Vibration Resonant Frequencies Research Articles

Magnetoelectric effects in a heterostructure of magnetostrictive fiber composite and piezopolymer film

Abstract Magnetoelectric (ME) effects in composite heterostructures comprising ferromagnetic (FM) and piezoelectric (PE) layers realize mutual transformation of magnetic and electric fields and form the basis for the development of highly sensitive magnetic field sensors, electrically tuned electronic components, and energy harvesting devices. ME effects result from a combination of magnetostriction of the FM layer and piezoelectricity in the PE layer due to mechanical coupling between the layers. In this work ME effects are studied in a flexible heterostructure containing a magnetostrictive fiber composite (MFC) and a piezopolymer layer. MFC is a set of microwires made of amorphous FeCoSiB alloy with high magnetostriction and arranged in a plane parallel to each other in a polymer matrix. MFC exhibits strong in-plane anisotropy of magnetization and magnetostriction resulting from demagnetization effects in microwires. Anisotropy leads to the dependence of the linear and nonlinear ME effects characteristics on the orientation of dc magnetic field in the plane of the heterostructure. For the fabricated heterostructure at the resonance frequency of bending vibrations, a linear magnetoelectric coefficient of 24 V/(Oe∙cm) was obtained, and the efficiency of nonlinear generation of the second voltage harmonic reached 1.6 V/(Oe2∙cm). ME effects in MFC heterostructures can be used to create magnetic field sensors and electronics devices that are sensitive to the field orientation.electronics devices that are sensitive to the field orientation.

Computational and experimental studies of vibration-protective properties of a pneumatic wheel of the MTZ-82 BELARUS tractor with external spring-hydraulic mini-suspension

BACKGROUND: Currently used in various sectors of the national economy, numerous wheeled suspensionless vehicles on pneumatic tires have a low level of vibration protection of the frame and limited cross-country ability. Therefore, the development and study of the design characteristics of a pneumatic wheel with increased elastic-damping properties and cross-country ability is a relevant technical problem. AIM: Development of the design and study the vibration-protective properties of a pneumatic wheel with an external spring-hydraulic mini-suspension to improve the ride smoothness and cross-country ability of large-sized suspensionless vehicles. METHODS: A description of the design of a wheel with mini-suspension and a support roller is presented. The wheel modeling was carried out in the PascalABC software, which takes into account the nonlinearity of the total force of the pneumatic tire and the spring-hydraulic mini-suspension, which is installed parallel to the tire at an angle to the vertical axis of the wheel. The test method consisted of comparison of free and forced vibrations of the rear pneumatic wheel of the MTZ-82 BELARUS tractor with a 400-965/15.5-38 tire, which operated without and with mini-suspension at a vertical load of 0.6 tons and various excessive pressure in the tire. RESULTS: The results of computational and experimental studies show that if the tire is radially compressed by 75 mm, the excess pressure inside the pneumatic wheel almost does not change, and if the pressure in the tire decreases from 1.6 to 0.4 bar, the resonant vibration frequency of the standard wheel axle decreases by 25%, while the dynamic coefficient remains unacceptably high (more than 5), leading to the tire breakaway from the supporting surface. Installing a mini-suspension parallel to the wheel in the form of a spring-hydraulic shock-absorbing strut leads to an increase in the resonant frequency by 1 Hz, however, the resonant peaks are reduced by almost 3 times to a dynamic coefficient of 2.5...2, which significantly increases the ride smoothness of suspensionless vehicles and reduces the likelihood of wheel breakaway from the supporting surface. CONCLUSION: It was found with the studies that the proposed wheel with a mini-suspension as a spring-hydraulic strut and a support roller has a relatively simple design, ensures high vibration-protective properties with small amplitudes of kinematic disturbance and can be used to improve the ride smoothness and cross-country ability of wheeled suspensionless vehicles.

Stroboscopic sampling moiré microscope (SSMM) for investigating full field in-plane vibration of MEMS mechanical transducers

Precise analysis of the full-field in-plane vibration of microelectromechanical system (MEMS) transducers is crucial for assessing their device functionality and performance. As an example, in the context of frequency/amplitude modulation of Quartz Tuning Fork (QTF)-based atomic force microscopy (AFM) systems, understanding QTF’s in-plane vibration can significantly enhance accurate evaluation of tip-sample forces. Current methods, such as analytical and numerical approaches, have limitations when it comes to providing accurate measurements. To address these limitations, we proposed an experimental approach that combines stroboscopic and sampling moiré (SM) techniques. This method focuses on investigating the in-plane vibration of a QTF and utilizes the obtained results to measure the sensor’s dynamic properties such as vibration mode shape, resonance frequency (f0), and quality factor (Q). Nanometer-scale light pulses, generated using a custom-designed stroboscope, are synchronized with the QTF’s excitation voltage to freeze the vibration effectively, enabling imaging using a standard CCD camera. Subsequently, SM analysis is employed to extract the surface vibration profile, facilitating the measurement of vibration mode shape, f0, and Q. This technique shows promise for analyzing the dynamic behavior of various micro-devices compatible with the sample preparation process.

Investigating resonance frequency in advanced composite structures as the main part of bridge construction: a multi-physics simulation approach

This paper investigates the nonlinear vibration characteristics and resonance frequencies of a graphene oxide powders (GOP) reinforced beam structure, which is in contact with fluid, serving as a crucial component in bridge construction. Utilizing a multi-physics simulation approach, this study integrates both mathematical modeling and COMSOL simulations to analyze the behavior of the GOP-reinforced beam. The fluid in the analysis is modeled as incompressible, non-viscous, and irrotational, contributing to the interaction with the beam structure. The isogeometric approach, coupled with the harmonic balance method and the arc-length technique, is employed to solve the complex nonlinear partial differential equations (PDEs). This coupled method ensures the accurate capture of the nonlinear response and resonance frequencies of the beam, which are critical for the safe design and performance of bridge structures. The findings reveal the significant influence of GOP reinforcement on the vibration and stability characteristics of the beam, highlighting its potential to enhance structural performance under dynamic loading conditions. The study also emphasizes the importance of considering fluid-structure interactions in the design process, as the fluid’s presence substantially affects the vibration behavior. This research contributes to the understanding of the dynamic behavior of advanced composite structures in fluid environments, offering valuable insights for the design and analysis of bridge components. The results demonstrate the efficacy of the proposed simulation approach in addressing the complexities of nonlinear vibrations in fluid-structure interaction systems, paving the way for future developments in civil engineering applications.

Study on the global and nano-scale characterization of heat-induced changes in ordinary Portland cement paste

Cement-based composite materials can be damaged by distributed micro-cracking and degradation of hydration products when exposed to sustained high temperatures. In this study, a nano-scale characterization tool (dynamic nanoindentation) and global mechanical methods (vibration resonance frequency and damping) are employed to better understand the degradation of ordinary Portland cement paste subjected to high temperature exposures. A connection between the methods is demonstrated.

Analysis of Vibration Electromechanical Response Behavior of Poly(Vinylidene Fluoride) Piezoelectric Films

Studying the electromechanical response behavior of piezoelectric thin films under different loading conditions is of great value for the development and optimization of piezoelectric sensors and flexible portable electronic devices. This paper establishes the theory of large deflection vibration of rectangular four-edge simply supported piezoelectric thin films using the energy method, and analyzes the electromechanical response characteristics of vibration force (including resonant frequency and nonlinear vibration). Meanwhile, the electromechanical response behavior of Poly(vinylidene fluoride) (PVDF) films under different loading conditions (static and harmonic vibration) is analyzed. The study investigates the nonlinear vibration characteristics and resonance frequency variations under different film sizes and thickness conditions in the case of various loading conditions. The developed model can predict the resonance frequency associated with the plate dimensions. This study is of great significance for the research and application of laminated piezoelectric film sensors.

Data-driven prediction of rail neutral temperature for continuously welded rails using impulse-based vibration frequencies

Continuously welded rails (CWR) are prone to the development of high thermal-induced load along the axial direction. Excessive levels of load lead to risk of rail buckling and potential for derailment. Knowledge of the in situ rail axial load in CWRs is therefore important to ensure safe rail management. Field-deployable, nondestructive evaluation techniques for measuring the rail load, or a widely adopted alternative called rail neutral temperature (RNT), are desired. This study uses a data-driven approach to investigate if rail dynamic response data, collected in a non-destructive fashion, can be used to predict RNT. The study is based on a data set comprising rail equivalent strain, temperature and vibration resonance frequencies that was collected from a revenue-service rail over a period of nearly two years. All excited vibration resonance peaks are identified from other peaks caused by noise using spectral amplitude variance. Among these resonance peaks, potentially useful resonances are identified with respect to stacked spectra collected across a testing day using an assumed temperature-frequency relation. A subset of the identified useful resonances is then identified based on their consistent appearance across both testing locations and all testing days, strong correlation to effective strain, and strong correlation to each other. Three particular vibration resonances (or vibration modes -- these terms will be used interchangeably throughout this paper unless specified otherwise. The term mode does not necessarily indicate mode shapes or mode families.) emerge from this process as best candidates. A classic feature selection technique, Lasso linear regression, is then employed to identify critical power combinations of the three resonant mode frequencies. Two power combinations exhibit unique correlation to the measured equivalent axial strain at both test locations across all testing days, and thus show particular ability to predict RNT. The RNT is predicted at one test location using different models based on the power combination data from the other location, and vice versa, where the predictions satisfy standard RNT measurement accuracy expectations.

Resonance behaviour of magnetoelectric (PSLZT multilayer - NZFO) layered composites: A comprehensive theory – Experimental perspective

In recent years, compact antenna and miniaturized power transfer devices are among the interesting applications of magnetoelectric (ME) composites in low frequency (LF) / very low frequency (VLF) range. Here we elucidate, in general, analytical calculations used to understand, the vibrational modes and resonance frequencies of the layered ME composite and; Finite Element Analyses (FEM) with isotropic and anisotropic properties to accurately predict the resonance frequencies pertaining to the axisymmetric and asymmetric mode of vibrations with respect to significant ME response. Further, ME coefficient of the composite with Longitudinal - Transverse (L-T) configuration based on the interface coupling model were utilized to completely study the ME composites. The configuration optimized through the design was in particular corroborated experimentally with a representative PSLZT multilayer on NZFO based ME layered composite system. The PSLZT multilayer on NZFO based ME composite was fabricated by tape casting the constituent thick films and co-sintering process which are further analysed for their ME responses at their resonance frequencies. ME voltage spectrum showed a maximum of 7.74 V/cm.Oe at its axisymmetric resonance mode at 30.6 kHz. Various peaks at different resonance frequencies with respect to axisymmetric and asymmetric modes of vibrations agree well and validates the above modeling studies. Overall, the complete study provides a systematic design guideline for optimizing the ME composite configuration suitable for specific application with required resonance frequency.

Nonlinear dynamic behavior of single-layered black phosphorus with an attached mass

The investigation of black phosphorus-based (BP)-based mass sensors provides theoretical support for the development of mass-detection devices. This study examines the non-linear dynamic behavior of a rectangular single-layered BP (SLBP) with an attached mass through the utilization of molecular dynamics (MD) simulations and a nonlinear orthotropic plate model (NOPM) with a concentrated mass. The results indicate that significant deformation of an SLBP with an attached mass necessitates consideration of geometric nonlinearity, although the attached mass does not affect the deformation. Additionally, this paper discusses the impact of the attachment mass and the amplitude of harmonic force on the non-linear forced vibration of the SLBP. It is observed that as the attachment mass increases, the nonlinear vibration resonance frequency decreases, while the peak amplitude increases. Furthermore, the thermal nonlinear vibration of SLBP with an attached mass has been investigated, revealing that an increase in the attached mass leads to a decrease in the nonlinear vibration frequency but an increase in the amplitude of the nonlinear vibration of SLBP with an attached mass. Overall, comparison with MD simulation results, this investigation suggests that NOPM with a concentrated mass effectively describes the nonlinear vibration behavior of an SLBP with an attached mass, providing theoretical support for designing such devices to detect attached masses.

Design and Fabrication of Ultralow Temperature Vibration Sensor Based on Self-Excited Vibration Resonance Frequency Test

Design and Fabrication of Ultralow Temperature Vibration Sensor Based on Self-Excited Vibration Resonance Frequency Test

A miniature piezoelectric actuator with fast movement and nanometer resolution

To accomplish fast movement and high positioning capability, a miniature self-moving piezoelectric actuator (MSPA) is developed with two groups of polyphenylene sulfide (PPS) transducers operating in the symmetric bending (SB) or counter symmetric bending (CSB) vibration. Each group includes the inner and outer legs, whose vibrations are orthogonal and horizontal to the ground, respectively; this interestingly imitates the stepping and swing functions of the forelimbs and hindlimbs of the gorilla in the ‘running on all fours’ gait. To examine the validity, first, by utilizing the model on the basis of Krimhertz transmission theory, the resonant frequency of the CSB vibration was structurally tuned to approach that of the SB vibration. Then, a MSPA prototype with the size of 30 × 45 × 49 mm and the weight of 25.2 g was fabricated to assess the moving, carrying, and positioning performance. In a tethered manner, the MSPA yielded the maximal speed of 562 mm/s (18.73 body length per second), the maximal payload of 485 g (19.25 times of its own weight), and the towing force of 0.5 N (corresponding to the towing force density of 19.8 N/kg). Moreover, it achieved the turning movements (whose directions, angular speeds, and steering radii are changeable) and in-situ rotations, climbed the slope of 12.5°, and moved on the curved floor. In an untethered manner, the MSPA produced the minimal step displacement of 31.9 nm. These results demonstrate that the MPSA possesses the large speed and the nanometer resolution owing to the bionic operating principle and the employment of PPS, and provides a new approach to design lightweight piezoelectric actuators.

A cascaded Nitinol Langevin transducer for resonance stability at elevated temperatures

Across power ultrasonics and sensing, piezoelectric ultrasonic transducers commonly experience degradation in mechanical, electrical, and dynamic performance due to the relatively high sensitivity of piezoelectric materials to changes in temperature. These changes, arising for example through high excitation voltages or environmental conditions, can lead to nonlinear dynamic behaviours which compromise device performance. To overcome this, the excitation signal to the piezoelectric material is often pulsed, mitigating the influence of temperature rises. However, there remain constraints on suitable candidate piezoelectric materials for power ultrasonic devices. As a novel approach to mitigating the influence of temperature on the properties of piezoelectric materials, the phase-transforming shape memory alloy Nitinol is incorporated into the piezoelectric stack of a Langevin power ultrasonic transducer, in a cascade formation. The underlying principle is that the nonlinear hardening response of Nitinol to rising temperature can be used to dynamically compensate for the nonlinear softening of the piezoelectric materials. Thus, the dynamic response of the transducer can be linearised at elevated excitation levels. In this study, two configurations of Langevin transducer are designed and characterised. One transducer incorporates a Nitinol middle mass, and in the second, titanium. A combination of electrical and thermomechanical characterisation is undertaken, where it is demonstrated that the nonlinear softening of the piezoelectric stack can be mitigated through control of the Nitinol microstructure. The vibration amplitudes of the Nitinol-middle cascaded transducer are higher and more stable when the Nitinol is austenite rather than a combination of martensite and austenite at room temperature. It has also been shown that the vibration amplitude and resonance frequency of Nitinol-middle cascaded transducer remain stable as temperature changes from 20 °C to 45 °C, dependent of the excitation voltage. Moreover, the self-heating experiment demonstrates the resonance stability of the Nitinol-middle cascaded transducer for continuous operation.

Quantitative nanopatterning of fg-scale liquids with dip-pen nanolithography

The ability to precisely pattern nanoscale amounts of liquids is essential for biotechnology and high-throughput chemistry, but controlling fluid flow on these scales is very challenging. Scanning probe lithography methods such as dip-pen nanolithography (DPN) provide a mechanism to write fluids at the nanoscale, but this is an open loop process as methods to provide feedback while patterning sub-pg features have yet to be reported. Here, we demonstrate a novel method for programmably nanopatterning liquid features at the fg-scale through a combination of ultrafast atomic force microscopy probes, the use of spherical tips, and inertial mass sensing. We begin by investigating the required probe properties that would provide sufficient mass responsivity to detect fg-scale mass changes and find ultrafast probes to be capable of this resolution. Further, we attach a spherical bead to the tip of an ultrafast probe as we hypothesize that the spherical tip could hold a drop at its apex which both facilitates interpretation of inertial sensing and maintains a consistent fluid environment for reliable patterning. We experimentally find that sphere-tipped ultrafast probes are capable of reliably patterning hundreds of features in a single experiment. Analyzing the changes in the vibrational resonance frequency during the patterning process, we find that drift in the resonance frequency complicates analysis, but that it can be removed through a systematic correction. Subsequently, we quantitatively study patterning using sphere-tipped ultrafast probes as a function of retraction speed and dwell time to find that the mass of fluid transferred can be modulated by greater than an order of magnitude and that liquid features as small as 6 fg can be patterned and resolved. Taken together, this work addresses a persistent concern in DPN by enabling quantitative feedback for nanopatterning of aL-scale features and lays the foundation for programmably nanopatterning fluids.

Identification of pathogenic bacteria using the spectra of native DNA molecules

The purpose of detecting low-frequency (relative to infrared and ultraviolet) resonance absorption of an electromagnetic field in the centimeter wavelength range using DNA molecules at a frequency corresponding to the natural frequency of torsional vibrations of the native DNA helix is to find a relationship between the length of DNA (its spectrum) and the type of a bacterium. Instead of DNA solution, cultures of different bacteria that contained DNA were used and the resonance frequencies of torsional vibrations of the helices in DNA molecules were calculated for them. The cultures were placed in test tubes or in a cuvette and were subjected to microwave irradiation. Theoretical analysis was carried out with respect to the DNA reaction to external centimeter radiation and the resonant DNA frequencies of three types of bacteria such as E. coli M17, M. avium and Mycobacterium tuberculosis were determined. Peak absorption of the ultrahigh-frequency electromagnetic field by bacterial cultures was detected at frequencies close to the calculated natural frequencies of torsional vibrations of DNA helices of the said types of bacteria: 10.271 GHz, 10.317 GHz and 10.356 GHz, respectively.

Very High Cycle Fatigue Data Acquisition Using High-Accuracy Ultrasonic Fatigue Testing Equipment

Abstract Fatigue testing at ultrasonic frequency is a powerful method for rapid generation of high and very high cycle fatigue data. High accuracy of cyclic loading is the basis for reproducible test results, which can be obtained with closed-loop control of vibration amplitude and resonance frequency. Self-heating of test specimens can be suppressed by intermittent (pulse-pause) loading. In the present work, the high-accuracy ultrasonic fatigue testing equipment developed at the University of Natural Resources and Life Science, Vienna (BOKU) is described, and systematic investigations are presented that demonstrate the effects of cycling frequency, specimen size, and intermittent loading. Data obtained with additively manufactured (AMed) austenitic stainless steel 316L at 19 kHz are compared with electromagnetic resonation test results measured at 90 Hz. No influence of cycling frequency on fatigue lifetimes and fatigue limit was found when specimens of comparable size were used for tests at 19 kHz and 90 Hz. In contrast, the use of as-built specimens with smaller testing volume resulted in an increase in cyclic strength, demonstrating a size effect on fatigue properties. Polishing the surfaces of AMed specimens increased the fatigue limit by a factor of two. Furthermore, ultrasonic fatigue tests with intermittent loading and four different pulse lengths as well as continuous cycling were performed. The tests were conducted with wrought aluminum alloy 7075-T651 and with specimens containing small artificial surface defects. Similar lifetimes were measured in all testing series. Moreover, the same fatigue limit is found for all pulse lengths and for continuous cycling. This demonstrates that pulsed loading is a most suitable method to avoid specimen heating at ultrasonic frequency and that there is no influence on measured fatigue properties if ultrasonic loading is appropriately controlled. Measurement artifacts could be identified and avoided by measuring and recording all load amplitudes during ultrasonic fatigue tests.

The Apparatus for Thermomechanical Analysis of Clay-based Ceramics

Abstract A dynamic thermomechanical analysis (D-TMA) apparatus is described for measuring the resonant frequency of the flexural vibration and the internal damping of the sample using the impulse excitation technique (IET). Since the measurement is conducted at temperatures up to 1250 °C, an electromagnetic impulser is used for excitation. The free vibrations are registered by an electret microphone, stored and then converted into a frequency spectrum using the fast Fourier transform, from which the resonant frequency can be found. The furnace is built from refractory porous alumina bricks and alumina fiber pads. The heating elements are four SiC rods connected to a temperature controller. The temperature is measured with a Pt-PtRh10 thermocouple in close proximity to the sample.

Novel acceleration measurement method during attenuation vibration of inertial sensor based on time domain sensing mechanism

This paper for the first time reports a novel characteristic of the time domain acceleration sensing mechanism. Acceleration measurement is insensitive to changes of vibration amplitude and resonant frequency because these two parameters are updated in real time during the measurement process, which is thoroughly different from other traditional acceleration sensing mechanisms. With this characteristic, an acceleration measurement method during the process of attenuation vibration is proposed. Furthermore, the analytic expression of acceleration measuring during the process is deduced. Thus, even if the signal, which is used for driving the proof mass of the time domain sensor in the resonant state, is cut off, the sensor can still work as normal. Finally, the theoretical analyses are experimentally verified. These results provide a theory foundation for designing an accelerometer that can be used in harsh environments, e.g., during sudden malfunction of the driving power supply.

Error Correction and Reanalysis of the Vibration Analysis of a Piezoelectric Ultrasonic Atomizer to Control Atomization Rate

Dynamic mesh atomizers have been widely used in various fields because of their compact structure, low energy consumption, and low production costs. The finite element method is an important technique to analyze the factors affecting the atomization performance of dynamic mesh atomizers. However, at present, there is a lack of decisive solutions to the basic problems of boundary setting in terms of the simulation and vibration displacement characteristics of atomizers under different vibration modes. In this paper, two errors were found in the Vibration Analysis of a Piezoelectric Ultrasonic Atomizer to Control Atomization Rate paper written by Esteban Guerra-Bravo et al. in 2021. First, in the finite element analysis, the boundary condition of the atomizing sheet was set to be fixed, which is inconsistent with the actual support situation and seriously affects the vibration of the atomizing sheet. Second, in the simulation result, from the first mode to the third mode, the growth rate of the maximum displacement at the center of the atomizing sheet was as high as 77.12%, even up to 221.05%, which is inconsistent with the existing vibration theory. In view of these errors, in this paper, the working principle of dynamic mesh atomizers is analyzed and the vibration equation of the atomizing sheet under peripheral simple support is derived. Through comparison with the literature, it was proven that the boundary setting and vibration displacement of the atomizing sheet in the original paper are unreasonable. By measuring the atomizing rate of the atomizing sheet under different boundary conditions, it was proven that the peripheral freedom of the atomizing sheet should be greater than or equal to 1, namely, peripheral freedom or peripheral simply supported. The vibration displacement theory was used for the simulation, and the relationship between the vibration displacement and resonant frequency of the atomizing sheet under peripheral simple support was measured. It was found that with the increase in the resonance frequency, the maximum displacement of vibration modes with only nodal circles was larger than that of the other vibration modes, and the maximum displacement increased slightly with the increase in the number of nodal circles by about 0.98%.

Анализ систем обеспечения безопасности стендовых испытаний энергоустановок на основе топливных элементов, применяемых на автомобильном транспорте

A theoretical analysis is given related to the ways to reduce the negative impact of motor vehicle exhaust gases on the environment. The possibility of using hydrogen as an energy source for an electric power plant used in the road transport is considered. The operation of a high-power fuel cell battery is advisable on both passenger cars and trucks. However, such technologically complex systems require additional tests at the development stage for verifying the fire safety and tightness of the structure. The systems of storage, transportation, preparation of hydrogen and safety assurance during the performance of such bench tests are analyzed. Fuel cell stack test benches must be provided with additional protection against occurrence of fires and explosions. It is based on a gas-analytical fiber-optic resonant (vibration frequency) sensor that monitors the accumulation of explosive gases. The key parameters of this system are the inertness and speed of the individual elements. A block diagram of a test bench for a fuel cell stack with a power of 150 kW is presented, the hydrogen pressure is reduced to 2–2.5 atm. During the operation of the installation, it is required to ensure continuous monitoring of the pressure in the system and in its individual parts, as well as to monitor the temperature regime of the gas supply in the fuel cell itself. The description of the principle of the test stand functioning is given. Its technological modules are identified, such as a hydrogen supply system, a cooling system, an air injection system, a power plant, and a block for simulating a potential load on an electric motor of the vehicle.

A mathematical approach to estimate micro-displacement of a dental implant using electromagnetic Frequency Response Analysis

The aim of this paper is to formulate a mathematical model of dental prosthetic using single degree of freedom (SDOF) to assess the micro-displacement under electromagnetic excitation. Using Finite Element Analysis (FEA) and values from literature, stiffness and damping values of the mathematical model were estimated. For ensuring the successful implantation of dental implant system, monitoring of primary stability in terms of micro-displacement is crucial. One of the most popular techniques for the measurement of stability is the Frequency Response Analysis (FRA). This technique assesses the resonant frequency of vibration corresponding to the maximum micro-displacement (micro-mobility) of the implant. Among the different FRA techniques, the most common method is the Electromagnetic FRA. The subsequent displacement of the implant in the bone is estimated by equations of vibration. A comparison has been made to observe the variation in resonance frequency and micro-displacement due to varying input frequency ranges of 1–40 Hz. The micro-displacement and corresponding resonance frequency were plotted using MATLAB and the variation in resonance frequency is found to be negligible. The present mathematical model is a preliminary approach to understand the variation of micro-displacement with reference to electromagnetic excitation force and to obtain the resonance frequency. The present study validated the use of input frequency ranges (1–30 Hz) with negligible variation in micro-displacement and corresponding resonance frequency. However, input frequency ranges beyond 31–40 Hz is not recommended due to large variation in micromotion and corresponding resonance frequency.