Material Damping Research Articles

State-space Bloch mode synthesis for fast band-structure calculations of non-classically damped phononic materials

Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced-order models of the unit cell. Rooted in the framework of the Craig–Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey–O’Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced-order model and demonstrate the underlying accuracy–efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties.

Optimal Design of a Leaf Flexure Compliant Mechanism Based on 2-DOF Tuned Mass Damping Stage Analysis.

This study proposed an innovative design of a leaf flexural-based 2-DOF tuned mass damping stage that can be integrated into a micro-electromechanical system precision positioning stage to reduce the displacement response of the precision positioning stage excited by a specific vibration frequency and to achieve the damping effect and vibration reduction without adding viscous damping materials. A prototype that conforms to dual-axis decoupling and has 2-DOF translation capability was designed using parallel and vertical arrangements of a leaf flexure. The Taguchi design method and the finite element method were used on the relevant design parameters of the primary mass stage to determine the best size configuration for the maximum off-axial stiffness ratio and the parameters of the tuned mass damper closest to the natural frequency of the primary mass stage with the minimum deflection. In addition, an optimization module, based on a genetic algorithm (GA), was used to optimize the design of the flexure size of the tuned mass damper. Finally, experiments were conducted, the vibration displacement response of the primary mass stage was observed, and the effect with or without the addition of tuned mass damping on the system vibration response was compared. The results indicate that the tuned mass damper can effectively reduce the response amplitude of the stage, where the maximum reduction rate in the experiment was 63.0442%, and the mass of the damper was highly positively correlated with the amplitude reduction.

Automatic model order reduction for systems with frequency-dependent material properties

The frequency response of vibro-acoustic systems can be improved by using various forms of damping materials. Their material properties are typically varying with the excitation frequency and are introduced by one or multiple complex-valued functions. Numerical models of such systems are typically large and require efficient solving strategies. In this contribution, a workflow to reduce the numerical complexity of systems containing frequency-dependent damping materials is presented. The functions modeling the material’s frequency-dependent behavior are approximated in rational form and the resulting transfer function is used in a Krylov based moment matching method. The approximation is performed automatically using the adaptive Antoulas–Anderson algorithm. As robust and efficient automatic reduction algorithms are vital for an efficient design process of vibro-acoustic structures, we also show an adaptive procedure to automatically find a reasonably sized reduced model for a given system under a certain tolerance. The algorithms are tested for two forms of damping materials common in vibro-acoustic systems: poroelastic materials following the Biot theory and a constrained layer damping material.

An analytical approach to design horns and boosters of ultrasonic welding machines

This paper presents a new design approach for two main components of an ultrasonic plastic welding machine, booster and horn, based on an analytical model. The design procedure is developed due to the lack of a comprehensive and precise analytical model for rapid design and analysis of these components. The previous analytical models use the one-dimensional wave equation that causes significant errors in designing components with large lateral dimensions. Three-dimensional vibrations are considered for developing an analytical model using the apparent elasticity method. In this way, longitudinal frequency equations are coupled with radial frequency equations by mechanical coupling coefficients. Also, the damping of materials is taken into account. The model can be adapted to calculate the resonant length of the components or calculate the resonant frequency. To verify the model, the results are compared to a numerical simulation. The difference between analytical and numerical resonance frequency is less than 0.02%. Moreover, an experimental modal analysis is performed, which shows 0.9% error with analytical results.Article highlightsA new design approach for boosters and horns has been developed based on an analytical model.Three-dimensional vibrations are considered in the model using the apparent elasticity method.The accuracy of calculating resonant frequencies is more than one-dimensional design method.

Concurrent Topology Optimization for Maximizing the Modal Loss Factor of Plates with Constrained Layer Damping Treatment.

Damping performance of the plates with constrained layer damping (CLD) treatment mainly depends on the layout of CLD material and the material physical properties of the viscoelastic damping layer. This paper develops a concurrent topology optimization methodology for maximizing the modal loss factor (MLF) of plates with CLD treatment. At the macro scale, the damping layer is composed of 3D periodic unit cells (PUC) of cellular viscoelastic damping materials. At the micro scale, due to the deformation of viscoelastic damping material affected by the base and constrained layers, the representative volume element (RVE) considering a rigid skin effect is used to improve the accuracy of the effective constitutive matrix of the viscoelastic damping material. Maximizing the MLFs of CLD plates is employed as the design objectives in optimization procedure. The sensitivities with respect to macrodesign variables are formulated using the adjoint vector method while considering the contribution of eigenvectors, while the influence of macroeigenvectors is ignored to improve the computational efficiency in the mesosensitivity analysis. The macro and meso scales design variables are simultaneously updated using the Method of Moving Asymptotes (MMA) to find concurrently optimal configurations of constrained and viscoelastic damping layers at the macro scale and viscoelastic damping materials at the micro scale. Two rectangular plates with different boundary conditions are presented to validate the optimization procedure and demonstrate the effectiveness of the proposed concurrent topology optimization approach. The effects of optimization objectives and volume fractions on the design results are investigated. The results indicate that the optimized layouts of the macrostructure are dependent on the objective mode and the volume fraction on the meso scale. The optimized designs on the meso scale are mainly related to the objective mode. By varying the volume fraction on the macro scale, the optimized designs on the meso scale are different only in their detailed size, which is reflected in the values of the equivalent constitutive matrices.

Controlling chaotic oscillations in a symmetric two-mass model of the vocal folds

Human phonation is a highly non-linear process in which subglottal flow emanating from the lungs induces self-oscillations of the vocal folds. In normal conditions, this results in the generation of a regularly pulsating volume velocity that becomes the source of acoustic waves, which once modulated by the vocal tract, get emitted outwards as voice. However, vocal fold oscillations can become chaotic under many circumstances. For instance, even in the case of healthy symmetric vocal folds, an excess value of the subglottal pressure can trigger chaotic motion. In this paper, we derive a chaos control strategy for a two-mass model of the vocal cords to revert the situation and render the motion regular again. The approach relies on slightly altering the system energy to move it to a stable state. Given that no external control forces can be applied to the vocal cords, it is proposed to add a third mass to the original two-mass model, which is assumed to be made of an ideal smart material. The mass of the smart material is presumed negligible in comparison to the two masses of the vocal folds model, but its damping and stiffness can be tuned to evolve with time. For a fixed subglottal pressure for which the motion is chaotic, it is shown how periodicity can be recovered using adequate damping laws, by either attaching the smart material onto the larger vocal fold mass or onto the smaller one. For the latter, chaos control turns to be more difficult and the damping of the smart material has to quickly vary with time. On the other hand, given that the subglottal pressure would rarely be constant in a real situation, we also introduce a damping law to avoid chaotic motion as the subglottal pressure augments or diminishes. Finally, it is shown that control can not only be achieved by acting on the damping of the smart material but also on its stiffness. A stiffness law to prevent chaotic oscillations and get a healthy pulsating volume velocity is therefore implemented. A brief discussion on the mid-long term potential of the presented solution for practical cases is included.

Three-dimensional strain evaluation of short-fiber-reinforced natural rubber using micro X-ray computed tomography

The vibration damping appears as a macroscopic material property due to the energy dissipation caused by the plastic deformation of the microstructure in the material, but the detailed mechanism is still unknown. This study prepared a damping material based on natural rubber (NR) and investigated its deformation behavior with/without fiber-shaped particles using synchrotron X-ray computed tomography (CT). High-resolution submicron X-ray CT was performed to evaluate the local strain in the microstructure from feature points scattered inside the NR. When the strain distribution changed under stepwise tensile loading, the NR-alone material deformed uniformly at the microscale, whereas the fiber composite rubber deformed nonuniformly. Furthermore, the number and volume of voids increased significantly with the compounding of fiber particles, and their values continued to increase depending on the strain amplitude and the loss factor. Controlling of non-uniform local strain and void formation will enable the design of damping characteristics.

MODELLING OF WORKING PROCESS OF EQUIPMENT WITH HYDRAULIC DRIVE FOR SEPARATION OF DAMP DISPERSIVE MATERIALS

A task of introduction of separation processes of damp dispersive materials are very actual for food and processing industry of Ukraine and other countries, because its solution will allow to resolve by most effective way a problem of utilization of such waste as alcoholic bard, beer pellets, beet press, coffee and barley slime. In most cases this waste is poured out in nearest reservoirs or on ground and that leads to environment pollution. But after separation from the waste of the liquid phase (waste dehydration) its hard phase can be used as a valuable additive to agricultural fodders or as a high calorie fuel. By article’s authors notion the most prospective method of separation of the damp dispersive waste is mechanical dehydration, that provides high productivity of the working process, low consumption of energy (in 240 – 800 times lower then under realization of thermal methods) and necessary final humidity of the waste (20 – 25% in case of utilization by a method of vibro-blowing dehydration). One of the most prospective types of equipment for mechanical separation of the damp dispersive waste are presses with hydraulic drive that have relatively compact dimensions, high energy efficiency and reliability and provide a possibility for wide-range and infinitely variable control of main parameters of a loading regime of the waste processing. There is a scheme of an improved and high effective installation with hydraulic drive for separation of damp dispersive materials is presented in the article. Besides there are elaborated equations of its mathematic model that connect working parameters of separation, design parameters of the installation and physical-mechanical characteristics of the processed material. These equations can be used for optimization of the installation’s design and for creation of its method of projecting calculation.

ELABORATION AND RESEARCHES OF A VIBRO-PRESS FOR DEHYDRATION OF DAMP DISPERSIVE MATERIALS

Vibro-pressing loading is one from most effective methods of dehydration of damp dispersive materials such as alcoholic bard, beer pellets, beet press, coffee and barley slime for their further use as valuable additives to agricultural fodders or as a fuel. Main efficiency characteristics of the equipment for dehydration by the method of vibro-pressing loading are: productivity of liquid removal up to 20 ÷ 25 t / h, energy efficiency 2,7 ÷ 3,2 kW / t, final humidity of processed material 20 ÷ 25%. High efficiency of the method conditioned by periodical overdistribution of solid particles of processed material in a press-form of the equipment with their mutual rotations, sliding and movements in locations of more stable balance, with more dense stacking of particles and removal of liquid from spaces between them. There are several types of drives for vibro-pressing equipment: mechanical (unbalanced), hydraulic and electromagnetic. Each this type of drives has some advantages and disadvantages. One of tasks of this article is to analyze these types of drive and to select an optimal variant that will provide maximal productivity of working process, minimal energy expenses and humidity of processed material. A scheme of a versatile vibro-press that can be equipped with unbalanced, hydraulic pulse or electromagnetic drive is presented in the article. There is elaborated dynamic and mathematic models of the vibro-press. Equations of the mathematic model set connection between of working parameters of dehydration process, design parameters of the equipment and physical-mechanical characteristics of processed material. These equations can be used as a foundation for elaboration of a design calculation method for determination of optimal parameters of the vibro-press depending from given characteristics of material and parameters of dehydration efficiency.

A new methodology for the simulation of tunnel rockburst due to far-field seismic event

Dynamic disturbance from far-field seismic events is one of the main causes for triggering rockbursts in underground excavations. In this study, a comprehensive methodology for the simulation of a remote seismic source is proposed. The methodology encompasses the processing of raw seismic waveform based on the synchro-squeezing transform (SST) method and numerical modelling using finite-difference code FLAC3D. The main contributions of this study are as follows. First, the raw waveform is processed and reconstructed into P- and S- waveforms using the SST method, which is superior to applying synthetic waveforms in seismic modelling. Secondly, an innovative source waveform and material damping calibration procedure is put forward based on the empirical scaling law, producing a generalized seismic source waveform with input level of energy. Furthermore, a seismic loading scheme in numerical modelling is proposed; a spherical point source is created for applying P- and S- waveforms in different theoretical directions. Numerical modelling results show that the theoretical directionalities of P- and S- waves are well differentiated and reflected using the proposed dynamic loading method. The peak particle velocity (PPV) and peak kinetic energy density distributions around openings are interpreted, demonstrating that the proposed methodology could assist in rockburst risk assessment and dynamic rock support design

Effects of multi walled carbon nanotubes and multilayer graphene on the damping and quasi-static compressive mechanical properties of novel EP/ZA22 composites

In order to develop novel high damping materials with excellent compressive mechanical properties and energy absorption capacity to meet the needs of buffering and vibration reduction in various fields, epoxy resin (EP) filled foam Zn-22Al (ZA22) composites were fabricated for the first time. EP can significantly improve the damping and compressive mechanical properties of the ZA22 foam due to the superposition of multiple damping sources and the support of EP to pores, respectively. However, the filling of EP will lead to brittleness in the compression process of the composites. It is found that the addition of multi walled carbon nanotubes (MWCNTs) or multilayer graphene (MLG) to EP can efficiently improve the toughness of the composites because of the increased energy consumption in the fracture process of EP, and the damping can also be further improved due to the increased interface density and the amount of polymer chains involved in friction.

Analytical model of large-diameter viscoelastic floating pile and application in pile low-strain integrity testing

Based on a three-dimensional fictitious soil pile model, a rigorous analytical model of a large-diameter viscoelastic floating pile is developed by considering the material damping of the pile and the soil. Subsequently, closed-form solutions of the pile dynamic response of this analytical problem are derived. The rationality and accuracy of the proposed model and its relevant theoretical solutions are verified by comparison with the results of previous studies. Finally, parametric analyses are further conducted to investigate the effects of the radial direction position, length of the fictitious soil pile, material damping coefficient of the pile, and soil-to-pile stiffness ratios on the dynamic response of the pile. Based on the obtained results, an appropriate method to eliminate high-frequency interferences and evaluate the material damping coefficient of a pile in actual pile low-strain integrity testing is established. Furthermore, the proposed methodology affords legible theoretical insights into the wave propagation in large-diameter viscoelastic floating piles.

Synthesis and research of basalt microfiber‐reinforced polyurethane elastomer composites

AbstractBasalt microfiber‐reinforced polyurethane elastomer composites (BMF/PUE) were prepared by semi‐prepolymer method in this study. The degree of microphase separation and quantitative analysis of H‐bonding formation in polyurethane were determined by infrared spectroscopy. The fiber surface and the morphology at the tensile fracture interface of the composite materials were observed by scanning electron microscopy. The mechanical properties of composite materials were further measured on an electronic universal testing machine. Dynamic thermomechanical analysis and acoustic impedance tube were used to study the damping and acoustic properties of composite materials, respectively. The results indicated that the composite material prepared by adding 6 g of basalt microfibers treated with 3 min' crushing had the best overall performance. Compared with the matrix, BMF/PUE showed good sound insulation performance with a much wider effective damping temperature range. On the basis of ensuring its excellent overall performance, the mechanical properties were increased by 50.4% in tensile strength, 28.1% in elongation at break, and 14.2% in tear strength.

A study on beam-to-column moment-resisting timber connections under service load, comparing full-scale connection testing and mock-up frame assembly

A new timber frame structural system consisting of continuous columns, prefabricated hollow box timber decks and beam-to-column moment-resisting connections is investigated. The hollow box timber decks allow long spans with competitive floor height and efficient material consumption. To achieve long spans, semi-rigid connections at the corners of deck elements are used to join the columns to the deck elements. In the present paper, experimental investigations of a semi-rigid moment-resisting connection and a mock-up frame assembly are presented. The semi-rigid connection consists of inclined screwed-in threaded rods and steel coupling parts, connected with friction bolts. Full-scale moment-resisting timber connections were tested under monotonic and cyclic loading to quantify rotational stiffness, energy dissipation and moment resistance. The mock-up frame assembly was tested under cyclic lateral loading and with experimental modal analysis. The lateral stiffness, energy dissipation, rotational stiffness of the connections and the eigen frequencies of the mock-up frame assembly were quantified based on the experimental tests in combination with a Finite Element model, i.e., the model was validated with experimental results from the rotational stiffness tests of the beam-to-column connections. Finally, the structural damping measured with experimental modal analysis was evaluated and compared with FE model using the material damping of timber parts and equivalent viscous damping of the moment-resisting connections.

Structural–Acoustic Response Analysis of Variable Stiffness Laminates with Inherent Material Damping

Sound radiation and transmission loss characteristics of variable stiffness composite plate reinforced with the curvilinear fibers are investigated numerically. The formulation is developed using higher-order shear flexible finite element model combined with Helmholtz wave equation. The governing equations obtained using Hamilton’s approach are further solved through the modal super position method to analyze the vibration response under steady state excitation. The inherent material damping of the laminate is accounted through the modal damping calculated using the modal strain energy approach. The acoustic pressure of the variable stiffness laminates is estimated using the Raleigh integral. Subsequently, acoustic response characteristics such as acoustic power level, radiation efficiency, directivity pattern, and transmission loss from the laminates are predicted using the estimated sound pressure for various forcing frequencies. A parametric study covering a wide range of design variables including center and edge fiber angles, lamination scheme, thickness ratio, and boundary conditions on the acoustic sound behavior arising from the vibration of curvilinear fiber composite plate is detailed. This study reveals that the acoustic response of the curvilinear fiber composite plate is significantly influenced by the curvilinear fiber angles at the center/edge fiber angle of the layers. It is hoped that the results obtained here will be useful for designers in developing structures with desired acoustic response characteristics.

An accurate solution method for vibration analysis of multi-span lattice sandwich beams under arbitrary boundary conditions

An accurate solution method for analyzing free vibration of multi-span lattice sandwich beams under arbitrary boundary conditions is proposed in this investigation. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions. In this paper, at boundaries and supports, the linear displacement springs and rotational springs are introduced to simulate the boundary and support forces of multi-span lattice beams, and by adjusting these elastic stiffness values, the arbitrary boundary conditions can be simulated furthermore. All the displacement field functions of multi-span lattice beams are uniformly expanded into an improved Fourier cosine series supplemented with four sine series, which are introduced to eliminate the discontinuity or jump at the boundaries and supports during the solution process. The unified vibration equation of multi-span lattice sandwich beams under arbitrary boundary conditions is constructed based on the energy method. The Rayleigh–Ritz method is used to solve the free vibration characteristics of multi-span lattice sandwich beams. Based on the current method, the free vibration characteristics of multi-span lattice sandwich beams under arbitrary number of spans, arbitrary boundaries and supports can be studied without modifying the solution algorithm and program. The correctness as well as the accuracy of the current method are verified through comparison with those obtained from other analytical approach. Numerical results are presented to show that the current method is very suitable for analyzing the free vibration of multi-span lattice beams under arbitrary boundary conditions. In addition to this, the geometric parameters, as well as the elastic modulus and damping of materials, are analyzed for their effect on the vibration characteristics of multi-span lattice sandwich beams under different boundary conditions.

Efficient band-structure calculations of non-classically damped phononic materials by Bloch mode synthesis in state space

Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced-order models of the unit cell. Rooted in the framework of the Craig-Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey-O’Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced order model and demonstrate the underlying accuracy-efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties. This investigation does not only extend the applicability of BMS techniques to the most generally damped models of periodic media, it also advances our understanding of the nature of damping modes and the non-trivial manner by which they contribute to the wave propagation properties.

Enhanced damping and thermal conductivity of hBN/silicone rubber composites via strong interfacial action

High integration and miniaturization of electronic systems require thermal conductivity and mechanical damping materials. In this study, hexagonal boron nitride (hBN) particles were modified by vinyltrimethoxysilane (V171) and hexadecyltrimethoxysilane (N3116) for comparing, and described as V171-hBN and N3116-hBN, respectively. The pristine and surface modified hBN were filled in vinylmethylpolysiloxane (VMQ), and then vulcanized to fabricate hBN/silicone rubber composites. The damping properties of V171-hBN/silicone rubber composites were significantly higher than that of pristine hBN/silicone rubber composites, while N3116-hBN/silicone rubber composites were in contrast. The strong interfacial action in V171-hBN/silicone rubber composites came from the chemical bond by vinyl groups on the surface of V171-hBN taking part in the vulcanization of VMQ. This strong interfacial action led the deformation of hBN, and the internal friction between layers of hBN significantly increased to dissipate more energy. As a result, V171-hBN/silicone rubber composites with excellent damping and thermal conductivity as well as good mechanical properties were obtained.

On the influence of surface sealant on the nonlinear dynamics of jointed structures

As structural dynamics and acoustics form increasingly important aspects of technical products, gaining detailed insight into a system’s resonating behavior is crucial during the development process. In jointed structures, a system’s damping and thus its structural dynamic behavior is mainly influenced by the damping within the joint rather than the material damping of the individual parts. Various studies have been conducted on the influencing factors and the nonlinear character of damping in mechanical joints. However, they focus on a dry metal-to-metal contact whereas in the industrial application of drivetrain systems, surface sealants are commonly applied between the contact partners. Therefore, this paper provides an experimental study investigating the influence of surface sealants on the structural dynamic behavior of jointed structures via the example of the Brake-Reuß beam. Special focus will be placed on the influence of the assembly process and the necessary adaptions to existing test setups to increase the reproducibility.

Study on the Damping Dynamics Characteristics of a Viscoelastic Damping Material

Viscoelastic damping materials are an effective means to control structural vibration, and are widely used in various fields. In this paper, we use the Dynamic Mechanical Analysis (DMA) characterization data of viscoelastic damping materials and dynamic characteristics experiments to study the dynamic characteristics of structural damping, analyze and summarize the relationship between the performance of damping materials with temperature and frequency, and explore the influencing factors of damping materials on structural vibration. The research shows that temperature and frequency have great influence on the performance of damping material, and the storage modulus and loss factor change regularly. The modal experiment analysis verifies that the viscoelastic damping material has a good suppression effect on structural vibration, which provides a theoretical basis for the development of damping materials with controllable temperature and frequency domains.