Global Damping Research Articles

Design and damping characterization of sandwich composite made of particle-filled hollow spheres and steel sheets

Sandwich composites made of particle-filled hollow sphere structures (PHSS) and steel sheets offer excellent lightweight and damping properties, ideal for high-speed machine tool components under dynamic loads. Previous research has focused on single particle-filled hollow sphere (PHS) and small PHSS, leaving a gap understanding of PHSS/steel sandwich composites. In this study a test rig was developed, and Design of Experiments and Response Surface Analysis were used to investigate the effects of sheet and core thickness (design parameters), filling ratio, and particle size (particle parameters) on the damping performance of PHSS/steel sandwiches. The results indicate that the design parameters have a significant influence on damping performance. The interaction between design and particle parameters also substantially affects damping. Minimizing particle size, increasing filling ratio, thinning the face layer, and thickening the core layer significantly improve structural damping. To address manufacturing tolerances, a finite element (FE) model-based optimization was developed to accurately determine PHSS material parameters. These parameters were used in an FE model of the PHSS-steel composite, with identified contact parameters minimizing measurement and simulation differences. The homogenized material model and the linear model using global damping parameters accurately reproduce the dynamic properties of the PHSS-steel sandwich composite in low vibration modes.

Numerical study of the linear and non-linear damping in an acoustically forced cold-flow test rig with coupled cavities

Quantifying the oscillation amplitude of thermoacoustic instabilities remains a critical and challenging issue, as it is a complex balance between driving and damping processes. The New Pressurized Coupled Cavities (NPCCs) setup designed for the study of acoustic damping is analyzed in this work. It is a cold-flow test rig mimicking the geometry of a liquid rocket engine and equipped with an acoustic forcing device. The chamber 1T mode triggers a strong non-linear harmonic response, while the 1T1L and 1T2L exhibit weak non-linearities. Disturbance energy budgets are used in large-eddy simulations to characterize the damping phenomena with the 1T2L and 1T1L forcing. The correct global damping of the system is retrieved, and local damping contributions are extracted. Then, a non-linear term representing the energy transfer to the harmonics is derived from non-linear acoustics theory. Combined with a linear model, this model correctly retrieves the limit-cycle of the 1T mode.

Damping prediction of highly dissipative meta-structures through a wave finite element methodology

Aiming at accurately predicting the global Damping Loss Factor (DLF) for Highly Dissipative Structures (HDS), the current study uses the Wave Finite Element (WFE) methodology. It starts by deriving the forced responses of a Unit Cell (UC) representative of the periodic meta-structure. Then it computes the DLF of the wave via the power balance. The Bloch expansion is employed. The response to a point force applied to the periodic structure is decomposed in the Brillouin zone, allowing the prediction via integration over the wavespace. The global DLF is derived based on the Power Input Method (PIM). The accuracy of the methodology is demonstrated through several cases from simple panels to complex meta-structures. For HDS, results of General Laminated Model (GLM) is exploited for wave DLF and PIM based on Finite Element Method (FEM) data is provided as reference approach for global DLF. The study discusses the influence of bending waves on the DLF estimation for HDS. A final case study with a meta-structure is also offered. The later consists of a doubly periodic coated sphere in a host rubber, it demonstrates the importance of Bloch modes.

Fibre-Based Nonlinear Viscous Damping Model Defined for Dynamic Analysis Using Distributed Plasticity Elements

ABSTRACT This paper presents a new nonlinear viscous damping model implemented in the fibre where a constitutive rule is defined between the strain rates and the damping stresses. This model is developed for nonlinear dynamic analyses using distributed plasticity frame elements with fibre cross-sections. The model is proportional to the initial stiffness of the fibre material, but the maximum damping stress is limited to avoid local and global high damping forces and prevent them from decaying or taking negative values when the structure is in the inelastic range. The manuscript details the formulation used to find the fibre strain rates, the damping forces at each level of the structure and its implementation using the Newmark method. The predictions of the model are compared with the real response of a reinforced concrete structure tested on a seismic table under high demands. Additionally, a numerical case study addressing the inelastic response of a steel structure and sensitivity analyses are presented.

Dynamic Performance of Monopile-Supported Wind Turbines (MWTs) under Different Operating and Ground Conditions

A monopile is the most popular foundation type for wind turbines. However, the dynamic performance of monopile-supported wind turbines under different operating and ground conditions is not fully understood. In this study, an integrated monopile-supported wind turbine model in a wind tunnel was employed to jointly simulate the operating and ground conditions. A series of wind tunnel tests were designed and performed to investigate the dynamic performance of monopile-supported wind turbines. These tests included seven operating conditions (seven wind speeds and corresponding rotor speeds) and four ground conditions (one fixed ground condition and three deformable ground conditions with different soil relative densities). According to the test results, the structural responses and dynamic characteristics were analyzed and discussed. This shows that the assumption of fixed-base support significantly overestimates the natural frequency but underestimates the global damping ratio. With the increase in soil relative density, the natural frequency slightly increases, while the damping ratio decreases more significantly. With the increase in the wind speed and rotor speed, the increase in global damping is larger on softer ground. A regression analysis was performed to estimate the global damping ratio under different operating and ground conditions.

Stability Analysis of Type II Thermo-Porous-Elastic System with Local or Global Damping

Stability Analysis of Type II Thermo-Porous-Elastic System with Local or Global Damping

Campbell diagrams, dynamics and instability zones of graphene-based spinning shafts

Carbon-based nanocomposite drive shafts have received considerable attention because of their excellent material and mechanical properties, with applications in modern aerospace, automotive industries and others. Therefore, for the first time, new Campbell diagrams, vibration and bifurcation points for multilayer shafts reinforced with three technologically justified distribution patterns of graphene nanoplatelets (GPLs) in the polymer matrix are presented and examined. A new formulation in the framework of a modified Timoshenko beam theory making use of the rotation angles of the cross sections of the shaft with five degrees of freedom is utilized. The modulus of elasticity of the nanocomposite material is estimated using the Halpin-Tsai micromechanical model, whereas the mass density and Poisson's ratio are computed by means of the law of mixtures. Hamilton's variational principle is used to derive weak and strong forms of motion equations of the shaft with classical and mixed boundary conditions. Assumptions for the derived model of the nanocomposite shaft are presented to clearly describe the mechanical state of the system. The Ritz-Chebyshev method is applied to discretize the governing equations and obtain the generalized nonlinear characteristic equations in matrix form including the gyroscopic effect and elastic stiffness caused by the rotation of the shaft. Verification of obtained results and convergence study were performed to show the correctness and advantages of the proposed solution method. The effect of different key parameters such as GPLs distribution and weight percentage, axial speed of the shaft, and boundary conditions, on its global damping, dynamics and instability zones are shown. For the first time, it is clearly shown how studied factors affect the shape of Campbell diagrams as well as the shift of natural frequency and bifurcation point of the graphene-based nanocomposite shafts.

Simulation of Deployable Cable Nets for Active Debris Removal in Space

Deployable cable nets have been proposed as promising systems for the active removal of space debris. The modelling and analysis of such systems during deployment, capture, and post-capture phases are crucial for the effective design of an operative mission. To this aim, accurate and effective simulation tools are necessary. We propose a finite element model of the cable net with lumped nodal masses and first-order cable elements. The nodal positions are assumed as the main unknowns of the problem. The large displacements and finite deformations are described by the Green-Lagrange strain tensor. The cable elements are assumed to react only in tension. Global damping is considered in line with Rayleigh’s hypothesis. The governing equations are solved numerically by means of the Runge-Kutta method with a variable time step. As an illustrative example, we present the simulation of the in-plane deployment of a planar, square-mesh net. The proposed approach turns out to be computationally effective, even if the accuracy of the numerical integration scheme needs to be improved, particularly in the final stages of deployment.

A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

AbstractThis paper presents a two‐dimensional corotational curved beam element for the dynamic analysis of curved viscoelastic beams with large deformations and rotations. In contrast with traditional straight beam elements, the novelty of the presented formulation lies in introducing a curved reference configuration, which follows the rotation and translation of a corotational frame, to measure the pure elastic deformation of the beam and describe the spatial position of an arbitrary material point. A curvilinear coordinate system is fixed on this reference configuration to measure the local deformation of the element. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. An accurate two‐node curved element and the Kelvin–Voigt model are introduced to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational accuracy, and computational efficiency of the presented formulation. Moreover, the effects of the internal damping and external damping on the dynamic response of a rotating curved beam are investigated.

An ALE formulation for the geometric nonlinear dynamic analysis of planar curved beams subjected to moving loads

This paper presents an arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for the geometric nonlinear dynamic analysis of planar curved viscoelastic beams subjected to moving loads. In the ALE description, the beam nodes can be moved in arbitrarily specified ways to describe the moving loads’ material positions accurately. The pure deformation and the deformation rate of the element are measured in a curvilinear coordinate system fixed on a curved reference configuration that follows the rotation and translation of a corotational frame. Based on Hamilton’s principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. Then, a standard element can be embedded within the element-independent framework. An accurate two-node curved element and the Kelvin-Voigt model are introduced in this framework to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational efficiency, and versatility of the presented formulation. The effect of internal damping, external damping, the inertia force of a moving mass, and the moment of inertia of the mass on the dynamic response of the beam are investigated. Moreover, the driving force for a prescribed motion of a mass along the beam is investigated.

Energy dissipation in reinforced concrete members before or after yielding

AbstractModels for the pre‐ and post‐yield energy dissipation in reinforced concrete (RC) members are developed using a database of about 1200 tests with over 18,000 load cycles. Before yielding, the equivalent viscous damping ratio exceeds 5%, especially if the member is initially uncracked. It can be considered by using either a dedicated pre‐yield hysteretic model with parameters established in the paper or global viscous damping and special provisions against double counting of energy dissipation. The post‐yield model can be combined with various post‐yield hysteretic laws. It accounts for the member's type, shear‐span‐to‐depth ratio and likely failure mode, the continuity, ratio, and surface characteristics of longitudinal bars, and for FRP wrapping, if any. Alternatively, it recognizes only four member types but accounts also for the transverse steel ratio and the normal stress due to the axial load.

Damping identification of offshore wind turbines using operational modal analysis: a review

Abstract. To increase the contribution of offshore wind energy to the global energy mix in an economically sustainable manner, it is required to reduce the costs associated with the production and operation of offshore wind turbines (OWTs). One of the largest uncertainties and sources of conservatism in design and lifetime prediction for OWTs is the determination of the global damping level of the OWT. Estimation of OWT damping based on field measurement data has hence been subject to considerable research attention and is based on the use of (preferably operational) vibration data obtained from sensors mounted on the structure. As such, it is an output-only problem and can be addressed using state-of-the-art operational modal analysis (OMA) techniques, reviewed in this paper. The evolution of classical time- and frequency-domain OMA techniques has been reviewed; however, the literature shows that the OWT vibration data are often contaminated by rotor speed harmonics of significantly high energy located close to structural modes, which impede classical damping identification. Recent advances in OMA algorithms for known or unknown harmonic frequencies can be used to improve identification in such cases. Further, the transmissibility family of OMA algorithms is purported to be insensitive to harmonics. Based on this review, a classification of OMA algorithms is made according to a set of novel suitability criteria, such that the OMA technique appropriate to the specific OWT vibration measurement setup may be selected. Finally, based on this literature review, it has been identified that the most attractive future path for OWT damping estimation lies in the combination of uncertain non-stationary harmonic frequency measurements with statistical harmonic isolation to enhance classical OMA techniques, orthogonal removal of harmonics from measured vibration signals, and in the robustification of transmissibility-based techniques.

Mitigation of wind induced accelerations in tall modular buildings

This paper compares two methods of mitigating wind induced vibrations in tall modular buildings. Tall buildings experience wind induced motion which can result in serviceability and habitability issues associated with occupant discomfort. Modular construction, in which volumetric modules are assembled around a reinforced concrete core, can be particularly susceptible to wind induced accelerations due to the tall slender form of the core and the small and uncertain contribution of the modules to global lateral stiffness and damping. This study analyses the acceleration response of modular buildings. Broadly speaking, for this form of construction, two approaches exist to mitigate excessive vibrations; increasing core dimensions or the addition of auxiliary damping. This study evaluates these two approaches for a large number of archetype modular structures in order to investigate which method is more effective. Of more than 6000 archetypes studied, it was found that over 40% required vibration control measures to meet ISO acceleration limits. Installing a Tuned Liquid Damper (TLD) proved significantly more efficient than increasing RC core dimensions; a 1% increase in damping achieves a similar level of acceleration reduction to approximately a 2100 mm increase in core breadth and depth. The estimated level of auxiliary damping available from a TLD is sufficient to control accelerations for the majority of archetypes considered. A method for developing curves defining the maximum feasible height of a modular building based on its dimensions and the provision of an optimum TLD is also developed. The results show that modular buildings can be used as a viable form of construction for high-rise buildings and quantify the extent to which the maximum heights of modular tower buildings can be increased using existing vibration control technologies.

Simulation of the Vibrations Produced to the Human Body During Operation of the Bucket Wheel Excavators. A Case Study of ERc 1400-30/7 Type Excavator

Abstract The paper deals with the analysis of the dynamic response over time of the excavator boom during operation. For a start, we determined the variation in time of the forces acting on the rotor shaft, due to the excavation. These forces have high values and a slow variation over time, which depends on the rotation speed of the bucket wheel and the number of buckets installed on it. A virtual model of the BWE boom was proposed, for which the dynamic response in time due to the excavation forces was determined, for a point in the main cabin of the BWE. A virtual sensor has been attached to this point corresponding to seat of the operator. The simulation of the dynamic response over time was performed taking into account a global damping of 2% of the critical damping. The simulation was performed both for the excavation of a homogeneous material and for the case of a shock (a sudden appearance of an inclusion of hard material during the cutting of the homogeneous material).

Modelling and Validation of Joint Properties for NVH Simulation Model of an Electrified Passenger Vehicle Drivetrain


 
 
 The constantly changing automotive market, which is characterized by the progressing electrification of vehicles, presents challenges with respect to the acoustic behaviour of powertrains. As indicated frequently, the characteristic noise of electric cars differs from that of conventional drives. In particular, energy dissipation of the assembled housing parts from material and joint damping; is an important aspect. In modelling the NVH behavior of electric vehicles or drivetrains in general, the breakdown of global material and local joint damping is not yet state of the art. Instead, measured global modal damping values from similar constructions are frequently used. Often, a constant degree of damping is defined for all modes. However, moderate changes in the geometry of components or in the load level can lead to severe fluctuations in the damping. In order to improve predictability and to be able to estimate the effects of constructive changes in natural frequency, mode shape, and damping, the goal will be to take into account the global material and local joint damping separately. For that, a local model which is able to take the joint properties into account has to be developed. The analytical based Iwan model for the contact interface was expanded upon to facilitate model updating against forced response measurements on a simple mass spring structure in one dimension and to extend the model from one-dimensional to three-dimensional.
 
 

Finite element model to investigate the dynamic instability of rectangular plates subjected to supersonic airflow

In this paper, a numerical method is presented to study the dynamic behaviour of an isotropic rectangular plate subjected to aerodynamic loads induced by parallel supersonic airflow. A finite element model, based on bi-dimensional polynomial displacement functions and linear Piston theory, is used to study the dynamic behaviour of the solid plate coupled with aerodynamic loads. The developed approach is able to model flat plates and shallow shells in which the fluid–structure coupling at the interface is applied synchronously using a monolithic method. The solid model is based on Sanders’ shell theory. The stiffness and damping matrices that result from application of the aerodynamic load are coupled with those obtained from a structural model and are calculated using analytical integration. By assembling the matrices, the global mass, damping and stiffness matrices for the plate are obtained and then dynamic equations of the governing problem are derived. The eigenvalues of the system are calculated using the equation reduction technique. The critical non-dimensional aerodynamic pressure of the airflow that induces flutter of the structure is determined for various boundary conditions and geometries. The obtained results are compared with other published research works and very good agreement is observed.

Water Oscillation Modelling Inside OWC Chamber for Wave Energy Conversion

Among wave energy converters (WECs), the Oscillating Water Column (OWC) system is considered as one of the most promising converters; this system works on the principle of water oscillations in an enclosed air chamber due to incident sea waves. The amount of pneumatic power that can be harvested depends on the elevation level, the water oscillations' frequency inside the chamber, and the chamber's global damping. A one-dimensional (1-D) unsteady model has been elaborated to analyze the water elevation's dynamic behavior. Great attention has been paid to determining the natural frequency and the global damping for maximum wave energy capture. The model is based on a water mass block moving periodically upward and downward as a piston inside the chamber, inducing the enclosed air to flow alternately through a turbine. The Lagrangian formalism has been adopted to derive the governing differential equation for the piston water motion. Then the poincare-Lindstedt method has been used to deal with the non-linearity of the problem. The elaborated model has been adapted to an OWC system in the case of monochromatic waves. Results have been compared to another referenced paper for validation and pertinence. Fair agreements have been noted.

Assessment of hysteretic damping in reinforced concrete structures using local hinge characteristics

Performance-based seismic engineering is nowadays adopted for economical design of structures to resist earthquakes and it requires nonlinear static pushover analysis to be performed. In this approach, the energy dissipation due to nonlinear behavior of the structures is taken into account by obtaining the equivalent viscous damping and this damping is evaluated from the global pushover curve of the structures. However, the global structural damping is basically due to energy dissipation at local joints of the structures deforming beyond yield rotation. This paper presents the methodology of estimating equivalent damping from the local hinge characteristics of the structures at element level by carrying out Pushover analysis of three structures viz 3D six storeyed, 2D two storeyed and a simple column RC structure. This damping is assessed by considering cumulative hysteretic energy dissipated at all the plastic hinges developed in the structures and is compared with that calculated based on formulations given in codes such as FEMA-440 and ATC-40. Damping agrees well with that given in FEMA-440, estimated from global pushover curve of structures for ductility value greater than 3. Also, nonlinear time history analysis is performed for all the structures to validate the structural performance.

A separation-based analytical framework for seismic responses of weakly-coupled electrical equipment

Weakly-coupled electrical equipment, consisting of a series of supporting posts interconnected by flexible connection parts, is commonly seen in power systems. Compared with general structures, weakly-coupled electrical equipment has two main characteristics—(a) the structural integrity of the equipment is weak due to the flexible connection parts and (b) material damping of the supporting posts and connection parts can be very different. Based on these characteristics, global vibration modes and proportional damping should be cautiously used. This restricts applications of common seismic calculation methods for the weakly-coupled equipment. Therefore, the authors developed a separation-based analytical framework for the weakly-coupled electrical equipment, which is presented herein. In this framework, usage of nonproportional damping and local vibration modes of posts and connection parts can be achieved. This framework also facilitated a modeling analysis, which investigate the mechanism of the weakly-coupled effect. It was found that the dynamic transmission of connection parts is the nature of the weakly-coupled effect, and the proportional damping can produce unacceptable errors for the weakly-coupled equipment. To further validate the analytical framework, we conducted shaking table testing on two insulator posts connected by a slidable busbar. The analytical method and conventional mode-superposition method were both employed to calculate the seismic responses of the specimen, and the calculation results were compared with the testing responses. Comparisons suggest the separation-based analytical framework is more applicable and effective for weakly-coupled electrical equipment.

Vibration analysis of super-yachts: Validation of the Holden Method and estimation of the structural damping

The hull excitation generated by marine propellers constitutes one of the most significant vibration sources affecting comfort on passenger ships. Consequently, the evaluation of the propeller-generated excitation through reliable numerical tools during the preliminary stage of ship design is fundamental. The Holden Method (HM) is an empirical tool utilized to calculate the propeller-induced pressure distribution on a ship hull. The present paper validates the HM, which is applied to a twin-screw, 54-m super-yacht. Finite Element Analysis (FEA) is used to benchmark the HM numerical predictions against a set of full-scale vibration measures. The outcomes show that the magnitude of the propeller-induced dynamic excitation predicted by the HM is overestimated. Thereafter, the calibrated propeller-induced forces and the diesel engine excitation are applied to the FE model to perform a series of forced vibration analyses and estimate the global structural damping coefficient of the super-yacht. The study highlights the necessity of developing new empirical methodologies, analogous to the HM, to be applied to modern small luxury vessels.