Frequency-wavenumber Domain Research Articles

Vibration behaviors of orthogonally stiffened cylindrical shell coupled with internal circular plates in wavenumber-frequency domain

In this paper, vibration characteristics of orthogonally stiffened cylindrical shell coupled with multiple internal circular plates are discussed using wavenumber analysis. The theoretical model and formulation for the orthogonally stiffened cylindrical shell coupled with internal circular plates are developed by employing a modified variational method. A unified variational modeling procedure is employed to ensure the continuity conditions between each substructure, including cylindrical shell, circular plate, longitudinal stringer, and circumferential ring. The displacement components of the cylindrical shell are described by Fourier series along the circumferential direction and orthogonal polynomials along meridional direction. Thus, the responses of the shell in wavenumber domain can be naturally obtained. Convergence studies for the theoretical model are conducted by finite element method to verify the reliability of the present method. The vibration behaviors of the coupled model under three typical external loads, including single point force, multiple uniformly spaced point forces, and line force, are studied based on the vibration fields in wavenumber domain. The results indicate that the circumferential modal coupling effect and modal contribution to the total vibrations are sensitive to the types of external excitations, which induces the different vibration behaviors.

City-scale buildings damage estimation based on broadband physics-based ground motion simulation of 2021 Ms 6.4 Yangbi, China, earthquake

This article proposed a computational workflow for city-scale building damage estimation based on broadband physics-based ground motion simulation. The dynamic stiffness matrix method in frequency-wavenumber domain is employed for broadband physics-based ground motion simulation of finite fault along with site response correction using equivalent-linear site response analysis approach. With simulated ground motion, seismic response of buildings, using multi-degree of freedom model, is simulated using nonlinear time history analysis, and building damage is evaluated based on a trilinear backbone curve of story’s nonlinear force-drift model. Main advantage of the framework lies in the employed dynamic stiffness matrix method for ground motion simulation, which can efficiently generate broadband ground motions in perfect parallel and naturally capture the physics of finite fault source, propagation path, and spatial variability characteristics of ground motion. To demonstrate the salient features of proposed workflow, the 2021 Ms 6.4 Yangbi earthquake is simulated with frequency resolution up to 20 Hz, and seismic damage of buildings in Yangbi county are estimated. Results show that most traditional wood-adobe structures suffer moderate to severe damage, and engineered seismic buildings (mostly RC frame) in Yangbi county suffer minor damage, which agrees with field investigation results.

On railway track receptance

Railway track dynamic stiffness is the relationship between track deflection and loading frequency. Its inverse, also known as receptance, is an important quantity that affects the track’s dynamic response under moving trains and noise and vibration characteristics. Despite its importance, there has been limited detailed study into receptance at lower frequencies (<1000Hz). Thus, this paper contributes two main novelties. The first is the presentation of a novel numerical approach well-suited to receptance calculation, and secondly, a parametric study identifying the key frequencies associated with different track components. The new approach is first presented, which uses a 3D periodic domain coupled with perfectly matched layers and is solved in the frequency-wavenumber domain. It is well-suited to the problem because it can capture dynamic wave propagation within the complex geometries associated with each track component, while using an efficiently-sized domain. The model is validated in terms of its ability to capture the dynamic response of 3D periodic structures, and also the behaviour of a railway track. It is then used to study the effect of two common modelling assumptions (beam-on-elastic foundation and symmetry) on the calculation of track receptance. It’s shown that ignoring wave propagation in the subgrade-earthwork layers induces errors in the ≈80−300% range at frequencies below 200Hz, and errors of ≈30% in the 200−440Hz range. It is also shown that the assumption of track centreline symmetry ignores some track bending modes and can also introduce errors (≈20%) at frequencies up to 1000Hz. Finally, the effect of the most common ballasted track components on receptance are analysed and new knowledge is presented regarding the typical frequency ranges associated with each.

Wall-pressure fluctuations associated with turbulent boundary layer of pump-jet duct and empirical spectrum modeling

This study establishes the relationship between the pressure fluctuation on outer wall of the pump-jet duct and the source term of velocity-field in the Turbulent Boundary Layer (TBL) based on the Poisson equation and develops it in frequency-wavenumber domain. The wall-pressure fluctuations caused by source terms of different TBL regions are investigated and the spatial-temporal distribution is compared through the wavenumber-frequency spectrum. The characteristics of turbulent structures are revealed in detail using the vortex scale and intensity. The empirical spectrum model is developed for the estimation of the wall-pressure fluctuations. Besides, the simulation of velocity-field source is carried out by using the Large Eddy Simulation (LES) numerical method. Results show that the logarithmic subrange has a dominant contribution to the wall-pressure fluctuations. The remarkable energy distribution at low-frequency and low-wavenumber domain is mainly reflected in the logarithmic subrange and a low-frequency diffusion exists due to the rotor and pressure gradient. The small-scale vortices corresponding to high-wavenumbers are in the viscous subrange and the contribution of large-scale vortices corresponding to low-wavenumbers are reflected in viscous, buffer and logarithmic subranges. The deformation and rotation forms of vortices migration represent in different subranges of TBL. Moreover, the empirical spectrum model can qualitatively predict the pressure fluctuations at different positions of the duct wall, providing a reference for engineering applications.

Circumferential modal coupling analysis of orthogonally stiffened cylindrical shell coupled with internal rectangular plate using semi-analytical wavenumber–frequency method

Orthogonally stiffened cylindrical shell coupled with internal rectangular plate is widely applied in engineering industries. The significant effects of the internal plate on vibration signatures of the shell have been demonstrated. Little attention has been paid to vibration analysis in the wavenumber–frequency domain. This paper aims to conduct the circumferential modal coupling analysis of the coupled model using the semi-analytical wavenumber–frequency method. The coupled model is disassembled into the stiffened cylindrical shell and rectangular plate. The interface potential between the shell and rectangular plate is derived based on a unified variational modeling procedure, in which the transformation of the coordinate system must be conducted. The displacement fields of the shell are expanded with the Fourier series along the circumferential direction. The vibratory field in wavenumber–frequency space is analytically obtained. The numerical method is utilized to illustrate the convergence and accuracy of the proposed method. The results demonstrate that the internal plate affects modal characteristics and then results in the alterations of the number and the shifts of resonance peaks. The phenomenon can be demonstrated by the circumferential modal contribution of the vibration response. Besides, it should be noted that the dominant circumferential modes for the input energy and vibrational energy are inconsistent owing to the strong shell–plate coupling effect.

Multi-Order Mode Excitation and Separation of Ultrasonic Guided Waves in Rod Structures Using 2D-FFT.

The ultrasonic guided wave technique is extensively used for nondestructive structural testing, and one of the key steps is to extract a single mode with certain purity from multi-order mixed modes. In this paper, the propagation of ultrasonic guided waves in the cylindrical rod is simulated first; the appropriate broadband excitation signal is selected to excite the multi-order modes in a specific frequency range; and the time-space signal containing multi-order modes is converted to the frequency-wavenumber domain signal by two-dimensional Fourier transform. In the frequency-wavenumber domain, the frequency-wavenumber ridge is extracted from the multi-mode frequency-wavenumber domain based on the dynamic programming method, and then the time-domain signal corresponding to a single mode can be reconstructed. By comparing the excited multi-order mode and the separated single mode with the theoretical results, it is observed that the two results are consistent. Thus, the employed mode-excitation method can accurately excite the multi-order modes in rod structures. Furthermore, the proposed method enables the separation of a single-mode wave with high purity, providing a foundation for future utilization of isolated modes.

Characterizing polycrystalline microstructures by reconstructing grain boundaries and velocity map from ultrasonic surface wave field

An ultrasonic material characterization method is proposed to reconstruct the polycrystalline microstructures from the field-measurement of ultrasonic surface waves. Two wavenumber–frequency domain filters are developed to extract specific wave components for the reconstructions. One is the evanescent-pass filter that can be used to reconstruct the grain boundaries. The other is the directional filter to map the surface wave velocity along a specific direction. The method is validated by numerical simulations, as well as by experiments, on an additively manufactured sample. Sub-wavelength resolution can be achieved by the proposed method if sufficient data is captured spatially within one wavelength of the surface wave.

Application of Damage Detection of Metal Structure Lamb Wave Modal Superposition Imaging Based on Scanning Laser Vibration Measurement

Metal structural plates are extensively used in various engineering structures due to their high strength, high-temperature resistance, toughness, and plasticity. However, they are susceptible to damage from external loads and impacts over time. The current Lamb wave detection methods suffer from dispersion and multimodal effects, leading to ineffective identification of damage information. In this paper, we investigate Lamb wave propagation in steel structure plates with flat-bottomed holes using a sinusoidal modulation five-peak wave signal. Finite element numerical models are developed, and an experimental platform is constructed using steel and aluminum boards. Experimental data is collected using a Scanning Laser Doppler Vibrometer (SLDV, PSV-500, Polytec Inc., Baden-Württemberg, German). The results demonstrate that, under the same frequency, the damage reflection energy for different modes is distinct. By fusing the data from the two modes, more accurate damage imaging results are obtained in the frequency-wavenumber (f-k) domain compared to single-mode imaging. Furthermore, experiments are conducted to locate damage in a steel board with a through hole and an aluminum plate with double flat-bottomed holes, confirming the feasibility of the proposed algorithm in isotropic plates.

Discontinuous Galerkin method for solving viscoacoustic wave equations with amplitude dissipation and phase dispersion separation in isotropic and anisotropic media

SUMMARY The standard-linear-solid (SLS) theory works well for viscoelasticity. However, the coupling of amplitude dissipation and phase dispersion makes it impossible to investigate their effects separately by the discontinuous Galerkin method (DGM). In this paper, we have derived newly viscoacoustic wave equations with amplitude dissipation and phase dispersion separation in isotropic and anisotropic media, based on a Fourier method, which is suitable for using a time–space-domain DGM on unstructured meshes. The basic framework of DGM is constructed and the amplitude-dissipation effect and the phase-dispersion effect in viscoacoustic wave equations are investigated. The original equation is first transformed into the frequency–wavenumber domain, where the amplitude dissipation and phase dispersion are separated effectively, and then the decoupled formulation is converted back to the time–space domain. The new equivalent and approximate equations can be obtained. Compared with the original equation, the newly approximated equation enables us to separate the amplitude-loss and phase-delay terms, respectively, and experiences four kinds of effects, namely acoustic effect, only amplitude-dissipation effect, only phase-dispersion effect and both amplitude-dissipation and phase-dispersion effect. Moreover, the stability condition and numerical dispersion for using DGM to solve the new and old equations are presented. Several numerical examples are used to verify the correctness and effectiveness of the modified approximate equations in viscoacoustic isotropic and anisotropic media. The numerical results in a cave and SEG/EAGE salt models demonstrate that the new equations combined with DGM have performances on viscoacoustic media with complex geological structures.

Surface defect identification based on broadband laser-generated Rayleigh wave with wavenumber filtering

As a non-contact, couplant-free and nondestructive technique, the laser ultrasonic technology has great potential for detecting surface defects. In this paper, we propose a surface defect identification method based on broadband laser-generated Rayleigh wave with wavenumber filtering in an area scanning mode. Firstly, a particular lowpass filter is constructed in frequency-wavenumber domain to extract the scattered wave generated by the defects, and then a surface defect image can be reconstructed based on the broadband scattered wave wavenumbers. Secondly, a threshold denoising method is employed to enhance the signal-to-noise ratio and improve the image sharpness. Thirdly, the experimental validation is carried out, in which a laser ultrasonic detection system is used to detect the surface defects of aluminum alloy specimens and identify their different parameters. The experimental results verify that the proposed method can identify the location, size and orientation of surface defects effectively, meanwhile, its imaging effect shows significantly superior to that of the conventional reflected wave energy and standing wave energy methods. Furthermore, the correlation between maximum local scattered wave energy and the depth of defects is found, which can characterize the severity of the surface defects.

A comprehensive analysis of guided-wave propagation in 3D-printed PLA plates with different infill densities – Experimental study

Thanks to its many advantages, additive manufacturing (AM) is witnessing a gigantic shift from small applications to the production of complex industrial components, including safety–criticalapplications like aerospace and civil construction. This arises the need to develop accurate and robust technologies for evaluating and monitoring the structural integrity of AM components. The objective of this study is to comprehend how ultrasonic guided waves (GWs) propagate in 3D-printed poly(lactic acid) (PLA) plates of different infill densities. The experimental investigation involves five intact PLA plates printed with infill densities ranging from 20 to 100% at a step of 20%. A scanning laser Doppler vibrometer was used to visualize GW propagation by performing full-wavefield area-scans. Spatial-time, frequency-wavenumber, and wavenumber-wavenumber analyses were performed to scrutinize the availableGW modes and their slowness profiles within the anisotropic structure. In addition, the tuning of the fundamental Lamb-wave (LW) modes at different excitation frequencies was examined, and the amplitude attenuation of the generally most pronounced mode (A0 mode) was investigated for different infill densities at an excitation of 50 kHz. A reference methodology is presented to experimentallyidentify more than five propagating modes in the frequency-wavenumber domain then obtain their phase-velocity dispersion curves. Significant variations are observed in the dispersion characteristics when lowering the infill density leading to the appearance of more modes at lower cutoff frequencies and drops in both the group and phase velocities in most of the cases. A complex behavior of the guided waves was observed in the dispersion curves of the 20%-infill plate, with possible mode interruptions/disturbance at an excitation frequency beyond 70 kHz. The appearance of shear-horizontal modes is noticed/strengthened at oblique propagation directions which may be attributed to mode conversion of the LW modes after obliquely interacting with the internal structure of the plates. Though high wave attenuation is a characteristic of the used polymer material, this attenuation is further increased at lower infill densities. The tuning behavior of the fundamental LW modes is also shown to be significantly affected by the infill density. The presented results can serve as reference propagation and dispersion characteristics for researchers working on similar materials and geometries. Such knowledge and understanding can be particularly useful for GW-based structural healthy monitoring of AM structures.

Transfer Matrix approaches for the prediction of impact sound radiation from layered floors

In this work, an efficient and accurate framework for the prediction of the direct impact sound insulation of layered floors is presented. Both floor models of infinite lateral extent and with simply supported boundaries are considered. For the infinite floors, closed-form mechanical admittance expressions are provided which relate directly to the transfer matrix elements of the conventional transfer matrix method (TMM). For floors with simply supported boundaries, an image source argument is employed for underpinning the modal version of the TMM, or mTMM, which approximately accounts for the boundary conditions by considering admissible trace wavenumbers only. It is demonstrated that both for the TMM and the mTMM, the radiated sound power can be evaluated directly in the frequency–wavenumber domain from a simple integral. The accuracy of the mTMM is confirmed in a numerical verification using detailed finite element models. The method is also extensively validated with laboratory measurements for a set of five heavy floors with stiff and resilient layers. A very good agreement between measurements and mTMM predictions is generally observed. The TMM and mTMM approaches yield very similar results above the critical frequency of the base floor, yet at lower frequencies, the inclusion of the finite-size and boundary conditions effects make the mTMM substantially more accurate.

Experimental determination of dispersion diagrams over large frequency ranges for guided ultrasonic waves in fiber metal laminates

Fiber metal laminates (FMLs) are of high interest for lightweight structures as they combine the advantageous material properties of metals and fiber-reinforced polymers (FRPs). However, low-velocity impacts can lead to complex internal damage. Therefore, structural health monitoring with guided ultrasonic waves (GUWs) is a methodology to identify such damage. Numerical simulations form the basis for corresponding investigations, but experimental validation of dispersion diagrams over a wide frequency range is hardly found in the literature. In this work the dispersive relation of GUWs is experimentally determined for an FML made of carbon FRP and steel. For this purpose, multi-frequency excitation signals are used to generate GUWs and the resulting wave field is measured via laser scanning vibrometry. The data are processed by means of a non-uniform discrete 2d Fourier transform and analyzed in the frequency-wavenumber domain. The experimental data are in excellent agreement with data from a numerical solution of the analytical framework. In conclusion, this work presents a highly automatable method to experimentally determine dispersion diagrams of GUWs in FML over large frequency ranges with high accuracy.

The axisymmetric screech tones of round twin jets examined via linear stability theory

Spatial linear stability analysis is used to study the axisymmetric screech tones generated by twin converging round nozzles at low supersonic Mach numbers. Vortex-sheet and finite-thickness models allow for identification of the different waves supported by the flow at different conditions. Regions of the frequency–wavenumber domain for which the upstream-propagating guided jet modes are observed to be neutrally stable are observed to vary as a function of solution symmetry, jet separation,$S$, and the velocity profile used. Screech-frequency predictions performed using wavenumbers obtained from both models agree well with experimental data. Predictions obtained from the finite-thickness model better align with the screech tones measured experimentally and so are seen to be an improvement on predictions made with the vortex sheet. Additionally, results from the finite-thickness model predict both symmetric and antisymmetric screech tones for low$S$that are found in the vortex-sheet model only at greater$S$. The present results indicate that the feedback loop generating these screech tones is similar to that observed for single-jet resonance, with equivalent upstream and downstream modes.

Semi-analytical simulation of seismic waves generated by a point source in 1-D layered half-space of double-porosity media

SUMMARYIn this study, we present a semi-analytical method to simulate the propagation of seismic waves in horizontally stratified double-porosity media. We solve the governing equations in the frequency–wavenumber domain and then compute the time–space domain solutions by Hankel and fast Fourier transforms. We conduct numerical simulations to study the properties of the seismic waves in the double-porosity media. The results show the existence of three P waves, one fast P wave and two slow P waves. The two slow P waves are highly attenuated and can be observed by assuming a low fluid viscosity. By comparing the fast P wave in a single-porosity medium and that in a double-porosity medium, we find that the double-porosity model predicts much higher attenuation of the fast P wave due to the local fluid flow between the background medium and the inclusions. We also study the parameters affecting the attenuation, such as the radius of the spherical inclusions, the viscosity of the pore fluid, the permeability of the background medium and the porosity of the inclusions. Finally, we present a cross-well survey model to investigate the seismic responses in the double-porosity media and compare them with the responses in the single-porosity media. We find that both the amplitude and velocity of the fast P wave decrease with the increase of the volume ratio of the inclusions.

Machine learning-based cement integrity evaluation with a through-tubing logging experimental setup

Assessing the integrity of the cement layer and the quality of its bond to the casing and formation is paramount to ensure that the wellbore is hydraulically isolated from the surrounding environment before permanently sealing the well. Such inspection is part of Plugging & Abandonment (P&A) operations, and it is usually achieved through well logging tools, which provide a vast amount of data that a skilled specialist interprets. The process is human-dependent, error-prone, and time-consuming. There has been an increasing interest in solutions that allow an automatic interpretation of the logging data since the recent panorama of the oil and gas industry indicates a growing P&A demand. Such solutions aim at reducing the dependence on human knowledge and consequently increasing the reliability and accuracy of the cement integrity evaluation. Therefore, this work presents an experimental setup capable of emulating defective cement layer configurations of real-world oil wells in single or multi-string arrangements. Such flexibility enables acquiring logging data for multiple well conditions and building a rich logging database to develop a supervised learning framework and define the most suitable model for performing the cement integrity evaluation. Several logging runs were performed, producing a database with 130 samples, including varied tubing eccentricity levels and cement layer conditions. A complete analysis of the data both in the time domain as well as in the frequency–wavenumber domain was performed, highlighting the complexity of the interpretation task. A resampling-based workflow was employed to evaluate machine learning models of different families. The models were tested under three scenarios, and accuracy and computational complexity metrics were computed to compare their performance. The results showed that shallow learning models can perform satisfactorily well even with less data available for training. The support vector machine stood out, achieving a mean accuracy score higher than 0.99 while being able to predict the cement sheath’s condition in less than 1 ms. This paper contributes to the research on the cement integrity evaluation by presenting a study that combines an experimental setup mimicking several oil well conditions and the employment of machine learning as a diagnostic tool, which has no precedents in recent literature regarding the acoustic logging knowledge field.

Progress in the reliable detection of near-surface reflectors when inspecting anisotropic and isotropic material using the total focusing method

Load-bearing components made of composite laminates of several centimetres in thickness, for example those used in wind turbine blades, are frequently used in the energy sector. These components are usually tested using conventional ultrasound techniques. A typical approach to increase the energy penetration depth is testing with lower frequencies. This leads to a decrease in sensitivity and consequently to reduced detectability of small defects compared to higher frequencies, especially for defects close to the surface. Another possibility is to use high excitation voltage or gain to improve penetration, but this also leads to a much more pronounced initial pulse with saturated or clipped A-scans, resulting in a loss of information. Consequently, the defects close to the surface are often indistinguishable to the initial pulse and are not detected. In comparison to conventional ultrasonic testing, the total focusing method (TFM) shows higher resolution of near-surface defects using the same frequencies. The TFM can be adapted to anisotropic media by consideration of the direction-dependent wave propagation. Therefore, sound paths not perpendicular to the surface, which show less clipping, can be used for imaging. In this paper, approaches for improving the detectability of defects close to the surface in carbon fibre-reinforced plastic (CFRP) and aluminium using full matrix capture (FMC) and the TFM are discussed. As a result, defects in CFRP with a depth of 0.9 mm and above can be detected. The presented methods also improve the signal-to-noise ratio (SNR) of near-surface defects in the TFM reconstructions up to 4 dB. The first approach filters the FMC pulses in the wavenumber-frequency domain, which reduces the aforementioned disturbances in the time-domain signals and thus improves the detectability of near-surface defects. The second approach is based on a maximum angle in the reconstruction step, which reduces the entries of the information matrix based on location. This procedure is similar to taking the directivity function of each array element into account. Therefore, only time signals with a high signal-to-noise ratio are considered.

Analytical study on vibration behaviors of pump-jet–shaft–submarine hull system in wavenumber–frequency​ domain

The pump-jet excitation is transmitted to submarine hull along rotor–shaft system and duct–stator system, which is one of the main causes of structural vibration of the hull. This paper proposes an analytical method for the coupled shaft–submarine hull system. The submarine hull is modeled as a jointed conical-orthogonally stiffened cylindrical–spherical shell coupled with several circular plates. The shaft is modeled with a three-dimensional beam and connected to the hull by bearings. A unified variational modeling procedure is developed to assemble each substructure. The hydrodynamic pressure acting on the rotor and the duct–stator system are respectively considered as single point force and multiple uniformly or non-uniformly spaced point forces acting on the shaft and the conical shell. The vibration displacements are analytically expanded with Fourier series in the circumferential direction. Thus, the wavenumber components that contribute to vibration responses are naturally separated and quantified. The convergence and accuracy of the proposed method are verified by the finite element method. The analytical study on vibration characteristics of the pump-jet–shaft–submarine hull system along distinct vibration transferring paths in circumferential wavenumber–frequency domain is conducted. The results indicate that the rotor excitation can excite more resonance peaks compared to the duct–stator excitation when neglecting the elasticity of the pump-jet propulsor. It mainly owns to the strong circumferential modal coupling and abundant modal contributions when the system is under the rotor excitation. Besides, the non-uniform distribution of external load contributes to the augmentation of resonance peaks compared to the responses under uniform load, which attributes to the participation of extra wavenumber components.

Dynamic response of a multi-scale layered saturated porous half-space due to seismic dislocation source by using a revised dynamic stiffness matrix method

The study investigating the dynamic response of seismic dislocation source in a layered saturated porous half-space, particularly the multi-scale characteristic of half-space, from crustal to geotechnical scale, is still lacking in the literature. particularly in will lead to the computation bottlenecks for multi-scale seismic wave propagation. Based on Biot's theory of wave propagation in a fluid-saturated porous solid, a dynamic stiffness matrix method is proposed to investigate the dynamic response of a multi-scale layered saturated porous half-space due to the seismic dislocation source. Assembling each layer stiffness matrix in the frequency-wavenumber domain, the global dynamic stiffness matrix is constructed to avoid errors accumulative compared to the reflection and transmission matrix method. The divergent index terms of the stiffness matrix with respect to thickness and wavenumber are extracted to revise the dynamic stiffness matrix adapted for multi-scale half-space. The seismic dislocation source action is equal to the external forces imposed on the total saturated porous half-space, which can obtain the dynamic response by using revised dynamic stiffness matrix method. The accuracy of the proposed method is verified via the comparison between the calculated results and of three published literatures. The multi-scale model with realistic near-surface fine structure is selected to investigate the effects of superficial fine structures on the dynamic responses. The numerical simulations results show that the presence of low-velocity saturated porous layers has a prominent impact on ground motion. The dynamic response seems to be sensitive to the porosity conditions, especially for high frequency, which cause the difference in variation of peak displacement value.

A Novel Approach to Tele-Ultrasound Imaging: Compressive Beamforming in Fourier Domain for Ultrafast Ultrasound Imaging

Tele-ultrasound imaging is useful in various situations. Plane wave imaging provides a method for ultrafast ultrasound with very high frame rates, which sacrifices image quality and leads to the problem of a large amount of data and low signal transmission speed in telemedicine imaging. In this paper, a novel compressive frequency-wavenumber domain beamforming method is introduced, which integrates Stolt’s f-k method and compressed sensing theory on the lateral wavenumber. The data load is reduced by the sparsity of the echo signal parallel to the transducer, which requires a smaller measurement matrix during compressed sensing to reduce memory usage and accelerate the transmission rate. The signal is compressed in the Fourier domain to obtain greater stability and better image quality after reconstruction than if it was compressed in the temporal domain. Simulated data and experimental acquisitions were used to compare compressive Fourier domain beamforming with conventional delay-and-sum (DAS) beamforming. The results showed that compressive beamforming within the wavenumber domain provides the image with higher quality from less data.