# Active Vibration Control Study of Harmonic Excitation for Voigt-Kelvin System
###### Abstract  
This paper presents research on active vibration control (A-V-C), which is being carried out to reduce structural vibration in the field of active vibration control and describes the most important method of implementation. Non-adaptive and adaptive systems feedback with adaptive algorithms are outlined. Electrodynamic shakers, used to excite an SDOF system to study its dynamic characteristics, are introduced. Signal analysis determines the response of a system under known excitation and presents it in a convenient form. The proposed method directly measures the payload displacement relative to the ground. We carry out a detailed investigation based on a realistic single-degree-of-freedom (SDOF), demonstrate the effectiveness of the proposed adaptive control law, estimate the control parameters, and show that the target dynamics of the isolator are attained. active control; SDOF; Voigt-Kelvin model +
Footnote †: journal: Applied sciences  
0000-0001-899-7000][PERSON]. [PERSON] and [PERSON] [5] discuss the development of a four-degrees-of-freedom car and seat model that utilizes road accelerations as inputs, and use numerical simulations to estimate the force and displacement requirements for the A-V-C. Finite element calculations recently made it possible to take the complex behavior of the adhesive into account; [PERSON] et al. [6] obtained convergence results for a dynamic case involving three-dimensional linearly elastic bodies connected by a thin, soft, nonlinear Kelvin-Voigt viscoelastic adhesive layer. [PERSON] et al. [7] found that PZT actuators can be used for A-V-C by reducing the vibration amplitude to induce the damping effect using the open loop system. A control scheme for an electro-dynamic shaker is proposed by [PERSON] et al. [8]; the controller is implemented by calculating the acceleration power's spectral densities, and a control signal is generated by applying an adaptive filtering technique. [PERSON] [9] discusses a single-degree-of-freedom system and uses an A-V-C system to control the vibration of the mass and actively control a system that includes a rotating, unbalanced example. [PERSON] and [PERSON] [10] introduced a novel self-powered A-V-C strategy to address the power supply limitations of traditional A-V-C methods. The findings of this study demonstrate that adjusting the duty cycles of pulse-width modulation control signals based on the derived relationship not only ensures the precise generation of the desired active control force but also enables the electromagnetic actuator to alternate between power-harvesting and power-consuming modes. [PERSON] et al. [11] propose a method for actively reducing the vibrations caused by magnetic anisotropy in sinusoidal brushless motors through current injection. The approach was validated on a prototype of a Surface Permanent Magnet Synchronous Motor. Traditionally, mechanical structure vibrations are addressed through passive damping or isolation. While these methods are widely used in various applications, they have inherent limitations. Passive damping works well at high frequencies but tends to be bulky, heavy, and costly when dealing with low frequencies. Vibration isolation typically faces contradictory requirements, as the isolation components must be flexible enough to minimize force transmission, yet rigid enough to prevent excessive relative movements. A-V-C can be employed to address such drawbacks and has been successfully applied in numerous fields. In addition to passenger cars, it is also used in marine applications [12; 13], railway vehicles [14; 15], vehicle seats [16], aircraft structures [17], helicopters [18], bridge towers [19], telescope orientation control [20], and bandsaw blades [21]. [PERSON] et al. [22] and [PERSON] et al. [23] developed a homotopy perturbation method for the prediction of stability lobes in the time domain for various machining operations as a function of the spindle speed and the chip load, and made comparisons between the results of numerical models and the results of experimental tests.