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At least 253 records · Page 14

Comparisons of Long-Term Schumann Resonance Records in Europe and North America

Two stations at a distance comparable with the wavelength in the Schumann resonance (SR) frequency range, one in Europe (Nagycenk, Hungary) and one in North America (West Greenwich, Rhode Island) have simultaneously monitored the natural vertical electric and horizontal magnetic field components in the frequency range of 3-25 Hz. This is a unique opportunity, as Schumann resonance stations are scarce and even fewer station have records with 5-6 year durations. The main purpose of this paper is to make comparisons in the SR time series measured simultaneously at the two field site, thereby providing access to global behavior on the seasonal and interannual time scales. The comparative measurements described here point out distinct differences in the nature of convection in South America and in Africa and reveal new aspects about the behavior of tropical continental convection on the ENSO time scale.

Satori, G.↗

Near-source and Remote Observations of Kilometric Continuum Radiation from Multispacecraft Observations

[I] Kilometric continuum (KC) radiation was first identified from Geotail plasma wave observations. Past authors have shown that this emission has a frequency range that overlaps that of the auroral kilometric radiation (AKR) but is characterized by a fine structure of narrow-bandwidth, linear features that have nearly constant or drifting frequency. This fine structure is distinct from that of AKR. KC also apparently has a distinct source region probably associated with the low-latitude inner magnetosphere, consistent with direction-finding and ray-tracing results. We present new high-resolution electric and magnetic field observations of KC obtained by the Polar plasma wave instrument in the near-source region. These observations show intense electrostatic and less intense electromagnetic emissions near the magnetic equator at the plasmapause. Simultaneously, Geotail, located at 20 to 30 RE in radial distance, observes KC in the same frequency range. These data support a possible mode-conversion source mechanism near a region of high-density gradient. High-resolution data obtained from wideband receivers on board both Polar and Cluster show closely spaced bands of emission near the magnetic equator that may be due to many nearby independent sources of EM emission perhaps associated with density fluctuations or cavities in the plasmasphere.

Menietti, J. D.↗

Multicolored microwave absorbers with dynamic frequency modulation

Microwave-absorbing materials are extensively used in intelligent electronic devices and stealth technologies where the ability to dynamically adjust microwave-absorbing capacity in response to specific requirements is vitally important. Herein, we report a new approach for constructing dynamically tunable microwave absorbers with ultrawide tunable frequency ranges that are simultaneously endowed with vibrant structural colors. Here, the methodology produces structural colors and adjusts absorption properties by constructing ZnO coatings with precisely adjustable thicknesses on a polypyrrole/melamine foam (PPy/MF) surface by atomic layer deposition (ALD) in conjunction with a pressure-driven strategy that regulates the compression ratio. The electrical conductivity, electromagnetic parameters, thickness, and pore size of the ZnO-coated PPy/MF (ZnO/PPy/MF) are effectively adjusted, and simply applying external pressure widens the tunable frequency range and the effective absorption bandwidth. As a result, the effective absorption frequency of ZnO/PPy/MF is dynamically adjustable from the S band to the Ku band, thereby covering 94.3% of the entire microwave spectrum. Moreover, the brilliant and uniform structural colors of ZnO/PPy/MF, which span various color categories, are precisely regulated by tuning the thickness of the ZnO coating by adjusting the number of ALD cycles. ZnO/PPy/MF is strongly hydrophobic, which endows it with remarkable self-cleaning properties. Therefore, ZnO/PPy/MF provides a conceptually novel platform for the development of next-generation smart microwave-absorbing materials due to its integrated dynamic frequency-regulating ability, brilliant structural coloration, and self-cleaning features.

36 MATERIALS SCIENCE↗

Dark Photon Dark Matter and Low-frequency Gravitational-wave Detection with Gaia-like Astrometry

Astrometric surveys offer us a method for searching for elusive cosmic signatures, such as ultralight dark photon dark matter and gravitational waves (GWs), by observing the temporal change of stars’ apparent locations. The detection capabilities of such surveys rapidly decrease at low frequencies, because the signals become hardly distinguishable from the background motion of stars. In this work, we find that the background motion can be well described by a linear model over time, based on which we propose a linear background subtraction scheme. Compared to the conventional quadratic subtraction, the advantage of linear subtraction emerges within the frequency range below 6 × 10 −9 Hz. Taking dark photons with purely gravitational interactions, dark photons with additional U(1) B or U(1) B−L gauge interactions, and low-frequency GWs as examples, we illustrate that the linear subtraction scheme can result in an enhancement of more than 1 order of magnitude in the exclusion limits of Gaia-like experiments in the low-frequency range.

Astrometry↗

Octave-spanning terahertz quarter-wave plates based on over-coupled Fabry–Pérot resonances in reflective metal–dielectric–metal metasurfaces

Compact devices for broadband polarization control in the terahertz (THz) regime remain challenging to realize due to the intrinsic phase dispersion associated with birefringent materials and resonant structures. Here, we demonstrate achromatic THz quarter-wave plates with near-unity efficiency and operating under a wide range of incidence angles, based on over-coupled metal–dielectric–metal reflective metasurfaces. The devices operate as single-port anisotropic Fabry–Pérot cavities, in which the phase dispersion of the over-coupled resonances is engineered to maintain an approximately constant relative phase delay between orthogonal field components over a broad frequency range. Four complementary metasurface designs operating at an incidence angle of 45° collectively cover the 0.25–3 THz frequency range accessible to a typical THz time-domain spectroscopy system. Each device exhibits an approximately octave-wide operational bandwidth, with axial ratios below 3 dB and polarization-conversion efficiencies exceeding 80% across most of the operating band. Systematic structural optimization suppresses coupling to diffraction and guided-wave modes, thereby further extending the usable bandwidth while preserving the required phase relationship between orthogonal polarizations. The demonstrated metasurfaces are compatible with wafer-scale fabrication processes, and experimental results show excellent agreement with simulations. These findings establish over-coupled reflective metasurfaces as a robust, scalable, and versatile platform for broadband THz polarization control.

36 MATERIALS SCIENCE↗

Use of a Microphone Phased Array to Determine Noise Sources in a Rocket Plume

A 70-element microphone phased array was used to identify noise sources in the plume of a solid rocket motor. An environment chamber was built and other precautions were taken to protect the sensitive condenser microphones from rain, thunderstorms and other environmental elements during prolonged stay in the outdoor test stand. A camera mounted at the center of the array was used to photograph the plume. In the first phase of the study the array was placed in an anechoic chamber for calibration, and validation of the indigenous Matlab(R) based beamform software. It was found that the "advanced" beamform methods, such as CLEAN-SC was partially successful in identifying speaker sources placed closer than the Rayleigh criteria. To participate in the field test all equipments were shipped to NASA Marshal Space Flight Center, where the elements of the array hardware were rebuilt around the test stand. The sensitive amplifiers and the data acquisition hardware were placed in a safe basement, and 100m long cables were used to connect the microphones, Kulites and the camera. The array chamber and the microphones were found to withstand the environmental elements as well as the shaking from the rocket plume generated noise. The beamform map was superimposed on a photo of the rocket plume to readily identify the source distribution. It was found that the plume made an exceptionally long, >30 diameter, noise source over a large frequency range. The shock pattern created spatial modulation of the noise source. Interestingly, the concrete pad of the horizontal test stand was found to be a good acoustic reflector: the beamform map showed two distinct source distributions- the plume and its reflection on the pad. The array was found to be most effective in the frequency range of 2kHz to 10kHz. As expected, the classical beamform method excessively smeared the noise sources at lower frequencies and produced excessive side-lobes at higher frequencies. The "advanced" beamform routine CLEAN-SC created a series of lumped sources which may be unphysical. We believe that the present effort is the first-ever attempt to directly measure noise source distribution in a rocket plume.

Panda, J.↗

An investigation of hydraulic-line resonance and its attenuation

An investigation of fluid resonance in high-pressure hydraulic lines has been made with two types of fluid dampers (or filters) installed in the line. One type involved the use of one or more closed-end tubes branching at right angles from a main line, and the other type was a fluid muffler installed in-line. These devices were evaluated in forced vibration tests with oscillatory disturbances over a 1000-Hz range applied to one end of the line and with oscillatory pressures measured at various stations along the main pipe. Limited applications of acoustic-wave theory to the branched systems are also included. Results show varying attenuations of pressure perturbations, depending on the number and location of branches and the type of muffler. Up to three branches were used in the branch-resonator study, and the largest frequency range with maximum attenuation was obtained for a three-branch configuration. The widest frequency ranges with significant attenuations were obtained with two types of fluid mufflers.

Sewall, J. L.↗

TRW plasma wave experiment for the IMP-H mission

The IMP-H plasma wave experiment is designed to extend knowledge of wave-particle interactions in the disturbed cislunar region, the distant geomagnetic tail, the upstream solar wind, and the flanks of the magnetosheath-shock interface. It is expected to identify plasma instabilities, study particle acceleration and heating at collisionless shocks and other discontinuities, analyze turbulent conductivity and field line merging, and provide new information on dissipation processes for suprathermal particles. Instrumentation for the plasma wave experiment is designed to measure local electric and magnetic field oscillations over the frequency range 10 Hz to 100 kHz. A 24 inch electric dipole, a 7 inch diameter air core search coil, and the associated preamplifiers are mounted on a spacecraft counterweight boom. The frequency range of 10 Hz to 100 kHz for both E and B is processed using an eight-channel spectrum analyzer located in the instrument main-body package (a standard IMP trapezoidal module, 3 inches high). Electric fields as small as 10-100 microvolts/meter and magnetic signals as small as 1-3 milligamma will be detected.

Virobik, P. F.↗

Analysis of proposed criteria for human response to vibration

The development of criteria for human vibration response is reviewed, including the evolution of the ISO standard 2631. The document is analyzed to show why its application to vehicle ride evaluation is strongly opposed. Alternative vertical horizontal limits for comfort are recommended in the ground vehicle ride frequency range above 1 Hz. These values are derived by correlating the absorbed power findings of Pradko and Lee with other established criteria. Special emphasis is placed on working limits in the frequency range of 1 to 10 Hz since this is the most significant area in ground vehicle ride evaluation.

Janeway, R. N.↗

Development of NDE/NDT Tools for High-Volume & High-Speed Inspection of CFRP Structures in Automotive Manufacturing

Main advantages of the air-coupled ultrasound testing (ACUT) and electromagnetic testing (EMT) techniques for NDE of CFRP composites were non-contact sensing, scalability for high-speed inspection, cost-effectiveness, and non-hazardous operation. Despite these advantages, no systems that would satisfy the project requirements were commercially available. Hence, one of the major efforts of the Michigan State University (MSU) team at the initial stage of the project was to close this technological gap by developing, optimizing, and validating array sensors that would provide sufficient sensitivity, spatial coverage, and resolution for robust defect detection. Optimization of the ACUT and EMT sensor designs was performed using experimentally validated finite element models. Initial experiments using array probes were conducted on relatively flat CFRP samples. In parallel, the MSU team designed and assembled a portable platform with two robotic arms. The robots were equipped with newly designed sensors that enabled high-speed NDE of curved CFRP parts. Presently, the developed robotic platform can be used as a demo/template NDE system, which is easily adaptable to manufacturing environments and in-line NDE. The ACUT NDE system developed by the MSU team used a high-power 4-channel pulser receiver for parallel data acquisition. The array probes were designed by stacking commercially available ACUT transducers, which operated in the frequency range between 100 kHz and 500 kHz. MSU optimized the excitation procedure and developed wave focusing cones so as to reduce the crosstalk between the transducers and to provide higher pulse repletion frequency (PRF). The through-transmission (TT) and single-side access (SSA) inspection modes were successfully implemented. In the TT-ACUT, structural defects in CFRP were detected by passing ultrasonic waves through the test part. Hence, the ACUT transmitters and receivers needed to be placed on the opposite sides of the test part. In the SSA-ACUT, guided waves (GW) were excited in the test part using the transmitters and were sensed by the receivers from the same side. Multi-channel TT-ACUT and SSA-ACUT provided high-speed NDE, and were successfully validated on CFRP test samples with interlaminar delaminations and other embedded defects The EM techniques developed by the MSU team included: 1) eddy current testing (ECT), 2) capacitive imaging (CI) and hybrid dual-mode imaging. In ECT, structural damage was detected in CFRP using coils sensor arrays. In ECT, the excitation magnetic field is generated by passing an alternating current through a coil, which is placed above the test sample. The excitation field penetrates the conductive sample and induces the eddy currents in its transect. In turn, the eddy currents generate the reaction field, which affects the total field sensed by a coil. Hence, the presence of structural flaws will alter the eddy current flow and the picked-up signal. ECT is mostly sensitive to local changes of the electric conductivity of the test sample, and CFRPs are mostly conductive in the direction of carbon fibers. Hence, ECT was well suited for the detection of fiber damage/fiber irregularities. The MSU team developed printed circuit boards (PCB) with coil sensor arrays optimized for NDE of CFRP. Unlike most commercial probes designed for ECT of metallic structures, the MSU array probes were designed for operation in [1-10] MHz frequency range, which was optimal for low-conductive CFRP. Multiple sensing topologies (coil groups excitation/sensing arrangements) were implemented and successfully validated. Capacitive Imaging (CI) technique developed by MSU was complementary to ECT. In contrast to ECT, which was sensitive to local changes of the electrical conductivity, the CI was sensitive to local changes of the dielectric constant. Therefore, CI could provide information about matrix damage/matrix irregularities in CFRP. The MSU CI sensor arrays were made of multiple circular or rectangular open-plate capacitors printed on PCB. Sensors of this type are not commercially available. In addition to ECT and CI, the MSU team developed a hybrid (dual-mode) inductive/capacitive measurement technique that synergistically combined the benefits of inductive and capacitive sensing for rapid NDE of fiber reinforced polymer (FRP) composite structures. Fiber damage and fiber irregularities in FRPs were detected by configuring hybrid sensors as coil sensors. Similarly, matrix damage, matrix irregularities and interlaminar delaminations were detected by configuring hybrid sensors as capacitive sensors. ECT and CI were performed sequentially by means of electronic switching. Hence, eliminating the need for mounting two separate sensor arrays on the probe. Portable robotic platform was developed by MSU for multi-technique high-speed NDE of CFRP test parts. The platform had two 6-axis robots, which enabled inspection of curved parts in approximately a 6×6×6 ft 3 active scan area. On the software side, the MSU team integrated scripts for NDE hardware control with scripts for robot motion control. MSU also implemented automated path planning for the robots, reconstruction of part’s surfaces via stereovision, 3D rendering of inspection data, and image processing algorithms for enhanced defect detection. Automotive composite parts manufactured by Plasan Composites from Phase I were used to validate the ACUT and EMT techniques on representative testbeds. Among those parts were three X-braces for a Dodge Viper, one composite calibration plaque with known defects at known locations, and four other test sections, including sections from a front splitter, a corner section from a composite hood, and a high-pressure RTM panel made using non crimp fabric. Other test samples included CFRP and GFRP calibration plates with fiber/matrix defects fabricated at MSU/CVRC.

36 MATERIALS SCIENCE↗

Experimental study of noise transmission into a general aviation aircraft

The effect of add-on treatments on noise transmission into a cabin of a light aircraft was studied under laboratory conditions for diffuse and localized noise inputs. Results indicate that stiffening skin panels with honeycomb would provide on the average 3dB to 7 dB insertion loss over the most of selected frequency range H1 to 1000 Hz. Addition of damping tape on top of the honeycomb treatment increases insertion loss by 2dB to 3dB. Porous acoustic blankets show no attenuation of transmitted noise for frequencies below 300 Hz. Insertion of impervious vinyl septa between the layers of porous acoustic blankets do not provide additional noise reduction for frequencies up to about 500 Hz. Similar behavior was observed for noise barriers composed of urethane elastomer, decoupler foam and acoustic foam. A treatment composed from several layers of acoustic foams does not increase noise attenuation for the entire frequency range studied. An acoustic treatment composed of honeycomb panels, constrained layer damping tape, 2 to 3 inches of porous acoustic blankets, and limptrim which is isolated from the vibrations of the main fuselage structure seems to provide the best option for noise control.

Vaicaitis, R.↗

Investigation of nonlinear E.M. phenomena in the tethered magnetospheric cloud

Nonlinear effects of parametric and of heating type, produced in a plasma under the action of an electric field E(sub 0)(e exp i(omega)t), are considered in this work in connection with the Tethered Magnetospheric Cloud (TMC) accompanying the Tether Satellite System (TSS). The theoretical results show that these phenomena should appear in the ionosphere at high altitudes Z greater than or = (150-200) km, particularly, at Z approximately = 300 km of the TSS system orbit. Therefore, it is of a special interest to search these phenomena by such a unique experiment as the forthcoming first TSS-I and by the future, perhaps modified TSS missions. Because of the parametric decay instability, new branches of wave may be excited both around the electron and ion Lengmuir frequencies Omega (sub 0) = 2(pi)f(sub 0) and Omega (sub 0) = 2(pi)f(sub 0) under the influence of high frequency (HF), (f less than or = 10(exp 6) to few 10(exp 6) Hz), strong electric waves. The heating of all the kinds of particles is growing up very quickly in the ionosphere with altitude in the extra low and very low frequency ranges, F approximately = (1 to 10(exp 4) Hz, discussed below. The temperatures (energies), for example, of the electrons accelerated by the electric field become larger than the ionization potential in this frequency range already at altitudes Z greater than or = (150 - 200) km when the amplitude of the electric field is the absolute value of E(sub 0) approximately = (1-2) mV/m. The sources of these electric fields may be in the TSS-I mission, that so called Phantom Loop (PL) - the Tethered Electrodynamic Tail (TET), and the different kind of electromagnetic oscillations produced by different kinds of instabilities in the TMC plasma. The growth rates of these instabilities will become very high in the TSS surrounding magnetoplasma. However, in the future TSS missions, special artificial sources (generators) of electric fields should be used for these investigations.

Alpert, Yakov L.↗

Vestibular afferent responses to microrotational stimuli

Intracellular microelectrode recording/labeling techniques were used to investigate vestibular afferent responses in the bullfrog, to very small amplitude (less than 5 deg p-p) sinusoidal rotations in the vertical plane over the frequency range of 0.063-4 Hz. Robust responses to peak accelerations as low as 0.031 deg/sec per sec were obtained from units subsequently traced to either the central portion of the anterior canal crista or the striolar region of the utricle. All of these microrotationally sensitive afferent neurons had irregular resting discharge rates, and the majority had transfer ratios (relative to rotational velocity) of 1-40 spikes/sec per deg/sec. Individual utricular afferent velocity transfer ratios were nearly constant over the frequency range of 0.125-4 Hz. Canal units displayed decreasing response transfer ratios as stimulus frequencies increased. These findings indicate that, although utricular striolar and central crista afferent velocity transfer ratios to microrotations were very similar, utricular striolar afferent neurons were more faithful sensors of very small amplitude rotational velocity in the vertical plane.

Myers, Steven F.↗

Whistlers in Neptune's magnetosphere: Evidence of atmospheric lightning

During the Voyager 2 flyby of Neptune, a series of 16 whistler-like events were detected by the plasma wave instrument near closest approach. These events were observed at radial distances from 1.30 to 1.99 R sub N and magnetic latitudes from -7 to 33 deg. The frequencies ranged from 6.1 to 12.0 kHz, and the dispersions fit the Eckersley law for lightning-generated whistlers. Lightning in the atmosphere of Neptune is the only known source of such signals. The frequency range of the whistlers (up to 12 kHz) indicates that the local electron densities are substantially higher (N sub e greater than 30 t0 100 per cu cm) than indicated by the in situ plasma measurements. The dispersion of the whistlers is very large, typically 26,000 sec Hz(exp 0.5). Based on existing plasma density models and measurements, the dispersions are too large to be accounted for by a single direct path from the lightning source to the spacecraft. Therefore, multiple bounces from one hemisphere to the other are required. The most likely propagation path probably involves a lightning source on the dayside of the planet, with repeated bounces through the dense dayside ionosphere at low L-values.

Gurnett, D. A.↗

Whistlers in Neptune's magnetosphere - Evidence of atmospheric lightning

During the Voyager 2 flyby of Neptune, a series of 16 whistler-like events were detected by the plasma wave instrument near closest approach. These events were observed at radial distances from 1.30 to 1.99 R sub N and magnetic latitudes from -7 to 33 deg. The frequencies ranged from 6.1 to 12.0 kHz, and the dispersions fit the Eckersley law for lightning-generated whistlers. Lightning in the atmosphere of Neptune is the only known source of such signals. The frequency range of the whistlers (up to 12 kHz) indicates that the local electron densities are substantially higher (N sub e greater than 30 to 100 per cu cm) than indicated by the in situ plasma measurements. The dispersion of the whistlers is very large, typically 26,000 sec Hz(exp 0.5). Based on existing plasma density models and measurements, the dispersions are too large to be accounted for by a single direct path from the lightning source to the spacecraft. Therefore, multiple bounces from one hemisphere to the other are required. The most likely propagation path probably involves a lightning source on the dayside of the planet, with repeated bounces through the dense dayside ionosphere at low L-values.

Gurnett, D. A.↗

Modeling of THz Lasers Based on Intersubband Transitions in Semiconductor Quantum Wells

In semiconductor quantum well structures, the intersubband energy separation can be adjusted to the terahertz (THz) frequency range by changing the well width and material combinations. The electronic and optical properties of these nanostructures can also be controlled by an applied dc electric field. These unique features lead to a large frequency tunability of the quantum well devices. In the on-going project of modeling of the THz lasers, we investigate the possibility of using optical pumping to generate THz radiation based on intersubband transitions in semiconductor quantum wells. We choose the optical pumping because in the electric current injection it is difficult to realize population inversion in the THz frequency range due to the small intersubband separation (4-40 meV). We considered both small conduction band offset (GaAs/AlGaAs) and large band offset (InGaAs/AlAsSb) quantum well structures. For GaAs/AlGaAs quantum wells, mid-infrared C02 lasers are used as pumping sources. For InGaAs/AlAsSb quantum wells, the resonant intersubband transitions can be excited by the near-infrared diode lasers. For three- and four-subband quantum wells, we solve the pumpfield-induced nonequilibrium distribution function for each subband of the quantum well system from a set of rate equations that include both intrasubband and intersubband relaxation processes. Taking into account the coherent interactions between pump and THz (signal) waves, we calculate the optical gain for the THz field. The gain arising from population inversion and stimulated Raman processes is calculated in a unified manner. A graph shows the calculated THz gain spectra for three-subband GaAs/AlGaAs quantum wells. We see that the coherent pump and signal wave interactions contribute significantly to the gain. The pump intensity dependence of the THz gain is also studied. The calculated results are shown. Because of the optical Stark effect and pump-induced population redistribution, the maximum THz gain saturates at larger pump intensities.

Liu, Ansheng↗

Structural Dynamic Analysis of a Spacecraft Multi-DOF Shaker Table

Finite element enforced response analysis was performed on a three axis expander head shaker table to aid in the design of the table structure and vibration control system. The payload for this shaker system is a generic spacecraft with a multitude of flexible modes across a broad frequency band. A Craig-Bampton representation of the spacecraft was used to expedite analysis of multiple shaker table designs. The analysis examines the required forces in the actuators for a constant amplitude base acceleration sine sweep test, the resulting forces in the spacecraft and table attachment restraints, and the resulting accelerations on the spacecraft structure. The results show the spacecraft response is very high at the spacecraft center of gravity (CG) due to the high CG offset and cantilever effect of the low frequency spacecraft bending modes. The high response can be addressed by "notching" the input vibration levels to avoid over-testing the spacecraft. At frequencies above 25 Hz, the spacecraft modal effective masses are very small, and the response of the shaker table dominates the response. Anti-resonances of the shaker table in the frequency range of interest reduce the acceleration output and require much higher actuator forces to achieve the acceleration specification. These effects may require stiffening the shaker structure to move the modes out of the test frequency range or increasing the shaker table damping.

Pray, Carl↗

Structural Dynamic Analysis of a Spacecraft Multi-DOF Shaker Table

Finite element enforced response analysis was performed on a multiple degree of freedom expander head shaker table to aid in the design of the table structure and vibration control system. The payload for this shaker system is a spacecraft with a multitude of flexible modes across a broad frequency band. A Craig-Bampton representation of the spacecraft was used to expedite analysis of multiple shaker table designs. The analysis examines the required forces in the actuators for a constant amplitude base acceleration sine sweep test, the resulting forces in the spacecraft and table attachment restraints, and the resulting accelerations on the spacecraft structure. The results show the spacecraft response at low frequencies is very high near the tip due to the low order spacecraft bending and axial modes. The high response can be addressed by notching the input vibration levels to avoid overtesting the spacecraft. At frequencies above 25 Hz, the spacecraft modal effective masses are very small, and the response of the shaker table dominates the response. Anti-resonances of the shaker table in the frequency range of interest reduce the acceleration output and require much higher actuator forces to achieve the acceleration specification. These effects may require stiffening the shaker structure to move the modes out of the test frequency range or increasing the shaker table damping.

Pray, Carl↗