Theoretical Resonant Frequency Research Articles

Acoustophoresis of monodisperse oil droplets in water: Effect of symmetry breaking and non-resonance operation on oil trapping behavior.

Acoustic manipulation of particles in microchannels has recently gained much attention. Ultrasonic standing wave (USW) separation of oil droplets or particles is an established technology for microscale applications. Acoustofluidic devices are normally operated at optimized conditions, namely, resonant frequency, to minimize power consumption. It has been recently shown that symmetry breaking is needed to obtain efficient conditions for acoustic particle trapping. In this work, we study the acoustophoretic behavior of monodisperse oil droplets (silicone oil and hexadecane) in water in the microfluidic chip operating at a non-resonant frequency and an off-center placement of the transducer. Finite element-based computer simulations are further performed to investigate the influence of these conditions on the acoustic pressure distribution and oil trapping behavior. Via investigating the Gor'kov potential, we obtained an overlap between the trapping patterns obtained in experiments and simulations. We demonstrate that an off-center placement of the transducer and driving the transducer at a non-resonant frequency can still lead to predictable behavior of particles in acoustofluidics. This is relevant to applications in which the theoretical resonant frequency cannot be achieved, e.g., manipulation of biological matter within living tissues.

A combined tri-dimensional fiber Bragg grating accelerometer for multi-directional measurements

In this research, a novel combined tri-dimensional accelerometer designed for vibration measurement in conventional rotating machinery is reported. The sensor utilizes a flexible hinge and fiber Bragg gratings (FBGs) which operates in three dimensions (3-D), allowing measurement along the X-axis, Y-axis, and Z-axis. The working principle and theoretical models of the sensor have been introduced and established. And then, the design and optimization of the sensor were achieved through nonlinear programming in MATLAB. To validate the theoretical resonant frequencies, Finite Element Method (FEM) analysis was employed, resulting in an accuracy that yielded an error of less than 5%. Experimental testing confirmed resonant frequencies of approximately 330 Hz, 350 Hz, and 560 Hz in the X-axis, Y-axis, and Z-axis, respectively, with sensitivities of 285.2 pm/g, 325.3 pm/g, and 202.2 pm/g within a frequency range of 0 Hz to 100 Hz. The sensor demonstrated a lateral interference level of less than 5.8% in all three-dimensional orientations. The high sensitivity and adaptability of the sensor make it suitable for monitoring mechanical equipment conditions, providing valuable insights for assessing the health and performance of rotating machinery.

Miniaturized methane detection system based on photoacoustic spectroscopy

AbstractAs an important means of trace gas detection, photoacoustic spectroscopy mainly detects gas concentration indirectly through the thermal effect of light. Methane detection system based on photoacoustic spectrum has great application prospect in environmental pollution detection and industrial production. As a container for loading methane, the shape and quality of the photoacoustic cell will have a huge impact on the final detection results. To improve the operability of the photoacoustic spectrum technology in practical application, this system improves the traditional photoacoustic cell. The integrated micro photoacoustic cell designed with 3D printing technology has a volume of 9 cm3 and a theoretical resonance frequency of 11 000 Hz. Based on LabVIEW platform, a frequency sweep program and a concentration acquisition program were set up in the experiment. The frequency sweep experiment was carried out in an environment filled with methane in the photoacoustic cell. Based on the theoretical knowledge of photoacoustic spectroscopy, it can be known that the sound pressure detected by microphones is proportional to the concentration of methane in the photoacoustic cell. Methane with gradient concentration is passed into the photoacoustic cell for concentration calibration experiment, and the second harmonic peak detected at different concentrations is linearly fitted, and the line R2 = 0.99919. By calculating Allan variance, it can be obtained that the minimum detection of the system can reach 6.89 ppm when the integration time is 49 s.

Optimal Design and Analysis for a New 1-DOF Compliant Stage Based on Additive Manufacturing Method for Testing Medical Specimens

In situ nanoindentation is extensively employed for online observing deformation and mechanical behaviors of bio-materials. However, the existing designs of the positioning stages have limited performances for testing soft or hard biomaterials. Consequently, this paper proposes a new structural design of a compliant one degree of freedom (01-DOF) stage with faster response. In addition to a new design, this article applies an analytical method to estimate the kinematic and dynamic behaviors of the stage. Firstly, the 01-DOF stage is designed with two modules, including a displacement amplifier with six levers and a symmetric parallelogram mechanism. Secondly, a kinetostatic diagram of the stage is built by pseudo-rigid-body method. Then, the dynamic equation of the proposed stage is formulated using the Lagrange method. In order to speed up the response of the indentation system, the structural optimization of the stage is conducted via the Firefly algorithm. The results showed that the theoretical first-order resonant frequency is found at about 226.8458 Hz. The theoretical consequences are nearby to the verified simulation. Besides, this achieved frequency of the presented stage is greater than that of previous stages. In an upcoming study, the prototype will be fabricated by additive manufacturing method or a computerized wire cutting method in order to verify the analytical results with experimental results.

Inverse Problem in Resonant Ultrasound Spectroscopy With Sampling and Optimization: A Comparative Study on Human Cortical Bone.

The Bayesian inference with prior knowledge has been proposed recently to solve the inverse problem in resonant ultrasound spectroscopy. It allows inferring the elastic properties of high damping materials, such as cortical bone with less dependence on the initial guessed values. In this method, the estimation of the stiffness coefficients is expressed as a probabilistic solution to the inverse problem, which can be achieved by sampling or optimization methods. However, the detailed performance comparison of these two strategies applied to high damping materials has not been fully studied. In this work, the full stiffness tensor of 52 transversely isotropic cortical bone specimens was obtained using Markov chain Monte Carlo (MCMC) sampling and particle swarm optimization (PSO), respectively. Results showed that the local probability distributions of stiffness coefficients estimated by the two methods are consistent. Compared with MCMC, the average calculation speed of PSO is ten times faster [614 s ± 59 s (MCMC) versus 53 s ± 22 s (PSO)]. The mean standard error between theoretical and experimental resonant frequencies was slightly smaller for PSO compared with MCMC. In conclusion, PSO, a global optimization strategy, is suitable to solve the inverse problem for high damping materials.

Study on vibro-acoustic characteristics of bamboo-based angklung instrument

The frequency (or pitch) content of bamboo angklung musical instruments was analyzed. The pitch of the rattle tubes was determined via a Pico oscilloscope recording both the time and frequency spectrum. Fast Fourier transform analysis identified the fundamentals and overtones of the individual tubes, which were compared with the calculated theoretical resonance frequency. The pitch, due to the coupling effects of two rattle tubes, slightly varied from the pitch of the individual rattle tubes. Although both rattle tubes (played simultaneously) displayed the fundamental frequencies in both tubes, the individual tubes played separately did not produce the exact frequency obtained from both tubes played simultaneously. The spectrum of both tubes produced sound output from the individual tube, which is shown by two prominent peaks, corresponding to the pitch of the individual tube. Although the long and short tube show an individual fundamental frequency of 528 Hz and 1095 Hz, respectively, for C5 tube (when played separately), the coupling of both tubes produced the first and second peaks (when played simultaneously) at 546 Hz and 1093 Hz. Due to the disparity of the fundamental frequency, the inner diameter and length of the tube was utilized for the theoretical resonance frequency calculation.

Analytical modelling and experimental validation of compliance-based low-frequency resonators for water circuits

Transmission losses of compact compliance-based resonators in water circuits are investigated. Experiments are performed to measure the anechoic transmission losses (TLan) of flexible-plate resonators and a gas resonator designed for frequencies between 10 and 100 Hz. The measurements are compared to theoretical results based on a lumped-element model and a finite-element model. The TLan is measured using a robust form of the multi-microphone method, which gave identical results for open and closed pipe acoustic terminations at the transmission side of the setup. When an estimate of the reflection coefficient at the termination is known, good results are obtained with only one transmission-side microphone. When TLan is high, a single microphone is sufficient on each side. For the flexible-plate resonators the TLan measurements are in agreement with theory except close to resonance, where the transmission signals are below the detection limit. Due to assumptions of a rigid cavity wall and a clamped top-plate, the theoretical resonance frequencies are too high except for the thinnest plate which displays static deformation stiffening. This deformation stiffening limits the possibility to lower the resonance frequency by using a thin flexible plate in a circuit with high static pressure. Low resonance frequencies are easier to reach with a gas resonator, in which a piston separates the water from a volume filled with air. For the gas-resonator, the measurements agree with the theoretical predictions when assuming a significant damping. The friction between the air-water-separation piston and cavity wall is suspected to cause this damping. Theory predicts that the TLan of both resonators designed for same resonance frequencies in absence of losses are equivalent. They therefore have quite similar performances except close to the resonance frequency. The flexible-plate resonator has a higher quality factor and higher (TLan) around the resonance frequency. The gas resonator is more complex and needs more maintenance but allows fine tuning of the resonance frequency by varying the gas volume.

Using an Equivalent-Circuit Model to Design Ultra-Wide Band-Stop Frequency-Selective Surface for 5G mm-Wave Applications

In this work we propose a system of two frequency-selective surface (FSSs) with an ultra-wide band-stop response for 5G millimeter-wave applications. The analyses are based on the equivalent circuit method, which predicts the transmission characteristics for a plane wave with normal and oblique incidence, and the scattering matrix technique, which provides the result of the cascaded structure. The geometries used in the single-layer FSSs are simple to design, and a series of basic equations are described in order to calculate the inductance and capacitance of conducting strips. FSSs prototypes were fabricated and measured in an anechoic chamber. The first FSS is shaped with the four-arms star geometry, which has a resonant frequency at 27.92 GHz for both measured and simulated results. The second FSS is based on the quasi-square geometry, whose resonant frequency for the experimental and numerical results are 35.68 GHz and 35.76 GHz, respectively, for the transverse electric polarization. These two single-layer FSSs present theoretical resonant frequency at 28 GHz (FSS #1) and 35.8 GHz (FSS #2). Cascading of the two FSSs was realized by using an air gap whose effect was analyzed. A gap space in the order of about λ/4 matched with the predicted resonant frequency of the individual structures. Numerical and measured results show excellent agreement with a maximum error of 1.03%. All measured results closely follow those of simulated ones, thus validating the design approach and applications.

Longitudinal-transverse coupled vibrations of variable-height asymmetric beams: Modeling, analysis, and case study

In general, the cross-sectional centroids of the variable-height asymmetric beam change in the height direction. The Timoshenko beam theory does not consider the influence of the varying cross-sectional centroids and cannot accurately reveal the vibration of variable-height asymmetric beams. Considering that the cross-sectional centroids are dislocated, we propose a novel dynamic model for the variable-height asymmetric beam element. The proposed dynamic model is based on the rigid-plane assumption and can reflect its main mechanical characteristics. The non-collinear axial forces produce the complementary moment. The rotational radiuses of the two ends of longitudinal fibers are not equal. After retaining the main mechanical characteristics, the variable-height element is roughly treated as a constant-height element to simplify the governing differential equations. A bonded-type piezoelectric transducer with variable-height asymmetric beams is taken as an example to verify the developed dynamic model. The theoretical and experimental resonant frequencies are 39338 Hz and 38704 Hz, respectively, with a difference of 634 Hz and a relative error of 1.638%. The calculated displacement vibration shapes are consistent with the experimental results. Finally, the modeling differences between variable-height symmetric and asymmetric beams are clarified from three aspects.

Double-beam modeling and experiments of resonance behaviors of AFM-based nanowires

This paper proposes a novel double-beam model to study the dynamics of a nanowire measured by an atomic force microscope (AFM). Analytical expressions for the dynamics of system are derived considering the nanowire surface properties. The AFM tip-nanowire interactions affected also by the nanowire surface properties are modeled as a spring, which is calculated based on the extended Hertzian contact theory and verified via experiments. The resonance behaviors of the system are then investigated both theoretically and experimentally, and the theoretical resonance frequencies agree well with experimental ones. Dynamic studies based on the proposed model show that, the special surface properties of the nanowire at nanoscale are mainly due to the distributed force induced by the residual surface stress. Also, the relationship between the driving deflection of AFM cantilever and the boundary conditions of the nanowire is discussed, and it is found that the dynamic experiments propose an advantage of much smaller deflection compared to that of the static experiments, which may prevent possible occurrence of the nanowire boundary lift-off.

Effective determination of Young’s modulus and Poisson’s ratio of metal using piezoelectric ring and electromechanical impedance technique: A proof-of-concept study

Accurate determination of Young’s modulus and Poisson’s ratio for metals is important to evaluate their performance and ensure the safety and reliability of the metallic structures. In this study, a new effective method for determining these material properties of metals is proposed using piezoelectric ring and electromechanical impedance (EMI) technique. In the method, two types of specimens were prepared. The first type was the cylindrical metal bar that incorporates the piezoelectric ring to form the bar-type transducer to realize the dynamic Young’s modulus measurement utilizing one-dimensional longitudinal vibration. The second type was the metal disk, which coupled with the piezoelectric ring to form the disk-type transducer to realize the dynamic Poisson’s ratio measurement utilizing two-dimensional radial vibration. Theoretical models were established to obtain the relationships between the resonance frequencies and the material properties. The EMI technique was adopted to measure these frequencies. By plotting the curves of the theoretical and experimental resonance frequencies versus the Young’s modulus and Poisson’s ratio, and identifying the intersection point of these two curves, the dynamic Young’s modulus and Poisson’s ratio can be predicted. Comparisons between the static and dynamic material properties are presented, and their differences are analyzed. This work demonstrates the feasibility of using piezoelectric ring and electromechanical impedance technique for effective determination of Young’s modulus and Poisson’s ratio of metal. Further efforts will improve the proposed EMI technique in hope of promoting the application in high portability measurement.

Oscillation properties of water droplets on a superhydrophobic surface and their correlations with droplet volume

In-depth understanding is limited to the oscillation properties of a droplet on a superhydrophobic surface, which are closely related to the contact line movement, droplet volume, and substrate amplitude, to name only a few factors. In the present work, we investigate the characteristics of droplet resonance amplitude, mode range, and resonance frequency, as well as their correlations with droplet volume (from 20 to 500 μL). In particular, the theoretical resonance frequency is mainly concerned and addressed. To this end, a model based on general hydrophobic surfaces proposed by Noblin et al. is employed, with its applicability to superhydrophobic surfaces examined. We propose a concept “virtual stationary point” for analyzing the errors from this model, with which we modify the model through using the correction coefficients. The main results are concluded as follows. 1) Under resonance, the change rate in droplet height rises with the increase of droplet volume and reduces with the increase of oscillation mode number. 2) Each number of oscillation mode corresponds to a frequency range, and the ends of adjacent mode ranges are connected to each other. These frequency ranges decrease with the increase of droplet volume. 3) Resonance frequency, <i>f</i>, decreases with the increase of droplet volume, <i>V</i>, and they are related approximated by <i>f</i> -<i>V</i><sup>–0.4</sup> under high mode numbers, which is different from <i>f</i> -<i>V</i><sup>–0.5</sup> as found on general hydrophobic surfaces. 4) Direct application of Noblin model to a superhydrophobic surface results in nonnegligible errors, because geometric characteristics in this case are different from those on a general hydrophobic surface, which leads to inaccuracy in counting the number of surface wave segments. In contrast, results from modified Noblin model accord well with experimental results.

A method for identifying false positive frequencies extracted from resonant ultrasound spectra for highly dissipative materials

Resonant ultrasound spectroscopy (RUS) is a nondestructive technique, and one of its applications is to determine the elastic constants of a solid by measuring its free-vibration resonant frequencies. For dissipative materials, the vibration spectrum peaks are broad and strongly overlapped, and in some cases, the resonant frequencies extracted by a linear prediction filter are considered to be false positive frequencies that cannot be paired with theoretical resonant frequencies. The inverse identification of elastic constants is also seriously influenced when these false positive frequencies are wrongly paired with theoretical resonant frequencies. In this paper, a new selection index and an extraction process for RUS resonant frequencies are studied to discard false positive frequencies. The change in the relative error between the theoretical and extracted frequencies was employed to update the traditional frequency selection index. An extraction process was proposed by combining a trial-and-error method and a Bayesian method. A bone-mimicking material (quality factor, Q ≈ 30) and the simulated resonant spectra were adopted to validate the proposed method. The performance of identifying false positive frequencies was effectively improved by using the new selection index. Moreover, the proposed process can be applied to enhance the pairing and estimation accuracy for RUS. Calculations of the elastic constants for distinct specimens presented good consistency. The new method proposed in this paper provides a better analysis of the elastic constants in highly dissipative materials and can help to extend the application range of RUS.

Enhanced coagulation by high-frequency ultrasound in Microcystis aeruginosa-laden water: Strategies and mechanisms

Ultrasonic treatment has attracted much attention because of its physical and chemical effects that are distinct from those of chemical agents. In particularly, high-frequency ultrasound is known as an effective method because the theoretical resonance frequency of the gas vesicles in Microcystis aeruginosa is in the high frequency range (>100 kHz), which causes gas vesicles collapse and changes the settleability of the algal cells. In this work, the effects of the ultrasonic frequency, acoustic power density and duration on enhancing coagulation to remove turbidity in algae-laden water were studied. In order to explain the mechanism, the morphology of algae cells, the changes in extracellular organic substances, the zeta potential and the formation of hydroxyl radicals were analyzed systematically. Finally, Zeta potentials and flocs morphology after adding PAC were investigated to verify the mechanism. The results showed that the frequency exhibited fewer effects than power and duration on coagulation. SEM images showed that there were more severe cellular damages at 430 and 740 kHz than other frequencies. Sonication could cause the collapse of gas vesicle inside the cell, which was due to the instantaneous high pressure generated by the ultrasonic cavitation instead of the resonance. Furthermore, sonication would result in an increase in proteins in extracellular organic matter (EOM) with continuous ultrasonic irradiation, indicating that a small amount of proteins could promote coagulation and that the accumulation of proteins would inhibit coagulation. Free radical content testing showed that the production of excessive free radicals was often accompanied by a deterioration of the coagulation. The proper mechanical effects were the main mechanism of ultrasonic enhanced coagulation. Thus, it was recommended that the appropriate ultrasonic condition was the one that resulted in a small amount of protein leakage and little generation of free radicals, which occurred at 740 kHz and 0.02 W/mL in approximately 5 min, and would significantly enhance the turbidity removal rate in algae-containing water from approximately 80–90%.

Electromechanical equivalent circuit and coupled vibration of the radially composite cylindrical piezoelectric transducer

Electromechanical equivalent circuit for the radially composite cylindrical piezoelectric transducer in coupled vibration is deduced. The transducer is composed of a piezoelectric cylinder sandwiched by two concentric metal cylinders. Equivalent elasticity method is used to study the coupled vibrations of the three cylinders. A ratio named the mechanical coupling coefficient is introduced to divide the coupled vibration into the radial and longitudinal vibrations. The electromechanical equivalent circuits for the transducer and the resonance frequency equations are obtained. When the height is close to the radius of the transducer, the coupling between the radial vibration and the longitudinal vibration is strong. The thicker is the piezoelectric cylinder, the larger is the effective electromechanical coupling coefficient. Several prototypes of the transducer are fabricated. It is demonstrated that the theoretical resonance frequencies are in good agreement with the numerical and experimental results.

Elastic properties measurement of human enamel based on resonant ultrasound spectroscopy

ObjectivesTo investigate the elastic properties of human enamel using resonant ultrasound spectroscopy (RUS). MethodsSix rectangular parallelepiped specimens were prepared from six human third molars. For all specimens, the theoretical resonant frequencies were calculated using the Rayleigh-Ritz method, knowing the specimen mass density and dimensions, and using a priori stiffness constants. The experimental resonant frequencies were measured and extracted by RUS. Then, the optimal stiffness constants were retrieved by adjustment of the theoretical resonant frequencies to the measured ones based on the Levenberg-Marquardt method. The engineering elastic moduli, including Young’s moduli, shear moduli, and Poisson’s ratios, were also calculated based on the optimal stiffness constants. ResultsThe five independent stiffness constants C11, C12, C13, C33, and C44 were 90.2 ± 6.65 GPa, 34.7 ± 6.90 GPa, 29.5 ± 4.82 GPa, 83.5 ± 8.93 GPa, and 37.0 ± 10.9 GPa, respectively. Young’s moduli E11 and E33, shear moduli G13 and G12, and Poisson’s ratios υ12 and υ13 were 71.7 ± 7.34 GPa, 69.2 ± 7.32 GPa, 37.0 ± 10.9 GPa, 28.1 ± 4.35 GPa, 0.303 ± 0.098, and 0.248 ± 0.060, respectively. SignificanceElastic properties are critical for developing dental materials and designing dental prostheses. The RUS method may provide more precise measurement of elastic properties of dental materials.

Actively adjustable step-type ultrasonic horns in longitudinal vibration

Actively adjustable longitudinal step-type ultrasonic horns are proposed and studied. The horn is composed of a traditional ultrasonic horn and piezoelectric material. In practical applications, this kind of step-type ultrasonic horn is mechanically excited by an ultrasonic transducer and the piezoelectric material is connected to an adjustable electric impedance. In this research, the effects of the electric impedance and of the location of the piezoelectric material on the performance of the horn are studied. It is shown that when the electric resistance is increased, the resonance frequency of the horn is increased; the displacement magnification is increased when the piezoelectric material is located in the large end and decreased when the piezoelectric material is located in the small end of the horn. The displacement magnification for the piezoelectric material in the large end is larger than that for the piezoelectric material in the small end of the horn. Some step-type ultrasonic horns are designed and manufactured; the resonance frequency and the displacement magnification are measured by means of POLYTEC Laser Scanning vibrometer. It is shown that the theoretical resonance frequency and the displacement magnification are in good agreement with the measured results. It is concluded that by means of the insertion of the piezoelectric material in the longitudinal horn, the horn performance can be adjusted by changing the electric impedance and the location of the piezoelectric material in the horn. It is expected that this kind of adjustable ultrasonic horns can be used in traditional and potential ultrasonic technologies where the vibrational performance adjustment is needed.

Mechanical Vibration Measurement of Solidly Mounted Resonator in Fluid by Atomic Force Microscopy.

The very small vibration of a solidly-mounted resonator (SMR) in fluid may trigger a relatively large motion of the covering fluid, which was implied by our protein-related experimental results. Therefore, a series of experimental methods for characterizing the mechanical longitudinal vibration of the SMR and the corresponding out-of-plane dynamic response of the fluid above the SMR surface is described in this paper. A SMR device with theoretical resonance frequency of 2.5 GHz was driven by an amplitude-modulated (AM) signal, in which the amplitude is modulated by a signal of the second resonance frequency of the atomic force microscope (AFM) cantilever. A lock-in amplifier is used to demodulate the vibration response of the AFM cantilever, which is proportional to the amplitude of the sample vibration in contact mode and tapping mode. The amplitude-frequency curve of the SMR surface is obtained in contact mode with a relatively stronger interaction force between the AFM tip and the SMR surface. The amplitude-frequency curve of the motion of the liquid above the SMR device and the peak amplitude of the fluid at different distances above the SMR surface are measured in tapping mode with a relatively weak interaction force between the AFM tip and the fluid sample.

Compact design of a novel linear compliant positioning stage with high out-of-plane stiffness and large travel

Since most of the XY positioning stages with large travel range proposed in previous studies suffer from low out-of-plane stiffness and loose structure, this paper presents a novel two degrees-of-freedom large travel linear compliant positioning stage with high out-of-plane stiffness and compact size. The linear guide compliant mechanism of the stage takes spatial leaf spring parallelograms as the basic units, which are serially connected to obtain large travel, high out-of-plane stiffness, and compact size simultaneously. The theoretical static stiffness and dynamic resonant frequency are obtained by matrix structural analysis. Finite element analysis is carried out to investigate the characteristics of the developed stage. The analytical model is confirmed by experiments. It is noted that the developed stage has a workspace of 4.4 × 7.0 mm2, and the area ratio of workspace to the outer dimension of the stage is 0.16%, which is greater than that of any existing stage reported in the literature. The results of out-of-plane payload tests indicate that the stage can sustain at least 20 kg out-of-plane payload without changing the travel range. And the positioning experiments show that the developed stage is capable of tracking a circle of radius 1.5 mm with 10 µm error and the resolution is less than 2 µm.

An Experimental Topographic Amplification Study at Los Alamos National Laboratory Using Ambient Vibrations

Abstract An experimental study aimed at investigating potential topographic amplification of seismic waves was conducted on a 50‐m‐tall and 185‐m‐wide soft‐rock ridge located at Los Alamos National Laboratory near Los Alamos, New Mexico. Ten portable broadband seismograph stations were placed in arrays across the ridge and left to record ambient vibration data for ∼9 hours. Clear evidence of topographic amplification was observed by comparing spectral ratios calculated from ambient noise recordings at the toe, slope, and crest of the instrumented ridge. The inferred resonance frequency of the ridge obtained from the experimental recordings was found to agree well with several simple estimates of the theoretical resonance frequency based on its geometry and stiffness. Results support the feasibility of quantifying the frequency range of topographic amplification solely using ambient vibrations, rather than strong or weak ground motions. Additionally, comparisons have been made between a number of widely used experimental methods for quantifying topographic effects, such as the standard spectral ratio, median reference method, and horizontal‐to‐vertical spectral ratio. Differences in the amplification and frequency range of topographic effects indicated by these methods highlight the importance of choosing a reference condition that is appropriate for the site‐specific conditions and goals associated with an experimental topographic amplification study.