Lowest Natural Frequency Research Articles

Experimental Investigation on the Transfer Behavior and Environmental Influences of Low-Noise Integrated Electronic Piezoelectric Acceleration Sensors

Acceleration sensors are vital for assessing engineering structures by measuring properties like natural frequencies. In practice, engineering structures often have low natural frequencies and face harsh environmental conditions. Understanding sensor behavior on such structures is crucial for reliable measurements. The research focus is on understanding the behavior of acceleration sensors in harsh environmental conditions within the low-frequency acceleration range. The main question is how to distinguish sensor behavior from structural influences to minimize errors in assessing engineering structure conditions. To investigate this, the sensors are tested using a long-stroke calibration unit under varying temperature and humidity conditions. Additionally, a mini-monitoring system configured with four IEPE sensors is applied to a small-scale support structure within a climate chamber. For the evaluation, a signal-energy approach is employed to distinguish sensor behavior from structural behavior. The findings show that IEPE sensors display temperature-dependent nonlinear transmission behavior within the low-frequency acceleration range, with humidity having negligible impact. To ensure accurate engineering structure assessment, it is crucial to separate sensor behavior from structural influences using signal energy in the time domain. This study underscores the need to compensate for systematic effects, preventing the underestimation of vibration energy at low temperatures and overestimation at higher temperatures when using IEPE sensors for engineering structure monitoring.

TRANSFORMATIONAL MODEL OF A PLANE ROD DEFORMATION, RESTRAINED ON DOUBLE-SIDED SLIDING SUPPORTS

A linear transformational model of the dynamic deformation of a plane rod is constructed. The end sections of the plane rod are restrained on two-sided sliding supports of finite length, excluding the displacements of the surface points of end sections in the transverse direction. To describe the deformation process of restrained sections of the rod, the S.P. Timoshenko?s shear model is used. For unfixed part the classical Kirchhoff – Love model is used. The conditions for the kinematic coupling of the restrained and free sections of the rod are formulated. Based on the Hamilton – Ostrogradsky variational principle, the equations of motion, the corresponding boundary conditions, as well as the force conditions for the coupling of the sections are obtained in a geometrically linear approximation. Based on the obtained equations of motion, exact analytical solutions of free and forced harmonic oscillations problem of the plane rod were constructed. It is shown that within the framework of the deformation models used, the problems of longitudinal and bending vibrations of the rod are separated. Of these, bending vibrations occurring in a relatively low frequency range are of greatest practical interest. For them, numerical experiments were carried out to determine the three lower natural modes and frequencies of vibrations, as well as the dynamic response during resonant vibrations of a plane rod on the marked frequencies made of a unidirectional fiber composite based on ELUR-P carbon fiber and XT-118 epoxy. A significant transformation of transverse tangential stresses is shown during the transition through the boundaries from the free section of the rod to restrained one. Such transformation due to the difference in deformation models of the marked areas, as well as their pronounced localization in the areas of restrained areas located near the marked boundaries.

Active Vibration Control of Flexible Structures with Super-Coiled Actuators

Flexible structures show low natural frequencies and light damping and often suffer from various dynamic loads, leading to low-frequency vibrations. Active vibration control is necessary for precision operation and long-term service of such structures, and a flexible actuator with a large actuation force and stroke is a key limitation. In this paper, super-coiled (SC) actuators, fabricated from fibers by twisting and inserting, were introduced to actively suppress the low-frequency vibration of flexible structures. Two SC actuators were symmetrically mounted on both surfaces of a cantilever beam to generate actuation forces. The force model of thermally driven SC actuators was developed, and a dynamic model of a cantilever beam with SC actuators was then proposed and validated via experimental actuation. Three types of control strategies, open loop, velocity negative feedback, and linear quadratic regulator (LQR), were adopted for vibration suppression. The results show that the proposed model fits quite well with the experimental data, and the maximum error between the experiment and the prediction is 3.90% among various driven currents. In velocity negative feedback control and LQR control, a 91.83% reduction of dynamic response is achieved, which validates the feasibility of using the actuator for low-frequency vibration control.

Multiple internal resonance couplings and quasi-periodicity patterns in hybrid-shaped micromachined resonators

Micro- and nano-electromechanical systems may experience internal resonances, which are inherently strengthened by the systems' nonlinearities. In the present paper, we investigate the dynamics of a hybrid resonator, combining straight and initially curved microbeam shapes. The curved part length is tailored to monitor the three lowest natural frequencies and induce simultaneous internal resonances between first and second modes and second and third modes. We examine the nonlinear interaction of dual hardening and softening bending of the fundamental frequency response curves. Due to the specific frequency ratios, different types of subcombination internal resonances emerge, with quasi-periodic energy transfer among the modes. The subcombination may result in frequencies closely-spaced, which leads to quasi-periodic beating among the frequencies involved and, due to the strong nonlinearities, to the emergence of intermodulation products. We analyze the different patterns underlying the quasi-periodicity, which are intrinsically related to the frequency ratios and deeply affected by the nonlinearities.

Augmenting the seismic performance of unreinforced masonry loess - Cave with composite materials through shaking table testing

To improve the seismic performance level of existing masonry buildings, a composite reinforcement method of polypropylene packaging strap (PP) and cement was used to design unreinforced masonry loess-cave (URML) structural models with a scale ratio of 1:4, and shaking table tests were conducted on these models. Reinforcement measures were used to reinforce the earthquake-damaged URML structure, and vibration table tests were conducted again on the reinforced URML structure using the same loading procedure. A comparative analysis was conducted on the failure modes, acceleration response, displacement response, torsional effect, and energy dissipation capacity of two model structures under earthquake action, and their seismic performance was evaluated. The experimental results show that the overall seismic performance of the URML structure is poor, with a low natural frequency, large displacement response, and obvious torsional effect. It is close to collapse under the PGA = 0.8 g earthquake action; the model (RML) structure strengthened with PP strap and cement combination has an increased natural frequency, smaller displacement response compared to the unreinforced model, and it has a significantly controlled crack propagation. The destructive effect of the structural torsion effect is significantly reduced. Under the PGA = 0.8 g earthquake, only slight damage occurs to the water mud surface layer. The combination of the PP strap and cement reinforcement method can effectively delay the stiffness degradation of URML structures under strong earthquake action, increase the damage resistance of the structure, and effectively improve the overall seismic resistance of such masonry structures.

Active Vibration Control Using Loudspeaker-Based Inertial Actuator with Integrated Piezoelectric Sensor

With the evolution of the aerospace industry, structures have become larger and more complex. These structures exhibit significant characteristics such as extensive flexibility, low natural frequencies, numerous modes, and minimal structural damping. Without implementing vibration control measures, the risk of premature structural fatigue failure becomes imminent. In present times, the installation of inertial actuators and control signal acquisition units typically requires independent setups, which can be cumbersome for practical engineering purposes. To address this issue, this study introduces a novel approach: an independent control unit combining a loudspeaker-based inertial actuator (LBIA) with an integrated piezoelectric ceramic sensor. This unit enables autonomous vibration control, offering the advantages of ease of use, low cost, and lightweight construction. Experimental verification was performed to assess the mechanical properties of the LBIA. Additionally, a mathematical model for the LBIA with an integrated piezoelectric ceramic sensor was developed, and its efficacy as a control unit for thin plate structure vibration control was experimentally validated, showing close agreement with numerical results. Furthermore, the LBIA’s benefits as an actuator for low-frequency mode control were verified through experiments using external sensors. To further enhance control effectiveness, a mathematical model of the strain differential feedback controller based on multi-bandpass filtering velocity improvement was established and validated through experiments on the clamp–clamp thin plate structure. The experimental results demonstrate that the designed LBIA effectively reduces vibration in low-frequency bands, achieving vibration energy suppression of up to 12.3 dB and 23.6 dB for the first and second modes, respectively. Moreover, the LBIA completely suppresses the vibration of the fourth mode. Additionally, the improved control algorithm, employing bandpass filtering, enhances the effectiveness of the LBIA-integrated sensor, enabling accurate multimodal damping control of the structure’s vibrations for specified modes.

Vibration analysis of higher-order nonlocal strain gradient plate via meshfree moving Kriging interpolation method

In this paper, a higher-order nonlocal strain gradient plate model combining nonlocal elasticity theory with strain gradient theory in the form of adding signs is constructed. The governing equation for the higher-order nonlocal strain gradient plate model is derived by Hamilton’s principle. Two higher-order parameters with nonlocal stress and strain gradient are introduced here to explain the size effect and dispersive behaviour. The meshfree moving Kriging interpolation method is utilized to address the frequency of higher-order nonlocal strain gradient plate under complicated boundary conditions. Nonlocal elasticity theory, strain gradient theory in the form of add signs and minus signs on the effect of frequency are compared by degenerating the higher-order nonlocal strain gradient plate model. The other goal of this paper is to compare the present model with higher-order nonlocal strain gradient theory in the form of minus signs on the effect of frequency. It is shown that these two items can describe the size effect well. The present method can also produce lower natural frequencies corresponding to ultrahigh-order mode shapes and applied in a discrete medium.

On the Structural Behavior of MEMS Shallow Arch under Combined Effects of In-Plane Parallel Fields and Out-of-Plane Fringing-Fields

We propose to study the nonlinear stroke and lower-order modal interactions of a clamped–clamped shallow-arch flexible micro-electrode. The flexible electrode is electrically actuated through an in-plane parallel-plates field superimposed over out-of-plane electrostatic fringing fields. The in-plane electrostatic fields result from a difference of potential between the initially curved flexible electrode and a lower stationary parallel-grounded electrode. Moreover, the out-of-plane fringing fields are mainly due to the out-of-plane asymmetry of the flexible shallow arch and two respective surrounding stationary side electrodes (left and right). A nonlinear beam model is first introduced, consisting of a nonlinear partial differential equation governing the flexible shallow-arch in-plane deflection. Then, a resultant reduced-order model (ROM) is derived assuming a Galerkin modal decomposition with mode-shapes of a clamped–clamped beam as basis functions. The ROM coupled modal equations are numerically solved to obtain the static deflection. The results indicate the possibility of mono-stable and bi-stable structural behaviors for this particular device, depending on the flexible electrode’s initial rise and the size of its stationary side electrodes. The eigenvalue problem is also derived and examined to estimate the variation of the first three lower natural frequencies of the device when the microbeam is electrostatically actuated. The proposed micro-device is tunable with the possibility of pull-in-free states in addition to modal interactions through linear coupled mode veering and crossover processes. Remarkably, the veering zone between the first and third modes can be electrostatically adjusted and reach 22.6kHz for a particular set of design parameters.

Three-Dimensional Prestressed Tuned Mass Damper for Passive Vibration Control of Coupled Multiple DOFs Offshore Wind Turbine

Large megawatts offshore wind turbine (OWT) with low natural frequency and low damping is subjected to significant vibration from wind and wave actions in its service environment. The one-dimensional prestressed tuned mass damper (PSTMD) is further extended to a 3D-PSTMD for the control of vibrations of the OWT in this paper. A multiple DOFs coupled system of turbine, blades, tower, and foundation under aerodynamic and hydrodynamic forces is considered in this study of vibration mitigation at fore-aft and side-side directions. The dynamic model is derived with the Lagrangian equation, and the superiorities of the PSTMD are proved from the perspective of theoretical analysis. Aerodynamic and hydrodynamic loads are generated with the blade element momentum (BEM) theory and Morrison equation, and the dynamic responses of different systems are computed by using the Wilson-θ method. The analysis results indicate that a damping coefficient of the 3D-PSTMD corresponding to the first vibration mode can be tuned to take up values larger than that in traditional three-dimensional pendulum (TMD) (3D-PTMD). The bidirectional vibration suppression competences of the 3D-PSTMD in the dynamic responses when under aerodynamic and hydrodynamic loads are better than those of the traditional 3D-PTMD.

Tuning Wave Energy Converters to local wave conditions

A Wave Energy Converter (WEC) cannot operate efficiently if left alone floating to the mercy of the random sea surface. Moreover, high waves may impose destructive forces while contributing nil energy production in return. For a WEC to be efficient, its natural frequency should be close to the peak frequency of a wave spectrum. At the resonance or another lower natural frequency, dynamic responses are more regular, and thus, the power take-off system (PTO) can operate in a more efficient manner. This paper introduces a general systematic methodology for tuning the natural frequency of a resonant WEC for the desired degree of freedom and converting dynamic responses into power. A barge is used as a case study to tune its roll and heave natural period, which in general are much lower than the peak period of swells. The roll natural period is increased by hanging subsea structures to the sides of the vessel by means of mooring lines, see Fig. 1. The size of the structures and their entrapped water increase the roll mass moment of inertia to achieve the desired period. For the heave response, the natural period raises by adding skirts to the sides of the vessel, increasing the entrapped water. The resonant motions are significantly suppressed by means of the drag force acting on the subsea structures. Thus, the extreme drag forces acting on the structures act as a damper to the vessel response. These forces are transferred to the mooring lines, which can be converted into a rotary motion of a shaft of the PTO. Our application focuses on the Galapagos Islands, where narrow, low-frequency southerly swells with a typical 13 s peak period dominate the wave climate. This study allows for a systematic design of resonant-type WECs, which is necessary for the development of technical and economic feasibility studies of various novel and existing concepts.
 
 Figure 1: Schematic representation of resonant WEC with tuned roll natural period

Evaluation of Seismic Performance of Masonry Stone Pagoda: Dynamic Centrifuge Test and Numerical Simulation Analysis

This study provides a comparison of results from dynamic centrifuge tests and a finite element analysis model to confirm the behavior of a representative Korean stone pagoda cultural heritage structure against earthquakes. The indirect stiffness or physical state of the structure was estimated by measuring the natural frequency of the masonry stone pagoda. The actual natural frequency of the stone pagoda was measured to be 4.5 Hz. It was determined to have a lower natural frequency than other stone pagodas of similar size. For the experiment, a dynamic centrifugal separator test was performed on a 1/15 model. Data from an actual earthquake record, the Ofunato earthquake, were used, with various maximum acceleration levels ranging from 0.069 g to 0.424 g. In order to confirm the accuracy of the finite element analysis model, the measured natural frequency of the masonry stone pagoda was compared with the modal analysis of the finite element model. When the data obtained from the experiment and the PGA (peak ground acceleration) of the FEM analysis with a complex masonry stone pagoda using a validated model result were compared, it was found to have a low average error rate of 13%. This shows that structural behavior can be predicted for similar masonry stone pagoda structures using finite element method analysis in the future.

Serviceability Evaluation of High-Rise Buildings Exposed to Typhoon Proximity Effects Using ISO10137 and ISO6897

This study evaluates the vibration data of high-rise buildings during a typhoon by measuring the vibration data and using international serviceability standards. In order to do this, the horizontal vibration serviceability evaluation standards of each country were surveyed, but the standards that could be applied were limited to ISO10137 and ISO 6897. Despite the trend that the discomfort of residents increases as the number of high-rise buildings increases, the current standards are for high-frequency vibrations, such as machine vibrations or vertical floor vibrations, so there is an urgent need for research on new evaluation methods for low-frequency horizontal vibrations. As a result of analyzing the effects of typhoons on buildings, the study’s target building had low natural frequencies of less than 1 Hz, and the highest acceleration was observed to be amplified up to about 160 times due to the effects of Typhoon Danas and Chaba, but there was no change in the natural frequency. When this result was applied to the horizontal vibration serviceability evaluation, it was found that the likelihood of residents perceiving vibration was low during constant vibration, but during strong winds, the size of the top-floor horizontal vibration exceeded the average level of vibration perception proposed by ISO standards, so most residents of high-rise buildings would be likely to perceive the vibration as uncomfortable.

Nonlinear coupling vibration analyses of large-scale wind turbine system

With the development of wind energy, the unit capacity of wind turbine is becoming larger and the height of the support tower is getting higher. Limited by the transport conditions, the diameter of the tubular steel tower cannot further increase with the increase of the tower height, which results in the lower natural frequencies of the tower. The higher and more slender wind turbine towers are more sensitive to the external excitation and many tower collapses have occurred in recent years because of the interplay with the longer rotor blades. A 2 MW wind turbine system with a 120 m full steel tubular tower is taken as an example in this study to research the nonlinear coupling vibration mechanism under the normal operation case and the emergency shut-down case. An integrated model of large-scale wind turbine system including the tower, blades, hub, and nacelle is established by the open-source software FAST to study its nonlinear interaction vibration mechanism. Under the normal operation load case, the acceleration response of the steel wind turbine tower is greatly affected by the rotational frequency of the rotor. The maximum accelerations in the fore-aft and side-side directions both appear around the middle-upper height of the tower. Under the emergency shut-down load case, the maximum fore-aft acceleration response appears at the top of the tower, but the maximum side-side response still appears around the middle-upper height of the tower. The first-order vibration mode plays a dominant role in the top fore-aft acceleration and the second-order vibration mode has great contribution to the side-side acceleration under the emergency shut-down load case. The numerical results of this study can provide insight into the vibration control mechanism of the full steel tower.

Identification of nonlinear aerodynamic damping of cross-wind excited slender structures in atmospheric boundary layer flow

Due to the low natural frequency and low damping of slender structures, the crosswind aero-elastic effect become dominant around the vortex-resonance wind speed and can lead to undesired crosswind responses. For understanding and describing the aero-elastic effect of slender structures, aerodynamic damping is usually adopted. This study suggested an identification procedure for crosswind aerodynamic damping of slender structures by curve-fitting the probability density function (PDF) of the crosswind response. Firstly, the aerodynamic damping is described by a generalized Van der Pol (GVDP) model, and the analytical solution of response PDF, which is a function of the parameters of GVDP model, is derived by the equivalent nonlinear equation method. Next, the proposed identification method was validated by stochastic simulation of a crosswind-excited tall building. Finally, free-vibration wind tunnel test of a slender structure with slenderness ratio equal to 12 and 20 at open flat terrain was conducted and aerodynamic damping was then quantified by the present method. It is found that the present method provides a robust and accurate identification of crosswind aerodynamic damping of slender structures in atmospheric boundary flow.

Simple Mathematical Models for the Dynamics Of Spacecraft With Deployed Solar Panels

Most present day spacecrafts have large interconnected deployed solar panels having very low natural frequencies. The control torque applied to maneuver the spacecraft sets up transient oscillations in the spacecraft. The present work studies the nature of these interactions. The spacecraft in orbit can be modeled as a free rigid mass with flexible elements attached to it. It is shown that the oscillations of the spacecraft body are characterized by the dynamic characteristics of the flexible panel even if the mass and mass moment of inertia of the body is signifcantly higher than that of the flexible panels. A simple model consisting of an Euler-Bernoulli beam attached to a mass can represents such a system. The infuence of various parameters of the Euler-Bernoulli beam and the rigid element on the disturbances caused in the rigid element are investigated. The characteristics are determined for a step and also for a torque input. The responses are obtained in terms of nondimensionalised quantities. It is demonstrated that using the simple model developed the responses of spacecraft body can be easily obtained.

Performance analysis on the structure of the bracket mounting for hybrid converter kit: Finite-element approach

Abstract An electric motor mounting bracket is used in electric vehicles, especially hybrid ones using a parallel hybrid configuration. This study aims to analyze the strength and performance of the initial design and topology optimized design. This study uses the finite-element method (FEM) in the bracket design modeling by applying topology optimization. The topology optimization results show a mass reduction of 50% from the initial design mass. In the case of static loading, the results of optimized design 2 have a stress of 142.19 MPa and a safety factor of 3.09. While optimized design 1 has a stress of 313.8 MPa and a safety factor of 1.4. In terms of dynamic loading, the initial design, optimized design 1, and optimized design 2 have the first natural frequency, which is higher than the operating frequency of the electric motor, respectively, 100.49, 69.043, and 74.864 Hz. Optimized design 1 has the lowest natural frequency and the highest amplitude compared to the initial design, and optimized design 2 has lower damping characteristics. The study results conclude that optimized design 2 is superior in static and dynamic loading.

Dynamic analysis of thick plates reinforced with agglomerated GNPs

In this work, the quasi-3D hyperbolic shear deformation theory (quasi-3D HSDT) is utilized to examine the dynamics of thick rectangular plates reinforced with rectangular nanofillers known as graphene nanoplatelets (GNPs). Agglomeration of the GNPs is incorporated and the mechanical characteristics like shear, elastic, and bulk moduli, Poisson's ratio, and density are analysed according to the mixture along with the Eshelby-Mori-Tanaka approach. Hamilton's principle is hired to derive the solving equations, the Navier approach is hired to present an analytical solution in the spatial domain, and the Newmark method is hired to provide an approximate solution in the time domain. The relevance of the dynamic response and the natural frequencies of the plate on several parameters are explored such as dispersion pattern and the GNPs percentage and agglomeration parameters. It is discovered that for a specific GNPs percentage, growth in the amount of agglomerated GNPs leads to lower natural frequencies and higher dynamic deflection. Meanwhile, for a specific mass fraction of the agglomerated GNPs, growth in the volume of clusters brings about higher natural frequencies and lower dynamic deflection.

BEM modeling for the hydrodynamic analysis of the perforated fish farming vessel

As the aquaculture industry progresses from coast to deep sea, the higher strength requirement for aquaculture infrastructure has promoted the rapid development of fish farming vessels. To consider the interaction between waves and floating aquaculture systems, the hydrodynamic and seakeeping performances of the perforated fish farming vessel are studied by using an efficient numerical method, which combines porous theory and potential flow theory. The linear pressure drop porous condition is incorporated into the potential flow boundary conditions. The submerged porous shell of negligible thickness is represented by a dipole distribution to construct a boundary element method (BEM) modeling the wave interactions with a fish farming vessel. A perforated fish farming vessel with openings on the sidewalls is taken for an example, and the effects of the openings and other important factors such as the opening ratio of the metal net and the number of openings on the motion response, wave load, and hydrodynamic coefficients are analyzed by numerical stimulation. The variation of the opening ratio is represented by the discharge coefficient. The natural frequencies of the modified fish farming vessel are significantly altered, and an improved seakeeping performance is exhibited, especially in terms of the roll, because of wave energy dissipation by the porous shell. The added mass and damping in the low frequency range significantly change due to the effect of tank fluid, which decreases as the discharge coefficient and the number of openings increase. With the increases in the discharge coefficient and the number of openings, the hydrodynamic coefficients of heave increase, with a lower natural frequency. The wave loads of surge, heave, and pitch exhibit a fluctuating behavior within a certain frequency range and become pronounced with the effect of tank fluid increases. The spectral analysis results indicate a better performance of the perforated vessel in the extreme sea state, making it feasible for offshore operations.

Computational modeling of sigmoid functionally graded material (SFGM) plate

The first-order shear deformation theory (FSDT) was used to explore the natural frequency response of functionally graded piezoelectric plates subjected to static electrical and mechanical strain in this present study. A monomorph model for a functionally graded piezoelectric plate with material properties that change according to sigmoid law with respect to plate thickness has been considered. A three-dimensional finite element model with a free tetrahedral element mesh was created using COMSOL 4.2 Multiphysics® software, with each node having three degrees of freedom. Variations in the FGPM plate’s free vibration boundary conditions, composition, and geometry have all been investigated. In free vibration analysis, non-dimensional natural frequency of FGPM plate initially decreasing considerably and then remaining almost constant with the increase in volume fraction index when material property graded by power law. When material properties are varied by sigmoid law, with an increase in volume fraction index, the non-dimensional natural frequency of FGPM plates remains virtually constant. FGPM plates have a lower non-dimensional natural frequency if the thickness to width ratio is greater. Non-dimensional natural frequencies of Clamped-Clamped FGPM plates (C–C–C–C) are greater compared to Clamped-Free FGPM (C–F–C–F) and Simply Supported Free FGPM (S–F–S–F).

A Nonlinear Impact-Driven Triboelectric Vibration Energy Harvester for Frequency Up-Conversion.

Energy harvesting effectively powers micro-sensors and wireless applications. However, higher frequency oscillations do not overlap with ambient vibrations, and low power can be harvested. This paper utilizes vibro-impact triboelectric energy harvesting for frequency up-conversion. Two magnetically coupled cantilever beams with low and high natural frequencies are used. The two beams have identical tip magnets at the same polarity. A triboelectric energy harvester is integrated with the high-frequency beam to generate an electrical signal via contact-separation impact motion between the triboelectric layers. An electrical signal is generated at the low-frequency beam range achieving frequency up-converter. The two degrees of freedom (2DOF) lumped-parameter model system is used to investigate the system's dynamic behavior and the corresponding voltage signal. The static analysis of the system revealed a threshold distance of 15 mm that divides the system into monostable and bistable regimes. In the monostable and bistable regimes, softening and hardening behaviors were observed at low frequencies. Additionally, the threshold voltage generated was increased by 1117% in comparison with the monostable regime. The simulation findings were experimentally validated. The study demonstrates the potential of using triboelectric energy harvesting in frequency up-converting applications.