Reduce Vibration Levels Research Articles

Development of vibration protection system with quasi-zero stiffness and adjustable parameters

Relevance. While performing the operation processes, the technological equipment emits vibration. Vibration is a consequence of increased dynamic loads in structural elements and interfaces between systems and their elements. The development of fatigue damage can significantly accelerate. Therefore, the solution of the problems related to reducing vibration levels is always relevant. Each type of protective system has a linear law of changing the stiffness. This does not allow the effective damping of low-frequency vibrations. Thus, the information review demonstrates the future of the research according to the creation of the vibration protection systems, constantly improving their parameters in the following aspects: minimizing overall dimensions and number of parts; increasing reliability, especially in resonant mode; providing the ability to operate in modes with low stiffness. The last factor determines the good damping of vibration emitted by the source. Aim. To study the possibility of the vibration protection system development with quasi-zero stiffness with the ability to effectively dampen low-frequency vibrations. Methods. Information and analytical review in the field of the research, search for the constructive solutions, preliminary design calculations and 3D modeling, description of the device being developed and its operating principles. Results. The research presents the results of development of the vibration protection system with quasi-zero stiffness and a fragment of an information review of existing vibration protection systems. The authors indicated the main shortcomings specific to all vibration protection systems: relatively large sizes, large number of elements, insufficient operating frequency range. The authors proposed a constructive solution for creating a vibration damping system with a nonlinear law of change in stiffness. This solution allows eliminating the above shortcomings and providing the possibility of effective damping of low-frequency vibrations. The authors created the method for calculating the constructive parameters of a vibration damping system. An example of calculation is given in the paper. This system differs from existing vibration protection devices in its low stiffness and small dimensions, and a wide operating frequency range of vibration damping. The efficiency of the system operating with nonlinear and quasi-zero stiffness is proved.

Delayed feedback active suspension control for chaos in quarter car model with jumping nonlinearity

Vehicles that operate on off-road terrain, such as rough and unpaved roads, sometimes suffer from severe vibrations. This vibration causes vehicle tires to lose contact with the supporting ground and subsequently collide with it. This jumping leads to nonlinear impact dynamics similar to those of a bouncing ball. In this study, a quarter car model with jumping nonlinearity is newly developed to represent the impact dynamics of an off-road vehicle under harsh terrain conditions. Subsequently, complicated vibrations, such as quasi-periodic and chaotic vibrations in the developed model, are identified using a bifurcation diagram and Lyapunov exponents. Additionally, delayed feedback (DF) control of the active suspension is designed for the developed model. The numerical results show that DF control is effective at eliminating chaos and reducing vibration levels. The noise robustness of the DF control is validated for sinus excitation and small random road noise. The results indicate that DF is effective even when road noise exists. Thus, this study demonstrates the feasibility of DF active suspension control for future suspension control design of the off-road vehicle.

SINGLE-DEGREE-OF-FREEDOM VIBRATION ISOLATION SYSTEM WITH ONE ADDITIONAL SUPPORT

Vibration isolation is one of the most effective methods for reducing vibration levels of supporting structures when installing vibroactive equipment (active vibration isolation) or vibration levels of vibro-sensitive objects relative to foundation vibration levels (passive vibration isolation). Damping devices utilizing high-speed fluid flow through apertures have found wide applications in shock vibration isolation and vibration isolation systems in aerospace and defense sectors. Recent research has led to the development of viscous fluid dampers (VFDs) for use in civil engineering, particularly in earthquake-prone areas. Scientists conducted experiments aimed at determining the ability of viscous fluid dampers to reduce damages and displacements of structures without increasing stresses. Mathematical models have been developed and are applied in vibration isolation systems. When vibroactive equipment is installed on building and structure support systems, vibrations with sufficiently high vibration parameters may occur, potentially leading to loss of load-bearing capacity. In such cases, vibration isolation is considered one of the most effective methods for reducing these vibration levels. In this study, a calculation method has been developed, and calculation dependencies and algorithms for calculating vibration protection systems with nonlinear characteristics (additional support connections, viscous fluid damper) have been derived for both single-degree-of-freedom and two-degree-of-freedom systems. The research involved an analysis of normative and scientific-technical literature on the subject: types, structural solutions, calculation, and analysis of vibration protection systems. The main method selected was based on the use of transfer functions of linear systems (the non-traditional "normal form" method). Calculations were performed using computer mathematics systems- Matlab.

Mitigating train-induced building vibrations with rubber bearings designed for horizontal earthquake isolation

As rail transportation, including high-speed railways and urban metros, rapidly expands, its proximity to residential areas decreases, raising concerns about ground-borne vibrations. This study investigates the main characteristics of ground-borne vibrations induced by high-speed railways and metros through substructure method based on 2.5D FEM-MFS (finite element method-the method of fundamental solutions). Besides, the study also delves into the vertical vibration behaviors of buildings caused by train operations, evaluating the effect of laminated rubber bearings designed for horizontal seismic isolation on the train-induced building vibration mitigation. Our findings highlight that the broadband vibrations from train operations might coincide with the natural vibration frequencies of buildings, potentially leading to resonance. Implementing isolators allows the natural frequencies of the vibration modes with larger effective masses to be significantly lower than the dominant frequencies of train-induced ground-borne vibration, reducing the high-frequency responses. Additionally, the vibration mitigation enhances with the increase in the thickness of rubber layer. This research not only aims to reduce vibration levels in buildings adjacent to railways, enhancing the living conditions and health of residents but also underscores the engineering innovations necessary for sustainable urban development.

Individual Blade Control Approach for Active Vibration Suppression of a Lift-Offset Coaxial Rotorcraft

This study explores the best vibration reduction using an individual blade control (IBC) actuation scheme for a lift-offset coaxial helicopter in high-speed flight. The rotorcraft dynamics analysis model consists of coaxial, three-bladed counter-rotating rotors and a finite element fuselage stick model constructed based on the measured data of the XH-59A helicopter. The XH-59A helicopter is well-known for its severe vibration level encountered during the flight (over 0.5g), leading to the cancellation of the development program. A special focus is given to assessing the accuracy and efficiency of the integrated rotor–body vibration predictions evaluated between the one-way and two-way coupling methods in reference to the flight data of the vehicle. The two-way rotor–body coupled results show excellent correlations with the test data for rotor blade loads and airframe vibrations. The best actuation scenarios are then sought for the minimum vibration at the rotor hub and the pilot seat. The IBC pitch actuation effectively reduces the vibrations at both locations of the rotorcraft. Specifically, a multiple-harmonic IBC actuation enables to suppress the pilot seat vibration by 93% compared to the uncontrolled case, achieving a significantly reduced vibration level (below 0.05g).

Dynamic response analysis of linear motion stage with track roller guides

This paper aims at characterizing the role of preload, friction and mass on the dynamic response of the linear motion stage used in the laser marking machine for black granite. A single-axis linear motion stage model was realized in Creo Parametric® CAE software. The mechanism design option was used to create a virtual mechanism with simulation entities for stiffness, friction, mass, damping, and motors. The experimental design was accomplished using Minitab® software to create the Taguchi orthogonal array. The simulation experiments with different values of preload, friction, and mass were conducted. The results show that increasing the linear bearing preload reduced the settling time. Increased elastic deformation increased bearing rigidity, which ultimately helped reduce vibrations and hence settling time. Furthermore, lower levels of friction reduced sticking and slipping, which led to reduced vibration levels and therefore a lower settling time.

Ground Vibration Response to Vibratory Sheet Pile Driving and Extraction

Sheet piles are extensively used as foundation structures in urban environments. However, the vibrations associated with sheet pile construction can potentially adversely affect existing buildings, as well as cause discomfort to nearby residents. This study aims to analyze ground vibration response during the driving and extraction of sheet piles. To this end, field tests of U-shaped sheet piles were conducted in Beijing silty clay, during which ground vibrations in the near-field were monitored. Subsequently, a numerical model was developed using the coupled Eulerian–Lagrangian method to simulate the pile–soil interaction characteristics and to investigate ground vibration intensity in the far-field. The research results indicate that the ground vibration response modes during the driving and extraction of sheet piles are distinctly different. Due to the entry effect, the critical depth during pile driving typically occurs in shallow soil layers, while during pile extraction, the critical depth generally corresponds to the pile’s embedded depth to overcome the soil locking effect. Ground vibrations rapidly decrease in the near-field (<6 m), while in the far-field (>6 m), the attenuation rate significantly slows down. Vibrations can be widely perceived by residents at radial distances of less than 12 m. Through a systematic assessment, it was concluded that sheet pile construction is unlikely to directly damage surrounding buildings but may inconvenience nearby residents. Additionally, a parametric analysis of the vibration source revealed that appropriately adjusting the driving frequency and amplitude can effectively reduce vibration levels.

Improving the quality of traction electric mo-tors for electric transportation

Problem. Despite the widespread use of asynchronous electric motors (ED) in electric transportation, they often fail to meet high reliability requirements. This is primarily due to their operation in a wide range of rotational frequencies, variable load modes, frequent stops and starts, and challenging road conditions. These factors result in significant vibrations of traction asynchronous EDs, leading to reduced reliability and service life. Goal: The goal of this study is to develop methods to enhance the reliability and longevity of traction asynchronous EDs by improving the design and manufacturing technology of the stator housing and rotor of the electric motor. Methodology: Analytical research methods were employed to investigate approaches for improving the quality of traction electric motors for electric transport. Experimental research methods were used to determine the technical condition of EDs based on their vibrodiagnostic parameters. Statistical methods were utilized to process experimental data. Results: Vibration levels, which are indicative of the technical condition of EDs, were selected as the primary criterion for assessing their quality. The proposed design and manufacturing technology for asynchronous electric motors enable the following: increased manufacturing and assembly precision of EDs, simplified assembly process, reduced number of sorted parts during inspection and bearing replacement, and the development of an asynchronous traction ED with a power capacity of 90 kW and a rotational frequency of 3000 rpm, meeting class D requirements with permissible vibration levels. Originality: This study presents developed methods for increasing the reliability and longevity of traction asynchronous EDs through experimental approaches. The one-sided arrangement of base surfaces in the stator housing and the attachment of rotor bearing units enabled the production of a vertical ED assembly consisting of two independently controlled units: a housing with a shield and a rotor with bearing units. Practical Value: The achieved reduction in vibration levels allows for a predicted 2-3 times increase in the lifespan of the developed ED, depending on operating conditions. Furthermore, the created ED meets all environmental standards' requirements for vibration levels.

Active control of flexible rotors using deep reinforcement learning with application of multi-actor-critic deep deterministic policy gradient

Vibration in rotating machinery is one of the main causes of machine failure. Active and passive control methods have been developed in order to reduce vibration levels and extend the operating speeds of machines. These controllers are either manually tuned or tuned during operation using adaptive control techniques and are tailored to a single vibration source. In the field of artificial intelligence, deep reinforcement learning has greatly impacted the field of continuous control, from mastering simple games to controlling multiple actuators in a robot doing complex tasks. Deep reinforcement learning agents are capable of finding optimal control policies without a model of the underlying system. This work proposes the multi-actor-critic deep deterministic policy gradient (MAC-DDPG) algorithm by integrating multiple criteria to train concurrent actors in a periodic system. Using the frequency footprint of each type of vibration, a cost function is designed to train the critics and actors. The proposed controller is evaluated on a test rig supported by two patented Smart Electro-Magnetic Actuator Journal Integrated Bearings (SEMAJIB). The proposed controller is capable of finding optimal control policies for reducing the synchronous vibration caused by the rotor’s unbalance and stabilizing a system with oil whip vibration. A derivative controller actor and a harmonic actor are used concurrently for controlling the vibrations. The proposed controller is able to reach unbalance vibration reduction up to 93%. In addition, the proposed controller is successful in completely eliminating oil whip instability with up to 99% reduction.

Исследование смягчения вибраций и переизлученного шума в зданиях, создаваемых при движении железнодорожного транспорта

Purpose: To present an integrated methodology that will model the entire environment, from the source of vibration to the re-radiated noise within buildings. Conduct a brief parametric analysis to show the potential of this approach in evaluating the effectiveness of mitigation measures for vibration and re-radiated noise. Methods: Estimate sound pressure levels generated in residential compartments as a result of train travel; analyze the coupled train-trail-ground-construction system; solve the acoustic part of the problem. Results: A numerical model based on the substructuring approach is considered. A measure to reduce the level of vibration and re-radiated noise inside the building has been studied, which consists in a continuous “floating slab-track” system, for which different values of the elastic mat stiffness under the slab have been considered. It has been found that the effectiveness of this measure comes from a positive combination of two essential factors: the frequency content of the response and the cutoff frequency assigned to each solution adopted. Practical significance: A comprehensive methodology for determining ground vibration and re-radiated noise caused by railway traffic is presented. The dependence is obtained, that the efficiency of reduction of vibration level and re-radiated noise inside the building, will be higher, if the solution with low cutoff frequency is applied and the response has the most significant frequency content at high frequencies.

Research on longitudinal vibration suppression of underwater vehicle shafting based on particle damping

A particle damper is applied to suppress the longitudinal vibration of underwater vehicle shafting in order to reduce vibration level and improve silence and stealth of underwater vehicles. The model of rubber-coated steel particle damper was established with discrete element method and PFC3D simulation software, the damping energy consumption law of collision and friction between particle and damper and between particle and particle investigated, the effects of particle radius, mass filling ratio, cavity length, excitation frequency, excitation amplitude, rotating speed and both stacking and motion states of particles on the system vibration suppression were discussed, and the bench test was carried out to verify the law. It revealed the mechanism of longitudinal vibration suppression of particle damping, established the intrinsic relationship between of total energy consumption of particle and vibration of system, and put forward the evaluating method of longitudinal vibration suppression effect by total energy consumption of particle and vibration reduction ratio. The research results show that the mechanical model of particle damper is reasonable and the simulation data is reliable; the rotating speed, mass filling ratio and cavity length have significant effects on the total energy consumption of particle and vibration reduction ratio.

Comparative experimental investigation of the vibration mitigation characteristics of ballasted track using the rubber composite sleeper and concrete sleeper under various interaction forces

The vibrations of railway track occur because of extreme impact load conditions due to the train operations with either wheel or rail irregularity. The vibrations result in track deterioration and severe environmental influences. Therefore, an urgent need exists to manufacture a sleeper/tie to mitigate these effects. This paper used a full-scale model with different kinds of sleepers to measure the vibration mitigation attributes and dynamic characteristics of recently recycled rubber composite sleepers (RCSs) when applied to ballasted railway tracks and compared them with concrete sleepers (CSs). A high-capacity drop hammer weight impact test was used to achieve this purpose, and the vibration effects on the track structural elements were analyzed. Two cases and a series of interaction force height (IFHs) impacts for both sleepers were applied. The results show that RCSs under the various impacts of the IFHs can reduce the peak acceleration of ground-borne vibration between 38.35%∼66.23%, and can decrease vertical vibration by 63.12%∼96.09%. The time and frequency domain investigations over the lateral and vertical directions of the track showed that the track with RCSs had lower vibration acceleration peaks, fewer frequency peaks, decreased velocity, and shorter vibration cycles than the track with CSs. RCSs significantly reduced vibration levels by −5.04 dB, 1.71 dB, and −2.46 dB (and 11.77 dB in case two) for the rails, sleepers, and ballast, respectively. Moreover, the RCSs decreased the VAL of ground-borne vibration between 10.6 dB ∼ 18.6 dB. Thus, in this study RCSs have shown the advantageous ability to minimize environmental issues, track deterioration, and noise.

Active Control System Applied to Vibration Level Control in High-Speed Elevators

This work presents an active control system applied to vibration level reduction in high-performance vertical transport, aiming at improving the passengers’ comfort in high-speed elevators. The control system design includes the use of a Proportional Integral Derivative (PID) control. Three strategies were proposed in order to achieve a 90% reduction in the vibration amplitudes: (I) the consecutive reduction of 90% of the displacements, (II) the consecutive reduction of 90% of the velocity, and (III) the consecutive reduction of 90% of the acceleration. The presentation of these three proposals allows their application for the use of different sensors. The performance of each strategy was evaluated through mathematical modeling and numerical simulations of a vertical transport with 4 degrees of freedom, submitted to excitations arising from rail deformations. Vibration and comfort levels in the cabin were numerically analyzed, taking into account ISO 2631 and BS 6841 standards for elevator lateral acceleration level and comfort level felt by passengers. Numerical simulations showed that the force required to reduce the vibration levels is practically the same for the three proposed strategies. However, strategy (III) – the successive reduction of 90% of acceleration – proved to be more efficient at improving passengers’ comfort level when compared to the other two strategies.

Vibration characteristics of tractor gearboxes

Problem. Improving the efficiency, quality, reliability and economy of tractor equipment is one of the most important tasks of modern society. This is due to the fact that in agriculture, tractors can perform up to 80% of various operations. The cost of production, product quality, compliance with the conditions of technological operations, etc. depend on the properties and reliability of tractors. The main factor limiting the effective use of tractors in agriculture is the problem of insufficient reliability of tractors, namely, the reliability of its individual components. One of the most important units is its gearbox. The existing methods for diagnosing tractor gearboxes are designed to detect damage, but they are not able to determine the quality of the gearbox at the design and manufacturing stage. Such an opportunity would greatly simplify the process of diagnosing tractor boxes. Goal. The purpose of the research is to assess the quality of design and manufacture of tractor boxes according to their vibration characteristics by identifying design and manufacturing defects, which will allow developing the ways to improve them. Methodology. Methods for detecting statistical data on the boundary values of structural vibrational parameters and their connection with the technical condition of tractors were used. Experimental research methods and mathematical methods for processing and modulating the results obtained were used as well as the methods of statistical calculation and comparison of vibration characteristics with permissible vibrations that do not affect the acceleration of the process of tractor parts wear. Results. Experimental studies of vibro-diagnostic characteristics of tractors were carried out. Studies were made to measure vibration diagnostic indicators; a spectral analysis of gearbox vibration was carried out. An assessment of the quality of manufacturing parts and assembly of tractor gearboxes was made. Such an assessment was carried out by analyzing the spread of the maximum and minimum vibration levels for a sample of gearboxes. Originality. An assessment was made of the possibilities of reducing vibration levels by observing the technology for the production of tractor boxes. This assessment was based on the analysis of minimum vibration levels of tractor boxes. Statistical processing of the results of experimental studies was carried out with the determination of the arithmetic mean, minimum and maximum vibrations, and the standard deviations of the vibration of gearboxes when the fourth gear of the third (transport) range is engaged. Practical value. Vibro-diagnostic characteristics of tractor boxes make it possible to evaluate the quality of design and manufacture by vibration levels. It was established that the vibration levels of boxes at the manufacturing stage reach 85-113 dB and exceed the permissible vibrations by 10-25 dB. The main sources of gearbox vibration are: defects in the quality of gears and bearing assemblies; their assembly, the use of low-quality bearings, large clearances of bearing fit in the housing, and the problem of gearbox assembly technology.

Studying footfall vibration criteria in a changing market and the effects on structural design

Design parameters for vibration criteria and tolerances from footfall induced vibration have long been categorized by general use with a focus on human comfort, with guidelines for offices, residential uses and hospital patient rooms. More stringent criteria required for sensitive laboratory and research equipment has typically been limited to select locations within projects. As the life science industry continues to expand, there is a growing trend to provide a leasable core & shell space that is already suitable for these more stringent equipment requirements while maintaining flexibility within the building. This paper reviews how 3D modelling can be utilized to demonstrate the expected vibration in large structures and study various iterations to determine how steel depth, steel weight, and composite structures can reduce vibration levels across the floorplate. Also discussed will be the implications of changing the structural design goals, with project examples of how other design considerations such as ceiling height, cost, and project schedules are impacted.

Vibration level reduction by floor coverings installed on wooden slabs

Effect of floor coverings on impact sound insulation can be described with a vibration level reduction (Δ La). In this study, tests with two floor coverings, eight wooden slabs and with a concrete mock-up slab were conducted by applying the method presented by Sommerfeld and the standard ISO 16251-1. The aim was to study the differences affecting the measured Δ La and the behaviour of the floor coverings installed on different slabs. The results suggest that the Δ La on concrete slabs do not correspond with the Δ La on wooden slabs. Thus, the floor coverings should be measured on wooden slabs when they are to be used within the timber construction industry. The results also show that the coverings should be measured on the wooden slabs where the products are expected to be used. In addition, a standardized test method for the wooden slabs corresponding the method of ISO 16251-1 should be developed.

Implementation of automation in vibration-isolating supports of new type for engines of sea and river vessels

In almost all areas of modern technology, the problem of vibration isolation arises, which is associated with the goal of improving the quality, reliability and productivity of various technical objects. One of the important tasks of shipbuilding is to reduce vibration levels of ship power equipment. This article proposes a non-linear control law for an electromagnetic hydraulic vibration-insulating support (EGVO) for ship power plants (SEP), which allows you to compensate for external harmonic disturbances at the SEP, which leads to an increase in their technological safety. The proposed control law of EGVO has advantages over various control laws of vibration-insulating systems of an active type for SEP. The proposed method can be used to create vibration-isolating active systems for various technical objects. The essential novelty of this method is a consistent synthesis of control laws and the creation of a single process of technological self-organization and control.

Glass Suspension Footbridge: Human-Induced Vibration, Serviceability Evaluation, and Vibration Mitigation

Glass suspension footbridges or glass-bottomed suspension footbridges, such as the Zhangjiajie Grand Canyon Glass Bridge in China, are increasingly constructed in scenic regions as tourist attractions due to the glass-bottomed and transparent characteristics. Being installed in the second phase as a constant load, the glass deck is not designed to participate in the load bearing of the whole structure and thus the structure requires larger load-bearing capacity from other parts and a slightly different load-bearing system. More importantly, the glass deck weakens structural integrity and results in slightly smaller structural stiffness, which may result in globally lower natural frequencies. These structures may inevitably be more sensitive to the pedestrian-induced excitations. This paper investigates the human-induced vibrations of a typical glass suspension footbridge in China. The investigations are first performed based on intensive parametric studies. Except for the boundary conditions, the interlayers of glass, the vertical rise–span ratio and the axial stiffness of main cables, other governing parameters of the modal parameters for this type of structures are also identified, including the pavement load of the bridge deck system, the central buckle, and the prestress of wind-resistant cables. It may guide designers to take effective measures to improve the dynamic behavior of this type of structure. Next, the vibration serviceability assessments were performed based on different standards and guidelines such as the UK National Annex (NA) to Eurocode 1 (2008), the Bro2004 specification of Sweden, the HiVoSS guideline, and the ISO standard. Comparisons show that the UK NA to Eurocode 1, the HiVoSS guideline, and the ISO standard are more suitable for the vibration serviceability evaluations. These three codes consider the pedestrian-induced vibrations in both lateral and vertical directions and also consider both a small number of pedestrians and crowd-induced loads with different densities. Furthermore, comfort limits are not defined by only one limiting value but sorted into different levels. This may provide reference for the vibration serviceability evaluations of the other glass suspension footbridges. The assessments also show that changing the structural parameters can only partially reduce vibration levels and may result in different modal parameters to dominate the vibration responses. Thus, they recommend taking vibration mitigation measures to improve the vibration serviceability and suggest performing careful response calculations to ensure the effectiveness of vibration serviceability design if via changing the structural parameters. Finally, tuned mass dampers (TMDs) are installed to the structure. The results show that the popular TMD may effectively reduce the vibration levels.

Investigation of random runway effect on landing of an aircraft with active landing gears using nonlinear mathematical model

Random runway roughness effect on the dynamic response of an aircraft with landing gears has been investigated using nine degree of freedom nonlinear mathematical model. The developed mathematical model incorporates nonlinear characteristics of air spring stiffness, landing gear damping, tire stiffness and damping of the oleo pneumatic main landing gears and nose gear. Equation of motion for aircraft and each landing gear have been written considering heave, pitch, roll of aircraft and three vertical motions of landing gears respectively for landing response analysis. The equations for longitudinal motion of each landing gear are also written from the mathematical model will be helpful for longitudinal dynamics. The aircraft touchdown and roll on with variable decent velocities on Grade E random runway represented by nonstationary random process. The excitation of different grades of random runway can be considered as stationary random process when the aircraft landing at constant sink velocity. This work mainly focused on finding the dynamic responses of the aircraft such as heave, pitch, roll acceleration, vertical forces and all the three landing gears vertical vibration levels while landing on random runways. The active landing gear system performance is compared with passive landing gear system by numerical simulation in MATLAB/SIMULINK. The investigation using nonlinear model predicted that the effect of active control landing gear provides significant reduction in vibration levels and vertical reactions during landing at various vertical velocities on random runways. To validate the above mathematical model a multi-body dynamics (MBD) model has been simulated in ABAQUS/CAE and the dynamic responses of landing gear forces are compared with those obtained from the nonlinear mathematical model. The nonlinear model responses are also compared with the results of other authors. This study is more useful to adopt active control landing gear in the aircraft to reduce the landing loads transmit on aircraft structure and landing gears due to landing impact. The reduction of vibration levels and vertical forces by the active system increase the fatigue life of landing gears and structural life of airframe.

Metamaterial plate with an arrangement of different resonators

Local resonant metamaterials have been widely studied for vibration suppression in the last 20 years. They produce band gaps, which are frequency regions where the wave is not allowed to propagate. They are an alternative to reduce vibration levels at lower frequencies when compared to phononic crystals, which require larger periodic cells to create band gaps at lower frequencies. The most common configuration for a local resonant metamaterial is a periodic cell of a known structure with one attached resonator. In this study, a plate with a periodic cell using two different resonators is analyzed. Some configurations of mass and stiffness for the two resonators will be discussed to pursue the best compromise between a wider band gap and a more considerable vibration attenuation. The dispersion relation for the proposed metamaterial unit cell will be calculated using the Wave Finite Element Method to evaluate these configurations. The frequency response function for a finite structure with the proposed arrangement will also be calculated using the Finite Element Method to compare the results.