil ductance ( coil ) and is assigned eual to e6 μ f to elimate the capacitance from the model. Fig. shows how changg shunted resistance affects the natural freuency of the ETVA. When the shunted resistance (R v ) varies from a very low value (short circuit voice coil) to a very high one (open circuit voice coil), the natural freuency of the ETVA and the peak value of (a out /a ) crease. Accordg to the bond graph model of Fig. 4, when the shunted resistance (R v ) creases, the duced current (i ducedflow bond ) the coil-rl circuit decreases; so the applied force (F α * i duced force bond ) from the voice coil to the SDOF mass-sprg system decreases. Ultimately, when the shunted resistance goes to a very high value, the duced current goes to zero and no force will be applied from the voice coil to the mass (M). n this case, the A

3 3-7 August, Sydney, Australia roceedgs of th nternational ongress on Acoustics, A whole system reduces to a SDOF mass sprg system. So, the natural freuency of the ETVA approaches to the natural freuency of the SDOF system (.8 Hz for the selected parameters). On the contrary, when the coil s wires are short circuited with no shunted resistance (R v ), the duced current the coil-rl circuit will be high; therefore the applied force (F GY - * i duced force bond ) from the voice coil to the mass (M) will be noticeable. This force tends to crease the apparent stiffness that the mass (M) sees, so the ETVA apparently becomes rigid and mass (M) motion follows the excited motion (a out /a approximately ). For the applications that the peak value of the (a out /a ) is gog to be used; higher resistance can give higher (a out /a ) peak value. Ratio of mass acceleration to MTS put acceleration Figure. Ratio of mass acceleration to put acceleration (a out/a ) versus freuency (Variable resistance is shunted to the voice coil) VOE OL WTH SUERONDUTNG WRES The simulation result of Fig. was for an ETVA with the coil resistance (R coil ) of Ohms. However, if the coil could be manufactured from a very low resistance wire such as a room temperature superconductg wire, the natural freuency of the ETVA would change a very wide freuency range. Fig. 6 shows that when the coil of ETVA is made of a very low resistance wire ( Ohms or less), the natural freuency of the ETVA can be shifted by approximately 8 times from Hz to.8 Hz when a variable resistor is shunted to the voice coil. Accordg to the bond graph model of the ETVA (Fig. 4), when the coil resistance is very low and the coil s wires are short circuited, R 3 can be considered negligible. So the only remag element is an ductance ( ), which is bonded to the gyrator (GY - ). Ratio of mass acceleration to MTS put acceleration freuency Hz... Ratio of mass acceleration to MTS put acceleration vs. freuency X:.88 Y:.6 X:.67 Y:.6 RR(coil) Ohms (short circuit coil) RR(coil)+Rv(shunted)8 Ohms RR(coil)+Rv(shunted)36 Ohms RR(coil)+Rv(very high resistance)(open circuit coil) Ratio of mass acceleration to MTS put acceleration vs. freuency RR(coil)+Rv(shunted) Ohms RR(coil with superconductive wire) Ohms 3 freuency Hz Based upon bond graph modelg techniue [3], when an ductance () is bonded to a gyrator, it acts like a capacitance () which is euivalent to a compliance a mechanical system (see Fig. 7). Figure 7. Bond graph prciple [3] Therefore when a low resistance coil is short circuited, a sense, a compliance is added to the SDOF system; so, the total stiffness of the ETVA creases and conseuence the natural freuency of the ETVA goes up. On the contrary, when a very high resistance is shunted to the voice coil, the duced current the coil decreases and the contribution of voice coil to the mass-sprg motion is negligible. So the total ETVA acts like a SDOF system and its natural freuency approaches to the natural freuency of the SDOF mass-sprg system. Generally, for the applications where the change the disturbance freuency is large, this type of ETVA would be uite useful. Literature review dicates that room temperature superconductg wires will be commercially available with to years time. Once such a technology is available, the creation of an adaptive ETVA with a widely variable natural freuency would be possible. EFFET OF A SHUNTED VARABLE NDUTANE ( V) ON THE NATURAL FREQUENY OF THE ETVA Another parametric study was done on a shunted variable ductance. Here, the coil model plus the electrical circuit (Fig. 3) consists of the coil resistance (R coil ), coil ductance ( coil ) and a variable ductance ( v ). n the bond graph model of Fig. 4, represents the coil ductance plus the variable ductance ( coil + v ), R 3 shows the coil resistance, and is set to a very high value, namely e6 μ f, to elimate the capacitance from the model. Simulation result for the ETVA with the shunted variable ductance is shown Fig.8. hangg ductance from 7. (mh) to (mh) changes the natural freuency of the ETVA by %. Accordg to the bond graph modelg prciples [3], when an ductance () is bonded to a gyrator (GY), it acts like a capacitance () which is euivalent to a compliance a mechanical system (see Fig. 7). Therefore, by varyg the shunted ductance, the compliance of the ETVA varies and conseuence its natural freuency changes. However, it should be noted that an ductance has some herent resistance and when the ductance is changed, the herent resistance of the ductor is also varied simultaneously; so, the shunted ductance is not controllable dependently from its resistance. Therefore, creatg an adaptive ETVA usg an ductance would not be a suitable choice. Figure 6. Ratio of mass acceleration to MTS put acceleration (a out/a ) versus freuency (for a very low resistance voice coil and a high resistance voice coil) A 3

4 3-7 August, Sydney, Australia roceedgs of th nternational ongress on Acoustics, A Ratio of mass acceleration to MTS put acceleration Figure 8. Ratio of mass acceleration to MTS put acceleration (aout/a) versus freuency (Variable ductance) EFFET OF A SHUNTED VARABLE AATANE () ON THE NATURAL FREQUENY OF THE ETVA The last parametric study was done by connectg a variable capacitance to the voice coil. The coil model plus the electrical circuit (Fig. 3) consists of the coil resistance (R coil ), coil ductance ( coil ) and a variable capacitance ( v ). n the bond graph model of Fig. 4, R 3 represents the coil resistance (R coil ). defes coil ductance ( coil ) and represents the variable capacitance ( v ). n the MATLAB simulations, the variable capacitance is varied from (a very low capacitance) which is euivalent to an open circuit, to μ f, 33 μ f and very high capacitance which is euivalent to a short circuit. Fig. shows the ratio of the mass acceleration to the put acceleration (a out /a ) versus freuency as shunted capacitance is varied. So, when a capacitor () is connected to a Gyrator (GY), it plays the role of an ductor and it is euivalent to a mass the mechanical system (See Fig. 7). Therefore, when the capacitance is varied, the apparent mass of the TVA is changed thus the natural freuency of the TVA. For the current selected parameters, when the shunted capacitance is varied from a very low value ( ) to 33 μ f, natural freuency of the TVA changes by 66%, from. Hz to. Hz. As is seen Fig., changg capacitance not only changes the natural freuency of the TVA but also the peak value of the (a out /a ) at the resonance freuency. Ratio of mass acceleration to MTS put acceleration (Aout/A) freuency Hz X:.876 Y:.6 Ratio of mass acceleration to MTS put acceleration vs. freuency X: 4. Y:.7 Ratio of mass acceleration to MTS put acceleration vs. freuency X:.747 Y:.4 X:. Y:.83 X:.6 Y:.668 LL(coil)7. mh LL(coil)+Lv (shunted)7 mh LL(coil)+Lv(shunted) mh LL(coil)+Lv(shunted) mh Open ircuit mf capacitance 33 mf capacitance losed ircuit freuency Hz Figure. Ratio of mass acceleration to MTS put acceleration (a out/a ) versus freuency (Variable capacitance) The peak value reduction occurs because of the coil resistance and the capacitance v. TVAs work most effectively when there is little dampg present the TVA. So, order to have an adaptive ETVA with good performance, all dampg and the coil resistance should be kept to a mimum. To analytically show the location of the ETVA resonance freuency and resonance peak amplitude as a function of capacitance, the followg steps are taken. f the dampg of the sprgs and resistance of the coil are kept very low, E. reduces to, aout ( + α ) s + 4 sx a ( ) s + ( α + + ) s + The natural freuency of the ETVA is derived by takg derivative of E. 6 and settg it to zero, d ds s a a out ( ) s d ds ( ( 4 ) s ± ( α / ) ( + α ) + ( + α ) s α ± ( α ) (6) ( α / ) s ( ) out iω α / a a ( iω) ω resonance freuency ( + Es. 8 and verify the MATLAB simulation results. Es. 8 and show that creasg capacitance ( ), not only decreases the natural freuency of the ETVA, but also the peak amplitdue of the (a out /a ) at the resonance freuency. t was mentioned earlier that dampg and capacitance both impact the resonance peak amplitude, but it is important to mention that if the coil resistance is high, when capacitance is creased, the peak amplitude drops more aggressively than without any dampg. n summary, a comparison between Fig., Fig. 8, and Fig. shows that a variable capacitance is the most effective way of changg natural freuency of the TVA than changg resistance or ductance. Moreover, comparison to other tunable TVA devices the literature, this device provides more tunability the natural freuency ( 6% ) than other methods. The parametric study and simulation results show that creatg an adaptive ETVA usg a variable capacitor would be the best viable choice. However, when room temperature superconductive wire technology is commercially available, a superconductive voice coil would create the best adaptive ETVA which is tunable a larger freuency range. EXERMENTAL VERFATON To verify the above simulation results, an experimental test rig was developed. Here section, the ability of a variable capacitance creatg an adaptive ETVA was examed and compared with simulation results. Similar experiment can be done for an ETVA with variable ductance and variable resistance. As is shown Fig., the designed apparatus consists of 4 axial staless steel sprgs (K e N/m, R e N.s/m), a steel disk (M.44 Kg), a voice coil (M coil.4 Kg, L7. mh, R Ohms, α. N/amp), and a circuit board consistg of various capacitors. A susoidal drivg displacement is applied to the ETVA system usg an MTS8 test mache. Two piezoelectric accelerometers are used, one attached to the steel disk and the other to the base plate of the test rig to measure the mass acceleration (a out ) and the MTS put acceleration (a ); respectively. The capacitance which is shunted to the coil was varied, similar to the simulation, meang from which is euivalent to an open circuit to ) ) (8) + () 4 A

5 3-7 August, Sydney, Australia roceedgs of th nternational ongress on Acoustics, A μf and then to 33 μ f which is euivalent to a short circuit. ractically, there are two possibilities for the variable capacitance circuit. Usg commercially available variable capacitors or design a customized arrays of capacitors from the available constant capacitors on a circuit board which covers the reuired capacitance range. However, the size of capacitors the array should be chosen such that a full range of tung (from very low (open circuit) to high (short circuit) could be observed with a good accuracy. Here this experiment an array of capacitors was put on a circuit board. Figure. assive Sgle umper Hydraulic Mounts Figure. Experimental Test rig of ETVA Open ircuit mf capacitance 33 mf capacitance losed ircuit Figure 3. Dynamic Stiffness of a Typical Fluid Mount versus Freuency [4] NEW SEM-ATVE FLUD MOUNT DESGN Figure. Experimental data for Ratio of mass acceleration to MTS put acceleration (a out/a ) versus freuency Experimental results are plotted Fig.. A comparison between Figs. and reveals that the experimental data and theoretical simulation data are very similar. t verifies the viability of the proposed ETVA design. Similarly, ETVA with a variable ductance and a variable resistance can be fabricated and tested, but here this paper those experiments are not shown. Sce the viability of the proposed ETVA is analytically and experimentally proven, the adaptive ETVA can now be used conjunction with a passive hydraulic mount to create a semi-active hydraulic mount. SNGLE UMER HYDRAUL (FLUD) MOUNTS Here this section, a brief discussion on sgle pumper hydraulic (or fluid) mounts is given. Sgle pumper fluid mounts are widely used the automotive and the aerospace applications [4]. A passive hydraulic or fluid mount, see Fig., consists of a fluid contaed two elastomeric cavities (or fluid chambers) that are connected together through an ertia track. When a susoidal motion is applied to the fluid mount, the fluid will oscillate between the two fluid chambers. The oscillatg fluid havg mass, bounces between the two chamber volumetric stiffnesses and the vertical (or axial) stiffness, and eventually goes to resonance at a freuency called notch freuency. At this freuency, the fluid mount dynamic stiffness decreases considerably and thus the transmitted force; therefore, providg cab noise and vibration reduction. To place the notch freuency to any desired location, the fluid mount designer needs to use appropriate ertia track length, diameter, fluid density and viscosity, and rubber stiffnesses. Fig. 3 shows a typical dynamic stiffness of a passive fluid mount versus freuency. Fig. shows the mathematical model of the new semi active hydraulic or fluid mount design where the lower chamber of a conventional sgle pumper fluid mount (Fig. ) is replaced by the proposed ETVA system. Fig. shows, the bottom fluid chamber, a piston is supported by a sprg. A fabric diaphragm (with high volumetric stiffness) is placed on the top of the piston, sealg the bottom fluid chamber. As fluid enters the bottom chamber, it moves the piston. When the piston moves, it moves the coil and out of the permanent magnet. As coil moves up and down the permanent magnet, current is generated the coil s copper wire. The coil has N turns of pure copper wire. The coil s wire has some ductance and resistance, but a variable capacitance is also added to the coil s electrical circuit, for the purpose of varyg natural freuency of the ETVA. With most fluid mount designs, great efforts are made to mimize flow losses and dampg; so, here aga ideally not only we would like to have very low ertia track flow losses, and rubber dampg, but also we would like to have very small resistance the coil wires and the entire electrical system. n this new design, volumetric stiffness of the bottom chamber is varied by varyg the shunted capacitance thus the notch freuency of the fluid mount. Figure. Variable Bottom hamber Volumetric Stiffness Fluid Mount Design A

6 3-7 August, Sydney, Australia roceedgs of th nternational ongress on Acoustics, A Figure. Bond graph Model of Fig. n order to derive the constitutive euations of Fig., its bond graph model was developed and it is shown Fig.. From the bond graph model (Fig.), the followg statespace euations are derived: 3 V A V 6 p 6 6 R A 8 pb p Apb R6 α α R () () () (3) ()) () (6) (7) n the above state-space euations, 3, 6,, and are the generalized displacement variables; p, p and p are the momentum variables. The state-space variables are defed as: 3 6 Relative motion across the mount Top chamber change volume F R V Ap 6 (8) To simulate the design of Fig., MATLAB rogram and the above State Space euations were used. The followg parameters were used for the MATLAB simulation. Table - Fluid Mount and ETVA arameters Used Matlab K r /3 Real comp. of vertical stiffness, N/m.e6 K r mag. comp. of vertical stiffness, N/m. A p Effective iston area, m. A t nertia track area, m 3.66e-4 A m ross sectional area of the mass, m 6.4e-4 f nertia track fluid ertia, N-S /m 8.64e R o R 8 nertia track flow resistance, N-S/m 6.4e6 K vt / 6 Top hamber Volume Stiffness, N/m.e K vb / ompressibility of the fluid, N/m.e K / Stiffness of support sprg K, N/m 87 M piston mass+ coil mass (kg).77 b R 6 Sprg Dampg, N.s/m. R coil R oil copper wire resistance, ohms.6 coil oil nductance (mh). α GY 7-8 Voice coil force sensitivity (N/amp) 3. v Shunted apacitance, μf Varies n the MATLAB simulations, the variable capacitance parameter,, was varied from a very low value (open circuit) to 33 μf. Fig. 6 shows the dynamic stiffness of the new fluid mount design versus freuency as the element is varied. The simulation shows that the notch freuency moves about Hz (more than %) and generally it is enough for fe tung of the notch freuency of a fluid mount. Fig. 7 shows that as the mass (coil+ piston) decreases, the notch freuency only moves 4 Hz while the shunted capacitance was kept at μf. This implies that the mass should not be kept very low. However, for the aerospace applications which weight is an important issue, the coil and the piston mass should be selected such that the change the capacitance gives the reuired freuency variation range while the mass of the mount is kept low. Fig. 8 shows that as the coil resistance, R decreases, the notch will be deeper for the same variation the capacitance. n order to get a deep notch, the coil resistance, R, should be kept as low as possible. p p Bottom chamber change volume Lower piston displacement nduced electrical charge the Voice coil-capacitor circuit Time tegral of the pressure drop the ertia track (ressure momentum) Lower piston momentum p flux lkage variable ( λ ) (Time tegral of duced voltage the voice coil-capacitor circuit) The put force (effort at bond ) is eual to: Figure 6. Dynamic Stiffness as variable capacitance parameter is varied from open circuit to 33 μf

7 3-7 August, Sydney, Australia roceedgs of th nternational ongress on Acoustics, A Dynamic stiffness Newton/meter. x 7 Dynamic stiffness of passive mount vs. freuency.. Open ircuit,.77 kg mf,.77 kg mf, 8 kg mf,. kg location by % with the change of shunted capacitance of the ETVA. As the capacitance is changed, the effective volumetric stiffness of the bottom chamber changes; and so does the notch freuency. When fluid mounts are manufactured, due to tolerances on all the fluid mount dimensions, material property variations, and variation elastomer moldg processes, the notch freuency never ends up at the right location on the st manufacturg pass. So with this new design, the notch freuency can be easily tuned to any desired location on the st manufacturg pass. Figure 7. Dynamic Stiffness at different piston weight ( is eual to μf) Dynamic stiffness Newton/meter f i H x 7 Dynamic stiffness of passive mount vs. freuency Open ircuit mf, R.6 Ohms mf, R.3 Ohms freuency Hz Figure 8. Dynamic Stiffness at different coil resistance ( is eual to μf) REFERENES. Lesieutre, G.A., Vibration Dampg and ontrol Usg Shunted iezoelectric Materials. The Shock and Vibration Digest, 8. 3(3): p l, D. and L. Ga, An Actively Tuned Solid-State Vibration Absorber Usg apacitive Shuntg Of iezoelectric Stiffness. Journal of Sound and Vibration,. 3(3): p Karnopp, D.., D.L. Margolis, and R.. Rosenberg, System Dynamics: A Unified Approach, nd Edt, John Wiley & Sons, New York. 4. Vahdati, N. and M. Ahmadian, Sgle pumper semiactive fluid mount. roceedgs of the 3 ASME nternational Mechanical Engeerg ongress, 3: p ONLUSONS An adaptive electromechanical tuned vibration absorber (ETVA) was troduced. t cludes a voice coil, a sgle degree of freedom mass sprg system and an electronic RL circuit. The electronic circuit (RL circuit) was added to the voice coil series and it was used to tune the natural freuency of the ETVA. The mathematical model of the ETVA was defed and parametric studies were performed to evaluate the effect of variable resistance, variable ductance and variable capacitance tung the natural freuency of the ETVA. arametric study showed that if the technology of room temperature superconductive wires is improved; usg a voice coil made of superconductive wires plus a variable resistance would create the best adaptive ETVA which is tunable a large freuency range (more than %). However among commercially available voice coils, it was shown that the variable capacitance is the most feasible approach to use at this pot time to vary the natural freuency of the ETVA. Natural freuency of the ETVA was varied by 66% when the shunted capacitance condition is varied from an open circuit to a short circuit. The viability of the proposed ETVA design was verified by developg an experimental test rig. omparison of the simulation results with the experimental data showed a remarkable correlation between the two. Experimental data revealed that a variable capacitance is able to change the natural freuency of the ETVA by 66%. The application of ETVAs creatg a variable notch freuency fluid mount design was studied. Simulation results showed that deed it is possible to vary the notch freuency A 7