Frequency Response Function Research Articles

Non-stationary response determination of nonlinear systems endowed with fractional derivative elements subjected to evolutionary stochastic excitation

This study proposes a statistical linearization-based approach for the analysis of the stochastic response of nonlinear systems endowed with fractional derivative elements under non-stationary stochastic excitation characterized by non-separable power spectral density. The method involves iteratively solving a time-varying fractional-order equivalent linear equation obtained by statistical linearization. Specifically, an analytical solution for the response power spectrum of the fractional-order linear system is developed within the frequency-domain random vibration context where the analytical time-varying frequency response function (FRF) is formulated as a convolution integral involving a modulated Fourier kernel and the impulse response function (IRF). The analytical solution for the IRF is obtained through eigen-analysis of the associated fractional linear system. To demonstrate the method’s efficacy, we examine fractional time-invariant/time-variant linear systems, along with a nonlinear system exhibiting cubic stiffness (Duffing oscillator) subject to a stochastic excitation with non-separable power spectral density of the Spanos-Solomos and Conte-Peng kinds. Pertinent Monte Carlo simulations demonstrate the accuracy and applicability of the proposed method.

Sensitivity analysis of frequency response functions with imaginary parts decoupling based on multicomplex-step perturbation

Imaginary perturbation is used in the complex step differentiation method to compute first-order derivatives, widely known as an effective approach for sensitivity analysis in structural dynamics. However, coupling of imaginary parts occurs in the damped frequency response functions when employing this method. To mitigate this coupling, a novel approach for sensitivity analysis based on multicomplex-step perturbation is proposed in this paper, for sensitivity analysis of Frequency Response Functions in structural dynamics. The structural parameters are perturbed in multicomplex domain, the dimensions of structural matrices are expanded using the Cauchy Riemann matrix representation, the equation of motion for sensitivity analysis in frequency domain is transformed to matrix operation in field of real numbers, imaginary term will not exist in the equation of motion for sensitivity analysis, the imaginary part of the frequency response function and the imaginary part of the perturbation are decoupled, the structural frequency response functions and the corresponding sensitivities are obtained from the dimension-expanded equation of motion. A truss structure and a solar wing are adopted to verify the accuracy of the proposed method. Results show that the sensitivity of FRFs can be effectively calculated using the proposed method. Compare to the finite difference method, the proposed method is not depended on the step-size selection procedure. The multi-order and mixed-order sensitivity matrices, especially Hessian matrix can also be obtained using the proposed method.

Simplified soil–structure interaction modeling techniques for the dynamic assessment of end shield bridges

In this paper, the dynamic behavior of four railway bridges with integrated retaining walls, considering the effect of soil–structure interaction (SSI), is investigated both numerically and experimentally. Among these bridges, two are single-span, and the remaining two are three-span. Each bridge is equipped with numerous accelerometers and is excited by a hydraulic actuator across various frequencies. Full 3D solid Finite Element (FE) models incorporating the railway bridges and surrounding soils are developed and calibrated using the Frequency Response Functions (FRFs) from each accelerometer. Furthermore, simplified 3D solid and 2D beam models are created for each railway bridge, incorporating springs and dashpots to account for the effect of surrounding soils. The values for these springs and dashpots are obtained from simple equations, except for the impact of the backfill soil in the simplified 2D beam models, which are derived from the impedance functions of the soil medium. The performance of these simplified models is then compared to the calibrated 3D models in terms of modal properties of the first bending mode and the maximum acceleration response during high-speed train passages. The results indicate that the simplified models closely align with the calibrated models in terms of modal properties and high-speed train passage response and can be used as simple and efficient alternatives for practical usage in bridge design.

Comprehensive analysis of a butterfly-shaped piezoelectric shunting vibration absorber for robust vibration reduction and isolation: Theoretical and experimental validation

The Piezoelectric Shunting Vibration Absorber (PSVA) has garnered attention for its effectiveness in vibration control. This paper aims to propose a novel PSVA capable of simultaneously amplitude reduction and vibration isolation under various conditions. The PSVA consists of a butterfly-shaped link component and a piezoelectric stack, connected to the structure to be damped via bolts. Subsequently, an equivalent schematic diagram of the PSVA is established, and its equivalent stiffness is determined. Taking a single-degree-of-freedom structure as an example, considering the dynamic stiffness of the shunting circuit, a dynamic model of the electromechanical coupled system is developed, obtaining the system’s acceleration response and force transmissibility frequency response functions. Following this, experimental equipment is designed and fabricated, and the performance of the PSVA is tested under various excitation conditions. Finally, inspired by the experimental results, a segmented inductance circuit is designed and tested for its capability to broaden the vibration control bandwidth.

Damage detection and localization in sealed spent nuclear fuel dry storage canisters using multi-task machine learning classifiers

Spent nuclear fuel (SNF) assemblies (FAs), composed of bundled radioactive fuel rods, are stored in stainless-steel canisters as an interim dry storage option until permanent storage solutions are available. Accidental damage to these canisters may occur during handling or transportation events. If such events occur, it is necessary to assess the integrity of FAs before long-term storage. Since the canisters are sealed shut and can only be opened in special handling facilities, non-destructive evaluation (NDE) is critical for detecting the FAs from the canister's exterior surface. In this study, two multi-task machine learning (ML) classifiers, a k-nearest neighbors (k-NN) and a convolutional neural network (CNN), are developed to simultaneously detect and localize internal FA damage. The classifiers were trained and tested on a dataset collected via experimental modal analysis on a 2/3-scale mock-up canister. The canister was excited from the bottom plate while accelerometers were also attached on the bottom plate at arbitrary locations to record the structural response. The differences in frequency response functions (FRFs) between an intact fully loaded canister basket (FLCB) system and the canister with simulated internal damage were calculated and used as input to the ML models. Results showed that both classifiers achieved high accuracy on the testing set. The k-NN classifier produced macro-F1 scores of 1.00 for the damage detection task and 0.996 for the localization task. The macro-F1 scores of the CNN were 0.991 for damage detection and 0.964 for damage localization. Additionally, dropout layers were added to the fully connected layers of the CNN to introduce model uncertainty. By testing the model 1,000 times, probability density functions (PDFs) were generated, and it was confirmed that the CNN produced confident predictions in both the damage detection and localization tasks. This multi-task ML method contributes to advancing NDE of SNF canisters and holds potential for field applications in inspecting actual SNF canisters.

Diagnosis of Voltage Losses of the Proton Exchange Membrane Water Electrolyzer with Nonlinear Frequency Response Method

Proton exchange membrane water electrolyzer (PEMWE) takes a central place in the hydrogen economy as a crucial technology for green hydrogen production. However, this technology still faces challenges, such as the cost of the materials, performance losses at high current densities, and durability. To overcome these obstacles, better comprehension of the phenomena occurring in the PEMWE is necessary. Typical electrochemical methods, such as polarization curves and high-frequency response measurements, lack detailed information about the individual contributions to the overall voltage losses and cannot point out the causes of the performance shortcomings. Therefore, the development of advanced diagnosis techniques for PEMWE is of importance both for the state of health analysis during the operation, as well as for the testing of new materials.In this work, a nonlinear frequency response (NFR) method was applied for the diagnosis of a lab-scale PEMWE. The NFR method represents an extension of the electrochemical impedance spectroscopy to the nonlinear domain by investigating the second-order frequency response function (FRF) in addition to the first-order FRF (equivalent to the impedance) [1]. Typical features corresponding to processes occurring in the PEMWE were observed in both the first- and the second-order FRFs. The experimental observations were interpreted based on a simple nonlinear model. The features observed at frequencies higher than 0.1 Hz were attributed to the electrochemical half-reactions, while a high current density feature observed at lower frequencies, could be attributed to the mass transport. During the analysis, the first-order FRF (impedance) was found not to be sensitive enough for the discrimination of the different sets of parameters and the second-order FRF had to be included for better parameter identification. The obtained parametrized model is dynamic and nonlinear and, thus, it can be utilized for model predictive control of the PEMWE and optimization of the overall green hydrogen production system.[1] Vidaković-Koch, T., Miličić, T., Živković, L.A., Chan, H.S., Krewer, U., Petkovska, M., Cur. Opin. Electrochem., 2021, 30, 100851

Vibro-acoustic modeling of the turbulent excited cavity-plate-exterior space coupled system

To mitigate flow-induced noise in sonar self-noise, this study introduces a vibro-acoustic modeling technique for sonar cabins. This technique couples a turbulent-flow-excited plate with the interior cavity and the exterior field within a unified model. Employing the Rayleigh-Ritz method, the Chebyshev spectral method, and the Rayleigh integral, the model accounts for general boundary restraints, wall impedances, and reinforcement configurations. Flow-induced responses are determined through the Monte Carlo quadruple integration of frequency response functions and the cross-spectral density model, which characterizes turbulent pressure fluctuations. The convergence and reliability of the present method are verified, achieving excellent agreement with numerical methods and previous results. The study reveals that periodic impedance arrangements in the cavity significantly attenuate sound wave propagation, especially when periodic arrangements are added at low frequencies. The reinforcement configuration perpendicular to the flow direction minimizes low-frequency vibrations. However, the influence of reinforcement on acoustic energy within the cavity is marginal and could potentially lead to increases under simply supported boundary conditions. This method effectively addresses vibro-acoustic challenges in sonar cabins, offering substantial practical value for the development of low-noise sonar systems.

Damage identification of reinforced concrete slabs using experimental modal testing and finite element model updating

Condition assessment and health monitoring of reinforced concrete structures is an essential part of their effective maintenance throughout their service life. Vibration-based damage detection and health monitoring is one of the most popular global approaches where experimentally measured modal parameters, such as frequencies, mode shapes, etc. are compared to their corresponding finite element counterparts to estimate possible stiffness loss. The present investigation implements a vibration-based parameter estimation algorithm for updating a finite-element (FE) model for damage assessment of reinforced concrete slabs using measured frequency response functions (FRF) data through a mixed numerical-experimental technique. An inverse eigen-sensitivity algorithm has been implemented to minimize the error function realized as the weighted differences in the mode shapes and frequencies of the FE model and the modal test data. Three reinforced concrete slabs were subjected to real physical damage conditions to verify the efficacy of the proposed methodology. The technique is found to be resilient in the presence of modal and coordinate sparsity. In general, damage can be assessed even if the portions of the structure are inaccessible to the users, thereby extending the possibility of its application to most of the practical configurations of reinforced concrete slabs.

The Effect of Proportional, Proportional-Integral, and Proportional-Integral-Derivative Controllers on Improving the Performance of Torsional Vibrations on a Dynamical System

The primary goal of this research is to lessen the high vibration that the model causes by using an appropriate vibration control. Thus, we begin by implementing various controller types to investigate their impact on the system’s reaction and evaluate each control’s outcomes. The controller types are presented as proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers. We employed PID control to regulate the torsional vibration behavior on a dynamical system. The PID controller aims to increase system stability after seeing the impact of P and PI control. This kind of control ensures that there are no unstable components in the system. By using the multiple time scale perturbation (MTSP) technique, a first-order approximate solution has been obtained. Using the frequency response function approach, the stability and steady-state response of the system at the primary resonance scenario (Ω1≅ω1,Ω2≅ω2) are considered as the worst resonance and addressed. Additionally examined are the nonlinear dynamical system’s chaotic response and the numerical solution for various parameter values. The MATLAB programs are utilized to attain simulation outcomes.

Reusability of Scrap Rubber, Tire Shredding, Recycled PVC and Fly Ash for Development of Composites with Vibration Damping Ability.

The study focuses on harnessing recycled materials to create sustainable and efficient composites, addressing both environmental issues related to waste management and industrial requirements for materials with improved vibration damping properties. The research involves the analysis of the physico-mechanical properties of the obtained composites and the evaluation of their performance in practical applications. Composite materials were tested in terms of their tensile strength and vibration damping capabilities, considering stress-strain diagrams, vibration amplitudes, frequency response functions (FRFs) and vibration modes. The research results have shown that by adding PVC and FA to the rubber-based matrix composition, the stiffness decreases and elasticity increases. The use of FA in the structure of composite materials causes an increase in the vibration damping possibilities due to the fact that it contributes to the chemical properties of the analyzed composite materials. Additionally, the use of PVC results in increased material elasticity, as evidenced by the higher damping factor compared to materials containing only rubber. Simultaneously, the addition of FA and PVC in specific proportions (60 phr) can lead to a decrease in stiffness and a greater increase in the damping factor. The incorporation of PVC and fly ash (FA) particles into rubber-based matrix composites reduces their stiffness and increases their elasticity. These effects are due to the fact that FA particles behave as extensions of chemical bonds during traction, which contributes to the increase in yield elongation. In addition, the use of flexible PVC increases the elasticity of the material, which is evidenced by the increase in the damping factor.

Apply frequency response function schemes for damage detection in composite nanoscale-pipes under transient conditions

Knowledge of Nanoscale-structures sustainability is strongly associated with the reliability and the performances of Nano-electro-mechanical systems such as Nanoactuators and Nano-sensors that are widely used in bio-applications. Therefore, the damages in these types of infinitesimal systems must be quickly and accurately detected, located, and repaired. In this study, a novel damage detection framework in Carbon Fiber Reinforced Polymer (CFRP) composite Nanoscale-Pipes (CNP) subjected to the fatigue effect of water internal pressure and thermal effect via Nanoscale-electrical capacitance sensors (NECS). First, a finite element model (FEM) of CNP damage is established, then the electrical potential difference (EPD) between the Nanoscale-electrodes (NEs) pairs before and after damage is measured. The distributed NECS measuring nano-electrodes are installed around the CNP and load the transient external excitations between each other. It is proposed and applied the transfer function (TF) of the CNP as an "open loop control" system to reflect the evolution of damage. The accuracy and reliability of the suggested technology are verified through the experimental results available in the literature. The results show that when the damage under NEs pairs has begun to grow, the signal amplitude value will change suddenly and sensitively, which demonstrates the effectiveness of the proposed method and the good potential for engineering applications.

A Method to Obtain Frequency Response Functions of Operating Mechanical Systems Based on Experimental Modal Analysis and Operational Modal Analysis

The characteristics of a mechanical structure under operating conditions may differ from those in a static state. It is often more desirable to obtain the frequency response function (FRF) of the operating structure in engineering applications. While operational modal analysis (OMA) can estimate modal parameters during operation, it fails to provide mass-normalized mode shapes for FRF synthesis. This paper presents a new method using experimental modal analysis (EMA) to compensate for the absent information in OMA. It categorizes operational mode shapes into changed ones and those that remain the same compared to the static state, applying different scaling techniques accordingly. This method adapts to changes in dynamic characteristics without altering the operating conditions. Stability is emphasized throughout the process. Two examples are provided to verify the method, considering noise and incompleteness in measurement, and disturbances in dynamic properties. The proposed method is proven to be feasible and reliable to capture the changes in operational FRFs.

Research on vibration response distorted similitude of cylindrical shells under modal distribution disorder

Similitude theory enables local-scale models to reflect the dynamic characteristics of full-scale models and is widely employed in engineering experimentation. However, shell structures, constrained by wall thickness, cannot undergo experiments through proportional downsizing. Existing similitude studies with retained wall thickness exhibit only minimal distortion, and accurate prediction of vibration responses is hindered by modal distribution disorder. To address these challenges, a method based on modified frequency response functions of natural frequencies and mode shapes is proposed. Scaling laws for natural frequencies and mode shapes of cylindrical shells with retained wall thickness are established. This method yields a maximum prediction error of 4.29 % for prototype natural frequencies, compared to 50.57 % for existing methods. Predicted prototype vibration acceleration responses correspond well with theoretical calculations in both frequency and amplitude, while existing methods fail entirely. The phenomenon of modal distribution disorder and the effectiveness of the proposed method in mitigating it are verified by modal experiments and response tests. Research reveals that the sensitivity of different modal frequencies to the wall thickness scaling factor varies, serving as the cause of modal distribution disorder. The modal distribution with the same circumferential wave number is unaffected by wall thickness. Modes above the bending frequency, with axial half-wavelength consistent with bending modes, are prone to disorder due to wall thickness distortion. During wall thickness distortion, a mode originally with the lowest frequency is surpassed towards lower frequency by the mode with larger circumferential wave number and the same axial half-wave number, leading to disorder. The proposed method addresses the challenge of minimal distortion in structural vibration response and poor performance, advancing the development of distorted similitude.

Identification of modal parameters of soil specimen based on impact force

This study used vibration testing signals of soil samples under external loading to identify modal parameters (including natural frequencies and damping ratios) with different compaction degrees. Based on these parameters, a novel approach was proposed for reliable roadbed vibration compaction control and compaction process optimization. The experimental section utilized six soil samples with varying compaction degrees as experimental subjects, using the hammering method as the excitation mode. Subsequently, the frequency response function and modal parameters of the sample system were obtained through the acquisition, analysis, and parameter identification of samples’ acceleration signals. Firstly, samples with compaction degrees ranging from 88 % to 97 % primarily exhibited three modes, with the second modal frequency response displaying the weakest amplitude, and the fundamental mode being the dominant one. Additionally, parameter identification results revealed that the fundamental modal frequency exhibited a significant negative exponential growth with increasing compaction degree, while the second and third modal frequencies showed significant linear growth. Furthermore, the average damping ratio also demonstrated a tendency toward linear change with increasing compaction degree. Finally, the feasibility of modal parameters being actively used in practical engineering is discussed. Consequently, this study aimed to propose an indicator system for accurately assessing the bearing level of compacted soils from a modal dynamics perspective and to integrate modal dynamic indicators with density-class indicators into further optimization design work on road compaction processes.

Dentists who can auscultate: Microphone-based toothbrushing quality monitoring system for electronic toothbrush

Tooth brushing is a widely recognized and effective method for daily oral care. However, the lack of real-time feedback for monitoring the brushing process can hinder individuals in maintaining their oral hygiene. Currently, only high-end electric toothbrushes offer evaluation functions based on built-in sensors, making them unaffordable for the majority of people. In this paper, we propose a novel and cost-effective wearable acoustic-based system (both hardware and software) for monitoring the quality of daily tooth brushing. Our system combines a throat-microphone and a Bluetooth earphone to capture brushing noises, which are unique acoustical signals generated from the air and the human body during tooth brushing, respectively. By leveraging the distinctive characteristics of brushing sounds in these two different conductive media, we introduce an intelligent detection algorithm based on Single-Input Multiple-Output (SIMO) modeling and frequency response functions (FRFs) to detect the corresponding brushing area. Through experimentation, we have found that the divergence of FRFs provides more stable features compared to general statistical features used in previous studies. After comparing various machine learning algorithms, we have selected XGBoost as the final detection model. Additionally, we utilize the Symmetric Nearest Neighbor (SNN) filter in the post-processing stage to further reduce the jitter noise in continuous detection. The final system achieves an average precision of 98.46% when tested on tooth brushing data collected from different volunteers. To enhance user experience, we have developed an Android App with a user-friendly interface that incorporates the detection system. With a total wearable hardware cost of less than 10 dollars, our system shows great potential for integration into future smart wearable devices.

A novel iterative model updating for jointed structures using nonlinear FRFs

A novel iterative model updating method is developed to identify the local nonlinear joint properties using the frequency response functions (FRFs) of assembled structures. In this paper, the least-squares fitting method was used to transform the sensitivity matrix into a square iteration matrix to match the dimensions of the objective functions and nonlinear joint model parameters. Leveraging the Newton’s iteration, the adaptive successive over-relaxation (A-SOR) was used to ensure iteration convergence while the multi-scale parameter adjusting (MPA) strategy was developed to degrade the ill-condition of the iteration matrix. Two updating examples of phenomenological equivalence models were applied to demonstrate the effectiveness of the proposed method. The nonlinear FRFs of a lap-type bolted joint beam system with Iwan model were simulated as the objective functions to identify the local nonlinear joint properties, as well as experimental investigations of a metal rubber isolation system with a high-order polynomial model. The proposed method was validated by the good agreement of the comparison results, and it indicated a better model updating performance with a much smaller condition number of the iteration matrix.

Simple diagnosis for layered structure using convolutional neural networks

In this study, we propose a structural health monitoring and diagnostic method for layered (multi-story) structures using a convolutional neural network (CNN). The proposed method is a primary diagnostic one, and its purpose is to allow quick identification of the location of an abnormality after detecting it. An abnormality is defined as a decrease in the stiffness characteristics (spring constant) of the outer wall of a multi-story structure when it deteriorates or is damaged. The proposed method has the following features. A modal circle is generated by multiplying the frequency response functions (FRFs) simulated by a mathematical model and the FRFs from the actual structure, in frequency space, and then a CNN learns the features of the abnormality from the modal circle and diagnoses it in the actual multi-story structure. We first verified the validity of the proposed method by considering a three-story structure as a numerical example. When the method was applied to three types of abnormal conditions, it was shown that the abnormal diagnosis could be performed correctly. Next, we constructed an experimental model of a three-story structure, and realized three types of abnormal conditions similar to those in the numerical model. We verified the applicability of the proposed method and showed that correct diagnosis of an abnormality was possible. Both the validity and applicability of the proposed method were thus confirmed.

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

Modeling the dynamic interaction between machine tools and their foundations

The performance of a machine tool is directly influenced by the characteristics of the floor, subsoil, and their interaction with the installed machine. Installing a machine tool in its operational environment poses a distinct challenge that bridges mechanical and civil engineering disciplines. This interdisciplinary issue is often overlooked within the individual separate disciplines. However, effectively addressing this challenge requires a comprehensive understanding of mechanical and civil engineering principles. To address this problem, the present study proposes a method for improved modeling of the dynamic properties of the machine tool by considering the foundation and the subsoil on which it is installed. The method is based on finite element modeling. Linear models of the system components and the connections between them were used. These, supplemented with damping expressed by complex stiffness, made it possible to determine the natural frequencies, mode shapes, and frequency response functions (based on which the transmissibilities were obtained). Based on the experimentally verified models of vertical and horizontal lathes, the sensitivity analysis aimed at estimating the impact of changes in system parameters on vibration transmissibility for a floor-type and a block-type foundation was conducted. Thus, it was possible to identify those machine tool-support-foundation-subsoil system parameters that had the most significant impacts on the vibration's transmissibility. After analyzing the cases discussed, it became evident that the transmissibility of vibrations is primarily influenced by two key factors. First and foremost, the properties of the structural loop of the machine tool played a significant role. Additionally, the characteristics of the subsoil on which the foundation was situated emerged as a crucial determinant in the observed vibration transmissibility.

An XYZ parallel nanopositioning stage with hybrid damping

It is well known that lightly damping linear dynamics of a piezo-hysteresis-compensated flexure-based stage severely limits its motion control bandwidth. To address it, a novel damped XYZ parallel flexure-based nanopositioning stage (3⊥(P⊥K∥K), P for prismatic, K for Cardan or Universal) with hybrid passive damping, which is composed of shearing–squeezing hinge damping and in-band damping by graded local resonators (GLRs), is presented. The dynamic modeling and optimization design are implemented based on the maximization of motion amplification ratio, first-order natural frequency, and inverse in-band H2 norm of frequency response function (FRF). The optimized GLR module has distributed dynamic characteristics. The approximate motion decoupling is verified by Jacobin matrix analysis and experiments. The static/scanning-frequency dynamic experiments and step/triangular trajectory tracking control with the low-order controllers for all-hinge damping and hybrid damping stages are implemented. The experimental results indicate the small crosstalks due to hybrid passive damping, as the static crosstalks in X-to-Z and Y-to-Z are 0.293% and 0.276%, respectively, and the dynamic crosstalks in X-to-Z and Y-to-Z are 0.922% and 0.910%, respectively. The capability of improving positioning precision and expanding control bandwidth by hybrid damping only with a low-order controller is also validated experimentally.