Structural Damping Model Research Articles

Feasibility of an inerter-based causal rate-independent damping model for the protection of seismically isolated structures

Rate-independent linear damping (RILD), also referred to as linear hysteretic damping, is a linear model of structural or material damping in which the energy dissipation per cycle is independent of the frequency. The resistive force of an ideal RILD model is in phase with the velocity to dissipate energy, while its amplitude is proportional to the displacement, which is suitable for the direct control of seismic response displacement when incorporated into a structure. The tuned Maxwell–Wiechert (TMW) model is a viable option for approximating the damping characteristics of RILD. However, the undesirable stiffness produced by the TMW model compromises the flexibility of the isolator, and thereby fails to deliver the benefits of RILD. To overcome this challenge, the addition of two inerter elements to the TMW model in series and parallel arrangements is proposed in this study to eliminate the undesirable storage stiffness. The parameters of the proposed model are determined using particle swarm optimization. Analyses of a 10-story building structure mounted on linear and nonlinear isolation systems demonstrated that the proposed model achieved lower interstory drifts and approximately 40% reduction in floor response accelerations, with similar isolator displacements compared with LVD when subjected to ground motions dominated by high-frequency components. Moreover, floor response acceleration mitigation was attained at the slight expense of isolator displacement, even when the proposed system was incorporated into nonlinear isolation systems and subjected to low-frequency ground motions.

Analytical Model of Structural Damping in Friction Module of Shell Shock Absorber Connected to Spring

Vibration processes play a significant role in the modern industry. In most cases, vibration reduces strength, reliability, and durability of industrial machines, mechanisms, and structures, as well as adversely affects the health of support staff. This study presents a new dry friction shell shock absorber design. The shock absorber contains two spring sections and a friction module with an open shell and an elastic filler; at the same time, the spring sections and the friction module work in parallel. The proposed device demonstrates good damping characteristics, capable of operating under high operating loads, and at the same time has compact transverse dimensions. With a nonmonotonic loading of such a shock absorber, due to the contact interaction of the filler with an open shell, part of the energy that is supplied to the system will be dissipated. In other words, in response to the action of an external nonmonotonic loading, the phenomenon of structural hysteresis occurs in the friction module of the shock absorber. To describe the deformation of the shock absorber, a mechanical and mathematical model of a shell with a cut along the generatrix, which is the main bearing link, has been developed. By means of the technique of quasistatic analysis of structural damping in nonmobile nonconservative shell systems with a deformable filler, the hysteresis loops of the presented shock absorber are analytically described. Using them, according to the known loading history, it is possible to predict the behavior of the considered nonconservative system at any time after the start of the loading process. At each stage of the cyclic loading, the distribution of stresses and relationships between the external loading and the piston displacement was studied. Inequalities are obtained for permissible loads under which the operation of the shock absorber is safe. Such shell shock absorbers are projected to be used in the mining, oil and gas, and construction industries.

Pancreatic cancer metastasis: Adhesion and stiffness

Pancreatic ductal adenocarcinoma (PDAC) cells undergo a semi-epithelial to mesenchymal transition. They express Cadherin proteins characteristic of both normal (E-cadherin) and cancer (N-cadherin) cells. Cadherins are involved in cell-cell adhesion. Additionally, cells must adjust their mechanical properties to undergo metastasis. We use Atomic Force Microscopy (AFM) to characterise the mechanical properties of PDAC cell lines from the primary tumour sites (PANC1, PL45) and from liver (CFPAC1) and lymph node (Hs766T) metastases. AFM measures forces using the optical lever system. To measure their stiffness, cells were probed using a rectangular cantilever with a three-sided pyramidal tip. The Hertz contact model was used to calculate Apparent Young's modulus (E) from the approach curve. The structural damping model was used to calculate the power-law exponent (α) from force curves with logarithmically oscillating contact part. To probe the adhesive properties of the cells, a single cell was attached to functionalised triangular tipless cantilevers, and then pressed against a confluent layer of cells. When the cell-cantilever is retracted, the contact of the attached cell with the cell layer is broken. The detachment exerts force on the cantilever, and this signal is also recorded by and analysed from the retract curve. PANC1 and PL45 cells are stiffer in a confluent layer as compared to single cells. CFPAC1 cells soften in confluent layers, and have lesser adhesion between them as compared to PANC1. CFPAC1 cells also have reduced cell-cell interaction with endothelial cells (EA.hy926) after inhibiting N-cadherin. Thus, N-cadherin inhibition can increase liver metastatic cell lines’ self-interaction and decrease interaction with endothelial cells. While primary tumour cell lines experience mixed mechanical response to surrounding cells, liver metastasis cells are softer and more viscous.

Comparison of Rheological Properties of Healthy versus Dupuytren Fibroblasts When Treated with a Cell Contraction Inhibitor by Atomic Force Microscope.

Mechanical properties of healthy and Dupuytren fibroblasts were investigated by atomic force microscopy (AFM). In addition to standard force curves, rheological properties were assessed using an oscillatory testing methodology, in which the frequency was swept from 1 Hz to 1 kHz, and data were analyzed using the structural damping model. Dupuytren fibroblasts showed larger apparent Young's modulus values than healthy ones, which is in agreement with previous results. Moreover, cell mechanics were compared before and after ML-7 treatment, which is a myosin light chain kinase inhibitor (MLCK) that reduces myosin activity and hence cell contraction. We employed two different concentrations of ML-7 inhibitor and could observe distinct cell reactions. At 1 µM, healthy and scar fibroblasts did not show measurable changes in stiffness, but Dupuytren fibroblasts displayed a softening and recovery after some time. When increasing ML-7 concentration (3 µM), the majority of cells reacted, Dupuytren fibroblasts were the most susceptible, not being able to recover from the drug and dying. These results suggested that ML-7 is a potent inhibitor for MLCK and that myosin II is essential for cytoskeleton stabilization and cell survival.

Comparative Analysis of Viscous Damping Model and Hysteretic Damping Model

A damping model is one of the key factors in dynamic analysis. Viscous damping and hysteretic damping models are commonly used in structural damping models. In this study, transient and steady responses are analyzed for a single degree of freedom system based on the two damping models. The attenuation coefficient and damped natural frequency are important parameters of the transient response. In addition, the vibration amplitude is an important parameter of the steady response. When the relative errors of the parameters for the two damping models are less than 10%, the threshold of the damping ratio is selected as 0.1736 and the threshold of the loss factor is 0.3472. The numerical examples show that the dynamic responses based on the viscous damping model are approximately equal to those based on the hysteretic damping model in small damping cases. With the increase in the damping ratio, the difference between the dynamic responses calculated by the two damping models gradually increases. In large damping cases, the two damping models must be distinguished, and the choice of the damping model depends on the characteristic of dissipate energy.

BEAM-TYPE ACOUSTIC METAMATERIAL DESIGN FOR VIBRATION SUPPRESSION WITH STRUCTURAL DAMPING

Vibration suppression of a beam-type acoustic metamaterial with periodic cavities filled by a viscoelastic membrane that supports a hollow mass still filled by a viscoelastic membrane that supports a local resonator is investigated. First, the proposed beam-type acoustic metamaterial is modeled as a one-dimensional mass-in-mass-in-mass (MMM) lumped parameter chain with structural damping, and then a mass-in-mass (MM) lumped parameter chain with structural damping is also given for comparison. For the two chains, the influence of structural damping on band structures are considered, and the loss factors associated with all propagating Bloch modes are compared. Finally, as an example, the beam-type metamaterials based on MM model with structural damping and MMM model with structural damping are designed to suppress vibration, respectively. The viscoelastic membranes act as structural damping. The finite element method based on Kirchhoff’s plate theory is developed to capture dynamic displacement fields of different metamaterials. Structural frequency response is calculated for different configurations of cantilevered structures when disturbance is considered. The results show that the proposed beam-type acoustic metamaterial based on MMM model with structural damping has higher dissipation and display high damping and does not sacrifice stiffness than MM model with structural damping.

Beam-type acoustic metamaterial design for vibration suppression with structural damping

Vibration suppression of a beam-type acoustic metamaterial with periodic cavities filled by a viscoelastic membrane that supports a hollow mass still filled by a viscoelastic membrane that supports a local resonator is investigated. First, the proposed beam-type acoustic metamaterial is modeled as a one-dimensional mass-in-mass-in-mass (MMM) lumped parameter chain with structural damping, and then a mass-in-mass (MM) lumped parameter chain with structural damping is also given for comparison. For the two chains, the influence of structural damping on band structures are considered, and the loss factors associated with all propagating Bloch modes are compared. Finally, as an example, the beam-type metamaterials based on MM model with structural damping and MMM model with structural damping are designed to suppress vibration, respectively. The viscoelastic membranes act as structural damping. The finite element method based on Kirchhoff's plate theory is developed to capture dynamic displacement fields of different metamaterials. Structural frequency response is calculated for different configurations of cantilevered structures when disturbance is considered. The results show that the proposed beam-type acoustic metamaterial based on MMM model with structural damping has higher dissipation and display high damping and does not sacrifice stiffness than MM model with structural damping.

Structural damping models for passive aeroelastic control

Aeroelastic qualification requirements are typically met by sizing aircraft to achieve adequate stability margins and keep peak gust responses below specified thresholds. A possible alternative approach is delaying flutter and alleviating gust response by embedding dissipative materials into structural components. This approach requires accurate damping models applicable to the analysis of complex configurations. In this paper, the effect of damping models in the evaluation of flutter boundaries and gust response of an aeroelastic test-bed is studied. In particular, three damping models completely different in frequency are considered to model the presence of skin patches for passive aeroelastic control: viscous damping, hysteretic damping and Biot damping models. In order to make them comparable the three models are tuned in order to dissipate the same amount of power at the flutter frequency by means of the introduction and definition of a generalized loss factor. The damping models are compared by evaluating their effect on flutter suppression and gust load alleviation. Finally, the sensitiveness of the stability and response aeroelastic analyses to the considered damping models are outlined and the obtained results are compared to provide modeling recommendations for passive flutter suppression and gust alleviation studies. The proposed methodology is applicable to any linear material model for which the related complex stiffness can be expressed in the frequency domain meeting the Hilbert restriction.

Increased damping through captured powder in additive manufacturing

This paper describes the retention of metal powder within additively manufactured structures to achieve increased damping. Solid and hollow (powder filled) aluminum cylinders were fabricated in using laser powder bed fusion where the internal, captured powder in the hollow cylinders served as an energy dissipation mechanism. Impact testing was completed to compare the frequency response functions of three cylinder geometries: one solid cross-section and two hollow cross-sections with different inner diameters and, therefore, different powder volumes. Increased damping with larger inner diameter was observed. The damping was quantified using a structural damping model.

First‐order virtual synchronization: A new methodology for online identification of structural damping in presence of seismic excitation

AbstractThis paper proposes a new method for online identification of damping properties in seismically excited structures. It is a major extension of the recently developed Virtual Synchronization Method (VSM) with the following benefits: Its formulation is simpler and contains fewer design parameters. It includes a sufficient condition which can be validated online to ensure whether it is successful in identification of the structural damping model. It is assumed that the parameters of the damping model are fully unknown whereas the stiffness and mass of the structure are known. Online measurements of the ground motion acceleration, displacement and velocity vectors are available. Using these data, a virtual copy of the original structure is created. Then, the error between the states of the two systems is calculated. It is employed for designing an appropriate virtual controller which forces the virtual system to synchronize with the original one. Consequently, the states of these two systems are used to propose a nonlinear adaptive law to estimate the unknown parameters of the damping model. Provided numerical examples show that the proposed online identification method is efficiently fast, promising and worthy of further studies.

Free flexural vibration of a partially wet tapered Timoshenko beam with intermittent mass and stiffness variations, eccentric tip mass and non-classical foundation

A compliant tower is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with parallel linear and torsional dampers (Kelvin-Voigt model). The superstructure adds to the kinetic energy of the system without affecting the potential energy, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its natural frequencies further. The empty space factor due to the truss-type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes satisfying the end condition. The weights are evaluated by the Rayleigh-Ritz (RR) method, and verified using finite element method (FEM). The weight of the superstructure acts as an axial compressive load on the beam. Kelvin-Voigt model of structural damping is included. A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. A parametric study is done for various magnitudes of tip mass and various levels of submergence. The computational efficiency and accuracy of the Rayleigh-Ritz method, as compared to the FEA, has been demonstrated. The advantage of using closed-form trial functions is clearly seen in the efficacy of calculating the various energy components in the RR method.

An AFM Dynamic Contact Model with Finite Thickness Correction to Study Micro-Rheology of Biological Cells

One of the major sources of error in Atomic Force Microscopy based Force Spectroscopic studies is bottom substrate effect, which comes due to assumption of infinite sample thickness. In the present work, anew experimentally validated mathematical correction for finite thickness of thesample is incorporated into a dynamic indentation model. This model is an extension of Sneddon’s static indentation contact model developed for conical tip indenters by incorporating the tip geometric effects, correction to hydrodynamic drag, viscoelastic nature of the sample and its finite thickness. The new model is applied to extract the viscoelastic properties of primary mesenchymal stem cells (MSC’s) extracted from human bone marrow and HCT-116 aggressive epithelial colorectal cancer cells. The micro-rheological studies indicated the presence of profound influence of infinite thickness assumption depending upon indentation depth and sample thickness at the point of indentation. The present model nullified this error and provided a better estimate of the rheological properties. The tests were conducted over a wide frequency bandwidth (0.5 to 126 Hz) and frequency dependent material properties were analyzed using power law structural damping model. It was found that MSC’s are stiffer and less viscous in nature compared to cancer cells.

Comparison of viscous and structural damping models for piezoelectric vibration energy harvesters

Abstract This work compares viscous and structural damping in a lumped-parameter model of a piezoelectric vibration energy harvester. The dynamic response and power harvested are solved in closed-form for devices with combined viscous and structural damping. The results are then reduced to get expressions for isolated cases of viscous and structural damping. The conditions that maximize the power harvested are determined. These devices generally have two maxima. One maximum is not sensitive to the damping model. The other maximum, however, has meaningful differences between viscous and structural damping models. The differences between the two models increase with increasing electromechanical coupling.

Application of differential transformation finite element method in aperiodic vibration of non-prismatic beam

The paper presents the combination of multi-step differential transformation method (MsDTM) and finite element method (FEM) in vibration analysis of non-prismatic beam. A new algorithm, named differential transformation finite element method (DTFEM), combines the advantages of both methods. It enables to solve a wide class problems and obtain solutions in the form of piecewise functions that are very useful in further analyses, especially in time-consuming computations of dynamic systems. In contrary to standard DTM, with the proposed method, we can successfully calculate vibrations of non-prismatic structures governed by partial differential equations with variable coefficients. The application of FEM reduces partial differential equation to system of ordinary differential equations depending on time. After applying multi-step DTM the system is converting into a set of recursive algebraic equations which can be solved in a symbolic way. The final approximate solution is composed of a sequence of single solutions obtained in every time interval.The algorithm of DTFEM was described and illustrated with an example of non-prismatic simply supported beam subjected to uniformly distributed load increasing nonlinearly in time. The results in the form of beam displacements, velocities and accelerations were compared with numerical approach based on Newmark method. Two cases of damping model were taken into account: structural damping model and external damping model represented by two viscous dampers. A very good agreement was found in both cases. Presented analyses show that DTFEM is more accurate, with the same time step, than Newmark method. Therefore, in some cases, it may be possible to obtain sufficiently accurate results faster. The main advantage of the proposed method is the solution’s form which is a function of time and not a discrete set of results.

High frequency, multi-axis dynamic stiffness analysis of a fractionally damped elastomeric isolator using continuous system theory

A spectral element approach is proposed to determine the multi-axis dynamic stiffness terms of elastomeric isolators with fractional damping over a broad range of frequencies. The dynamic properties of a class of cylindrical isolators are modeled by using the continuous system theory in terms of homogeneous rods or Timoshenko beams. The transfer matrix type dynamic stiffness expressions are developed from exact harmonic solutions given translational or rotational displacement excitations. Broadband dynamic stiffness magnitudes (say up to 5kHz) are computationally verified for axial, torsional, shear, flexural, and coupled stiffness terms using a finite element model. Some discrepancies are found between finite element and spectral element models for the axial and flexural motions, illustrating certain limitations of each method. Experimental validation is provided for an isolator with two cylindrical elements (that work primarily in the shear mode) using dynamic measurements, as reported in the prior literature, up to 600Hz. Superiority of the fractional damping formulation over structural or viscous damping models is illustrated via experimental validation. Finally, the strengths and limitations of the spectral element approach are briefly discussed.

Prediction of the damping properties of fiber-reinforced polymer composite panels with arbitrary geometries

In this work, the modal damping of multilayered, fiber-reinforced polymer composite laminates with an arbitrary geometry have been computed using a mixed finite element-meshless method. The meshless node distribution scheme is used in conjunction with the Lagrangian quadrilateral interpolating functions to ensure the continuity of interelemental displacements. Furthermore, since the distribution of the elements is not confined to the geometry of the problem, any arbitrary geometry can be readily analyzed by using the same node and element distributions. Using the classical plate theory, together with a structural damping model, modal response results have been produced for a number of multilayer fiber-reinforced polymer plate geometries, including triangular and circular as well as rectangular plates with different combinations of free and clamped edges. Comparison of these results with those reported in the literature shows that the proposed method can predict the modal properties of fiber-reinforced polymer laminates with arbitrary geometries and boundary conditions with a good degree of accuracy.

Viscoelastic response of neural cells governed by the deposition of amyloid-β peptides (Aβ)

Because of its intimate relation with Alzheimer's disease (AD), the question of how amyloid-β peptide (Aβ) deposition alters the membrane and cytoskeltal structure of neural cells and eventually their mechanical response has received great attention. In this study, the viscoelastic properties of primary neurons subjected to various Aβ treatments were systematically characterized using atomic force microrheology. It was found that both the storage (G′) and loss (G″) moduli of neural cells are rate-dependent and grow by orders of magnitude as the driving frequency ω varies from 1 to 100 Hz. However, a much stronger frequency dependence was observed in the loss moduli (with a scaling exponent of ∼0.96) than that in G′ (∼ω0.2). Furthermore, both cell moduli increase gradually within the first 6 h of Aβ treatment before steady-state values are reached, with a higher dosage of Aβ leading to larger changes in cell properties. Interestingly, we showed that the measured neuron response can be well-explained by a power law structural damping model. Findings here establish a quantitative link between Aβ accumulation and the physical characteristics of neural cells and hence could provide new insights into how disorders like AD affect the progression of different neurological processes from a mechanics point of view.

Hysteretic damping in an elastic body with frictional microcracks

Material stress strain curves often show dissipation via rate-independent hysteresis. Here we study an elastic plate with several randomly distributed and oriented frictional microcracks, loaded cyclically in plane stress. Computational solutions in ABAQUS show narrow hysteresis loops. Unlike the loops from Rowett׳s classic experiment (1914), or from simple hysteresis models such as the Bouc–Wen model (1967 and 1976), the present loops are pinched at the origin and partially resemble an ad hoc model proposed by Reid (1956). Such pinched loops have been revisited lately by others, but our results provide new justification for the same. We also propose a new simple scalar model that gives a better qualitative match with the numerically obtained hysteresis loops than any other model presently available. Our scalar hysteresis model may lead to better interpretations and modeling in, e.g., vibration response of structures with such internal frictional damping. Thus the contribution of this paper lies in adopting a dissipation model from micromechanics, idealizing the resulting dissipation loops, and presenting a new simple scalar equation that models such loops and can be easily incorporated into structural vibration damping models.

Modeling the Effects of Underwing Missile Canards on F-16 Limit Cycle Oscillations

This research evaluated various methods using ZONA’s Euler Unsteady Aerodynamic Solver against flight tests previously flown at USAF Test Pilot School, using underwing air-to-air missiles with removable canards, which allows the aerodynamics of the store configuration to be changed while maintaining identical mass properties. ZONA’s Euler Unsteady Aerodynamic Solver was employed with various linear flutter and nonlinear time-domain analyses. ZONA’s Euler Unsteady Aerodynamic Solver correctly predicted that removing the canards would delay limit cycle oscillation onset. However, all of the methods generally predicted onset earlier than flight test. Consistent with the results found by previous researchers, the nonlinear simulation still predicted divergent classical flutter rather than limit cycle oscillation until nonlinear structural damping was added and tuned to produce limit cycle oscillation. Without known structural damping characteristics, the nonlinear structural damping model needed to be arbitrarily tuned to match flight-test data. This research demonstrated a different tuning method from that had been used by previous researchers. Nonlinear structural damping plays an important role in limit cycle oscillation, but a better understanding of the actual nonlinear aerodynamic and structural effects is needed before reliable limit cycle oscillation predictions can be made for all configurations and throughout the flight envelope.

Damping properties of FRP cables for long-span cable-stayed bridges

In this study, the damping properties of carbon fiber reinforced polymer (CFRP) and basalt fiber reinforced polymer (BFRP) cable potentially applied in long-span cable-stayed bridges were simulated and evaluated based on experimental data and theoretical derivations. The modal shapes were first identified according to a previous dynamic test on FRP cables, based on which the modal damping ratios of the in-plane vibration were estimated by the structural damping model of mode-dependence. Meanwhile, the modal damping ratios of the out-of-plane vibration were evaluated by the combined Rayleigh and frequency independent damping (CRFID) model. The results show that (1) the modified equation for the modal damping ratio validated by the results of in-plane vibration of the steel cable can be used for modeling the damping ratios of FRP cables, (2) the coefficients of dynamic strain damping energy of CFRP and BFRP cables were derived by backward calculating and fitting the experimental data, which can represent the damping difference among each material, and (3) the modal damping ratios of the out-of-plane modes of different stayed cables were fitted by the CRFID model and show good agreement with the test results.