Vibration Damping Of Structures Research Articles

Identifying factors influencing the properties of vibroacoustic metamaterials using three different acoustic methods

Vibroacoustic metamaterials offer an approach for the targeted damping of unwanted structural vibrations and noise by integrating periodically arranged resonators into a matrix of bulk material. Fabrication using the Laser Bed Powder Fusion (L‐PBF) process allows the targeted integration of bulk resonators and powder depots, leading to an extension of the designable damping properties. In this work, we focus on the adaptation of acoustic methods to characterize the properties of metamaterial plates. The investigated vibroacoustic metamaterial plates are made of nylon PA 1.2, combining material and structural damping. We investigated the vibration behavior of the plates over a range of frequencies using acoustic impedance measurements in a custom‐built measurement tube and compared it with structural dynamics experiments using an electrodynamic shaker. The measurements allow for the identification of stop bands (frequency range with high damping) and influencing factors such as metamaterial design, mass, powder amount and surface on the frequency dependent damping properties. The adapted technique investigated in this work provides an experimental platform to characterize the complex interplay of acoustic metamaterial design and holds promise for scaling up metamaterial technology for industrial applications due to its simplicity, small space requirement, and low cost.This article is protected by copyright. All rights reserved.

Enhancing Structural Vibration Damping in Marine Machinery: A Comprehensive Numerical Investigation with Modal and Harmonic Analysis

This article presents a comprehensive study on the damping of vibrations in a motor-pump assembly using viscoelastic and constrained layer damping treatments. The assembly's structural model, designed using SolidWorks software, is subjected to modal and harmonic analyses in ANSYS. The primary goal is to mitigate vibration amplitudes originating from the motor and pump to enhance the assembly's operational performance. Three damping treatments are investigated: Free Layer Damping (FLD), Sandwich Constrained Layer Damping (CLD), and a novel Multilayer CLD approach. The viscoelastic material is modeled using the Prony series method, and its properties are incorporated into the finite element analysis Results demonstrate that the application of damping treatments significantly reduces vibration amplitudes compared to the untreated structure. Among the treatments, the Multilayer CLD approach exhibits the highest damping efficiency, reducing the maximum amplitude by approximately 52% compared to the base structure. The study showcases the advantages of utilizing viscoelastic and constrained layer damping techniques for enhancing vibration control and operational stability in industrial assemblies. The research findings contribute to the field of structural dynamics and vibration control, offering valuable insights into the design and optimization of mechanical systems subjected to dynamic loads. This study opens avenues for further research and practical applications aimed at improving the performance and reliability of motor-pump assemblies and similar industrial equipment.

Active Vibration Damping Using Rotor Torque Control in Electric Aircraft

Vibration damping in aerospace structures can decrease the likelihood of failures and instabilities and improve passenger comfort. This paper introduces the novel idea of damping vibration using the electric proprotors on aircraft without compromising flight control. The equations of motion of a cantilevered beam with a propeller at the tip driven by an electric motor are obtained using Hamilton’s principle, solved analytically in the frequency domain, and approximately in the time domain. Feeding back the beam tip angular rate to the motor torque is shown to asymptotically stabilize all transverse beam vibration modes. The overall vibration control consists of the inner rate feedback damping loop with an outer rotor speed control loop. Experimental frequency response and step response validate the models and show that the closed-loop damping in the first mode is three times higher than open loop with less than 1% rotor speed change for a 3% initial tip displacement. Theoretical results give good agreement with experiments. Parametric studies based on a 12 kg quadcopter indicate that if the rotor inertia is sufficiently large the proposed control can provide 8% damping with minimal impact on rotor speed.

Tuning of vibration absorbers by an effective modal coupling factor

The simplest family of vibration absorbers comprise inertia absorbers, with an inerter in series with a parallel or series dashpot–spring element, and stiffness absorbers, for which inerter and spring are interchanged. Vibration absorbers are tuned to a structure’s critical resonance, for which scalar structure-absorber equations are derived from an expansion in vibration modes with the absorber in either a free or clamped state. It is demonstrated that the influence from non-targeted residual modes is consistently represented by an effective modal coupling factor (EMCF), evaluated as the relative difference between free and clamped natural frequencies squared. While closely related to the coupling factor for shunted electromechanical transducers, the use of EMCFs determines an entirely new direction for the tuning of mechanical vibration absorbers on a flexible structure. For inertia and stiffness absorbers, the EMCF represents apparent mass or stiffness ratios that also account for the influence from residual modes. Therefore, analytical tuning expressions can be obtained from the derived modal frequency response functions, as demonstrated for a pole-placement method with the EMCF as a new governing absorber parameter. The accuracy of the proposed absorber tuning is validated by a simple numerical example, which shows that analytical tuning expressions can be used directly for vibration damping of flexible structures, provided that the EMCF is included correctly to compensate for the inherent modal interaction.

The effects of shear deformation and rotary inertia on the electrical analogs of beams and plates for multimodal piezoelectric damping

AbstractAnalogous electrical networks were previously derived from the Euler–Bernoulli and Kirchhoff–Love theories to represent beams and plates, respectively, for use in multimodal structural vibration damping. However, these networks do not account for shear deformations or rotary inertia, which can result in suboptimal vibration damping performance when used on moderately thick beams and plates. In this paper, we investigate the incorporation of shear deformation and rotary inertia using Timoshenko–Ehrenfest beam theory and Mindlin–Reissner plate theory to develop improved electrical networks that can more accurately represent thick beams and plates. Our findings suggest that the inclusion of shear deformation and rotary inertia can significantly improve the frequency coherence of the electrical networks and multimodal vibration damping for thicker structures. The electrical analogs presented here are of use for various applications, especially to conveniently design complex circuit topologies in fields spanning from vibration attenuation to energy harvesting.

Structural vibration damping by the use of poro-elastic layers: a summary

A properly designed limp porous materials such as fibrous layers can provide damping equivalent to conventional viscoelastic dampers while providing advantages such as light weight and effective sound absorption. This then allows porous layers to be used as multi-functional noise and vibration control solutions in automotive and aerospace applications. Further, the addition of bulk elasticity to the solid phase of the porous medium is beneficial since it improves damping performance compared to equivalent limp treatments. In the work summarized here, porous media, such as fibers and foams, were designed to serve as treatments for various vibrating structures to examine their damping effectiveness. Both analytical modeling and numerical simulation based on finite element methods were involved depending on the complexity of the structure. Specifically, a Fourier transform-based computational method was introduced as the key step to allow accurate prediction of a panel's spatial response based on its wavenumber-frequency spectrum. Parametric studies have been conducted to identify the optimal bulk properties that would allow a porous layer to provide the largest possible damping within a target frequency region. Finally, design concepts for achieving the maximum damping potential of porous layers are summarized.

Evaluation of the damping characteristics of a hybrid piezo-shunt nanocomposite using a two-step homogenization approach

Composite materials containing piezoelectric particles have attracted remarkable attention because of their distinctive electromechanical conversion characteristics. These supreme properties lead to their applications in various fields, such as vibration damping of structures. The damping parameter of dynamic systems is crucial, especially when they undergo resonance phenomena. Multi-phase polymer matrix composites consisting of piezoelectric particles are innovative material systems that have been recently introduced to convert the mechanical vibrations into electrical energy, and subsequently dissipate into heat through an internal electrical circuit. The present study aims to analytically investigate the viscoelastic characteristics of a shunted three-phase composite composed of a polymer matrix, electrically conductive nanoparticles and piezoelectric particles. The effective viscoelastic characteristics of a shunted composite are calculated using one- and two-step homogenization procedures and by considering the viscoelastic characteristics of constituent materials. The influence of several key parameters, namely, the non-dimensional frequency, the volume fraction of electrically conductive nanoparticles and piezoelectric particles, and the shape of the inclusions, on viscoelastic characteristics, such as phase angles, the storage modulus and loss modulus, are examined. The viscoelastic characteristics are considerably affected by these parameters, and the perceived behavior is justified by the governing equations. The assessment of results confirms that the damping characteristics can be improved by careful selection of a volume fraction of constituent materials and control of the excitation frequency of the smart composite, while avoiding additional costs and likely inconveniences in the fabrication process.

Numerical investigation into vibration damping in woven composite structures

This study numerically investigates the mechanism of vibration damping in woven composite structures using a decoupled multi-scale simulation scheme that considers the macroscopic woven structure consisting of bundles and resin-rich regions, as well as the microscopic structure in the bundles made of fiber and resin. For efficient macroscopic modeling of complicated woven structures, the embedded element technique is introduced to utilize separate meshes for bundles and resin regions. A special treatment is introduced for volumetric integration in the mesh overlapped between bundle and resin regions, which is required to calculate the strain energy and modal damping ratio of the entire woven structure. Using the developed scheme, the natural frequencies and damping ratios of braided and laminated composite cylinders are investigated. By comparing the vibration properties of two braided composites with different braided angles and two unidirectional laminates with different fiber volume fractions, the effects of the fiber volume fraction, braided angle, and out-of-plane waviness on vibration properties are discussed. Based on the mode shape and resultant energy dissipation within each bundle and resin-rich region, the braided composite with a large braided angle exhibited the best damping properties, mainly owing to the in-plane shear deformation in the crimped braided bundles.

Рассеяние энергии в муфтах переменной жесткости со змеевидной пружиной при крутильных колебаниях

The paper presents results of the theoretical research of the structural vibration damping in the variable stiffness couplings with a serpentine spring, which are rather widely used in the drives of the heavy engineering and machine tool products exposed to the vibration loads. When performing dynamic calculations of the drives of such machines, it is necessary to know the dissipative characteristics of their components and parts, including the indicated couplings. The paper considers the case of torsional harmonic vibrations characteristic for the coupling drive with a serpentine spring associated with twisting of the shafts connected by this coupling due to the attached parts imbalance. Quantitative characteristics of the torsional vibration energy dissipation in the couplings under consideration were studied and determined using the well-known method for estimating the vibration energy losses due to friction during slipping in the compressed parts’ contact. Mathematical model of the torsional vibration damping in a coupling was developed, which makes it possible to determine its quantitative characteristics in the form of vibration energy dissipation per cycle and the absorption coefficient depending on the coupling design parameters and the vibration process. The proposed model is implemented as an interactive application program in the MATLAB computer environment.

Экспериментальные исследования вибродемпфирования толстолистовой судовой конструкции

Object and purpose of research. This paper discusses thick stiffened plates for ship structures. The purpose is to determine the efficiency of vibration dampers (resonant anti-vibration straps with two reinforced vibration damping coatings installed on them). Subject matter and methods. Measurements of plate vibration spectra with and without vibration dampers stuck to the structure by means of a PVA-based self-adhesive tape. Main results. The study has established that efficient vibration damping of thick-plated structures is possible in principle. Conclusion. The study showed that vibration levels of thick-plated structure in a wide frequency band could be reduced by means of the dampers with the total weight considerably lower than the weight of the target structure itself.

Study on Hydraulic Dampers Using a Foldable Inverted Spiral Origami Structure

Hydraulic dampers for the vibration damping of industrial machinery and building structures are typically cylindrical. This study proposes a novel, axially free-folding hydraulic damper of the origami type to improve the structural characteristics of the conventional cylinder shape with restricted effective stroke in relation to the overall length. First, the basic design equation of the proposed origami hydraulic damper was derived by demonstrating that the fold line cylinders on the sidewalls will always meet the foldable condition of the origami hydraulic damper, that is, α=π/n and π/2n≤β≤π/n. Next, the fluid flow characteristics inside the origami hydraulic damper and in the flow path were analyzed; it was determined that the actual damping force exerted on the origami damper was proportional to the square of the velocity of motion. Equations of motion were developed considering the derived damping force equation, and a vibration analysis method using the Range–Kutta numerical analysis technique was established. A validation test system with an origami hydraulic damper in a mass-spring vibration system was developed, and vibration tests were performed with actual seismic waves to verify the damping characteristics and effectiveness of the origami hydraulic damper. Furthermore, the orifice hole diameter at the end of the origami structure as well as the type of internal fluid, were varied in the vibration tests. The effect of the main components of the origami hydraulic damper on the damping effect was analyzed, revealing that the orifice hole diameter had a more significant effect than the internal fluid.

Research on dynamic characteristics of novel filled damping block mesh-type rail pads for heavy haul railways

Currently, the commonly used rail pads for heavy haul railways are grooved rubber rail pads (GRRP) and prismatic thermoplastic polyester elastomer (TPEE) rail pads (PTRP). However, the rail pad of the traditional structure has an obvious stress concentration when compressed and limited damping performance, which severely limits the service life of the rail pad. This study proposes a novel filled damping block mesh-type rail pad (NFDBMTRP) suitable for heavy haul railways. The rail pad has better damping performance than that of the traditional rail pad under the same stiffness condition. When the rail pad is under pressure, its hexagonal mesh structure can ensure that the stress distribution of the rail pad is uniform. Meanwhile, the damping block filled in the hexagonal mesh cavity can absorb part of the energy so that the overall stress level of the NFDBMTRP is small, which is beneficial for prolonging the service life of the rail pad. On the basis of the vehicle–track coupled dynamics theory, the C80 truck–track coupled dynamics calculation model was established, and a field test of the heavy haul railway was conducted. The time and frequency domain signals of the rail and sleeper acceleration obtained from the test were compared with those from the simulation to verify the accuracy of the dynamics model calculations. Under the same stiffness (70 kN/mm), the dynamic response differences in the four rail pads were compared and studied. The dynamic calculation results showed that the NFDBMTRP not only has smaller acceleration than that of the other three rail pads on the rail, sleeper, and car body but also has the smallest wheel–rail vertical force and derailment coefficient. This implies that improving the damping of the rail pad is beneficial for improving the safety and stability of train operation and has a certain protective effect on the under–track structure. To sum up, the NFDBMTRP has better structural properties and vibration damping performance compared with the traditional rail pad, and has broad application prospects in the heavy haul railway fastening system.

Frequency domain homogenization of effective and localized viscoelastic response of unidirectional composites with imperfect interfaces

The locally-exact homogenization theory for unidirectional periodic composites with imperfect interfaces is generalized to estimate the effective complex moduli of viscoelastic composites in the frequency domain and recover corresponding localized stress distributions. In order to avoid complex mesh discretization, the Trefftz concept is adopted to obtain the analytical expression of internal displacements and stresses of representative unit cells by directly solving elastic partial differential equations. Physical coating and linear cohesive spring models are implemented at the interface between fibers and matrix. Besides, we also prove that the two imperfect interface models are equivalent under specified viscoelastic conditions. Comparisons against simulations available in the literature are given to validate the present method where good agreement is generally obtained. The effects of phase volume fraction, coating thickness and interfacial stiffness on five independent elastic constants are effectively investigated using the present models, further the local stress distributions within unit cells are presented to illustrate the effect of imperfect interfaces on material properties. Finally, the free vibration of Euler beams composed of unidirectional composites are studied through multiscale simulations to demonstrate importance of aforementioned microstructural parameters on damping of structural vibration, offering guideline for the structural and material design of aircrafts and satellites.

Effect of porosity on active vibration control of smart structure using porous functionally graded piezoelectric material

The present work investigates the active vibration control of host structure bonded with functionally graded piezoelectric material (FGPM) as sensor and actuator layer. The effect of porosity volume fraction (ψ) and volume fraction index (λ) on active vibration attenuation is investigated and compared with the dense FGPM sensor and actuator layer. For more real life applications of FGPMs, two piezoelectric materials (PZT-5H and PZT-4) are modelled smoothly in a particular direction. The mechanical and piezoelectric properties of FGPMs vary across the thickness and calculated using power – law expressions. In addition to dense FGPM, two different distributions of the porosities are investigated. Shear deformation theory of first order is used to simulate the vibration response of the host composite plate based on Hamilton’s principle. A well-established negative velocity feedback controller is deployed to obtain active vibration control of the composite structure. The numerical results reveal that the volume fraction index (λ) plays vital role in the active damping of structural vibration. The FGPM-◊ demonstrates 5.7% and 6.32% improved active vibration damping performance compared to FGPM-UD at ψ = 0.1 and ψ = 0.2 respectively. The present investigation can be utilized for further studies on active vibration control of host structures integrated with FGPMs.

SMC/TPE bi‐layer configurations for structural vibration damping applications

AbstractSheet molding compounds (SMCs) have considerable potential as lightweight alternative to traditional materials used in automotive components. However, despite their outstanding mechanical properties, their vibration damping characteristics are often relatively poor for several applications. Therefore, enhancing the vibration damping capability of SMCs represents a field with increasing interest. Application of viscoelastic layers to high stiffness materials, such as SMCs, represents an effective approach to add vibration damping functionalities to lightweight structural components. In this work, the incorporation of thermoplastic elastomers (TPEs) is studied as a novel strategy to enhance the structural vibration damping capability of SMCs. Several types of SMC and TPEs have been considered and the effect of TPE‐SMC thickness ratio on the damping and stiffness properties is investigated. The viscoelastic properties and vibration damping performance were evaluated by dynamic mechanical analysis. The effect of TPE addition on stiffness was studied by three‐point bending. Results reveal the potential of the incorporation of thin TPE layers as cost‐effective strategy to enlarge the vibration damping efficiency of SMCs while maintaining their overall high stiffness. It is expected that the bi‐material configurations presented in the current study will contribute to advance the development of new lightweight multi‐functional solutions for modern transport applications.

Control of damping of structural vibrations by using different mechanisms of energy dissipation

In current paper an influence of adding piezoelectric elements and connection of their electrodes to external resistive electric circuits on coefficients of vibration damping of piecewise-homogeneous viscoelastic structures was demonstrated on the example of a cantilever plate. The calculations were carried for two options of location of piezoelectric elements in relation to the plate (in the middle of the plate and nearby the clamped edge) and two options of mutual arrangement of a piezoelectric element and a viscoelastic layer (at one side of the plate and at opposite sides). One was demonstrated that damping coefficients for the first two the most energy-intensive vibration modes can be increased in different degree by using different mechanisms of energy dissipation. In this case the most preferable configuration for reaching the highest value of vibration damping coefficients is the option when piezoelectric element and viscoelastic layer located at opposite sides of the plate.

Vibration and damping performance of carbon fiber-reinforced polymer 3D double-arrow-head auxetic metamaterials

The vibration and damping performances of carbon fiber-reinforced polymer (CFRP) three-dimensional double-arrow-head (3D DAH) auxetic metamaterials are investigated in this paper. The negative Poisson’s ratio effects of the CFRP 3D DAH auxetic metamaterials are analytically studied by the energy method. 3D finite element models based on Modal Strain Energy approach are developed to analyze their vibration and damping characteristics. To validate the numerical models in the present study, the CFRP 3D DAH auxetic metamaterials are designed and manufactured. The sine-sweep response tests are conducted to investigate their vibration performances. The influence of different inclined corrugated angles, and fiber orientations on the natural frequencies, loss factors and the nominal Young’s modulus are plotted and discussed using validated numerical models. Meanwhile, the effect of Poisson’s ratio on the nominal Young’s modulus, natural frequencies and loss factors is also revealed explicitly. Furthermore, the comprehensive evaluation parameter that simultaneously characterizes the structural bearing capacity and vibration damping performance is further improved through parameter optimization.

Broadband vibration damping of non-periodic plates by piezoelectric coupling to their electrical analogues

Several solutions for multimodal vibration damping of thin mechanical structures based on piezoelectric coupling have been developed over the years. Among them, piezoelectric network damping consists in using piezoelectric transducers to couple a structure to an electrical network, where the transferred electrical energy can be dissipated. In particular, the effectiveness of coupling rods, beams and plates to their analogous electrical networks has been proven. This work is the first step going towards more complex structures. After defining and experimentally validating a fully passive electrical analogous network of a simply-supported plate, the study is extended to the damping of a non-periodic plate. The non-periodicities here studied include the addition of a local mass and a variable thickness. Numerical simulations and experiments show that in these cases, a broadband damping is achieved once the piezoelectric transducers are coupled to an adequate analogous network. A finite element model of the structure coupled to a 2D non-periodic electrical network is concurrently developed and validated, which is another contribution of the present work.

Application of Graphene Composites for Additional Vibration Damping in Smart Structures Based on Piezoelectric Elements

A smart-structure variant representing a piecewise homogeneous body composed of elastic and viscoelastic materials and piezoelectric elements the electrodes of which can be connected to shunting circuits is considered. One of the basic purposes of such structures is vibration damping. This paper deals with a variant in which the classic resistor in a shunting circuit is replaced by a graphene composite acting not only as a mechanically deformable body, but also as a resistor in a smart structure. The mathematical formulation of the problem of forced steady-state and natural vibrations in the structures composed of elastic and viscoelastic elements, piezoelectric elements, and graphene composites acting as a deformable body and a resistor is given. The results of numerical experiments demonstrate the applicability of graphene composites for implementing an additional mechanism of vibration damping in smart structures based on piezoelectric elements.

Controllability and actuator placement optimization for active damping of a thin rotating ring with piezo-patch transducers

A study on optimal actuator placement for controlling flexural vibration of a thin rotating ring is reported. Piezoelectric patch actuators and sensors may be applied with feedback control to provide active damping of structural vibration involving circumferential travelling waves. To determine the optimum patch positions, a model-based cost function is defined involving a time-weighted controllability Gramian, with balanced model realization for combined treatment of sensors and actuators in collocated pairs. Analytical and numerical results indicate that, without rotation, at least two actuator/sensor pairs are required to achieve controllability of any given set of natural vibration modes. Also, the optimal angular separation varies with rotational speed due to the combined influence of initial damping and Coriolis forces on the vibratory dynamics. To obtain a practical solution, a finite range of speeds is considered within a mini-max optimization criterion for the placement problem. Experiments have been conducted on a thin steel ring where a synthetic proof-mass-damper control law was used to suppress vibration involving the six lowest frequency vibration modes (with natural frequencies of 161, 442 and 846 Hz without rotation). The results show that, although a single actuator-sensor pair can achieve improved damping at high rotational speeds, the optimized configuration of two pairs provides effective damping over the full range of operating speeds.