Stiffness Damping Research Articles

Spatial and frequency identification of the dynamic properties of thin plates with the Frequency-Adapted Virtual Fields Method

Vibroacoustic inverse methods use the measured response of a vibrating structure to identify a structural parameter or a dynamic load. Two inverse methods are considered, the Force Analysis Technique (FAT) and the Virtual Fields Method (VFM). The Corrected Force Analysis Technique (CFAT) is a variant of FAT that corrects its singularity. This correction allows the method to be applied in the high-frequency domain, when the number of measurement points per flexural wavelength becomes small. In this study, the proposed novelty is the development of a Frequency-Adapted VFM (FA VFM) to the case of a Love–Kirchhoff plate. Thanks to this method, the VFM can now be applied to identify the equivalent bending stiffness and structural damping of a thin plate when the number of measurement points per wavelength is small. The method has previously been developed for an Euler–Bernoulli beam. An experimental identification of the complex bending stiffness of an locally damped aluminium plate using Laser Doppler Velocimetry (LDV) data and the developed method is performed. The experimental study shows for the first time that the FA VFM can be used to map the equivalent bending stiffness and structural damping as a function of position on a plate and identify these parameters as a function of frequency over a large frequency band. The results of the Frequency-Adapted VFM are compared with those of CFAT and the classical VFM approach. FA VFM results are more accurate than those of classical VFM and similar to those of CFAT.

Shaking table test and control effect analysis of structure with negative stiffness damped outrigger

A shaking table test was conducted on a negative stiffness damped outrigger (NSDO) structure, designed based on a real engineering project, to gain insights into the practical performance of the NSDO under earthquakes when equipped with nonlinear negative stiffness devices (NSD) and dampers. A low-friction NSD was designed, built, and verified by experiments to mitigate the potential issue adversely affecting its performance. The shaking table tests showed that NSD effectively increases the maximum deformation of the damper under moderate earthquakes. Nevertheless, the NSD had no influence on the initial and dynamic stiffness of the NSDO structure when the NSD was not activated due to low displacement. With the bell-shaped damping model to match modal damping ratios, a simplified fishbone numerical model was developed to simulate the response of the NSDO structure and to study the control effect of the NSDO through parametric analysis. The results revealed that the modal damping ratios were not uniform from mode to mode, and an inaccurate higher-mode damping ratio would significantly affect the response predictions during NSDO design. The initial tangential negative stiffness of the nonlinear NSD could be used to analyze the control effect under moderate earthquakes, while the secant stiffness was necessary for severe earthquakes. In addition, a combined seismic reduction curve was proposed for a two-level seismic mitigation analysis.

Local and global integrative retrofitting of reinforced concrete frames using in‐plane buckling steel braces

AbstractTwo large‐scale, single‐storey, single‐bay reinforced concrete (RC) moment frames, designed as per an outdated seismic code to represent a typical framing detail of a four‐storey building, have been tested under displacement‐controlled quasi‐static loading protocol as per ACI 374.1‐05. The RC frames include a plinth beam with brick infill underneath, a slab monolithically cast with the top beam and provision for applying axial load to the column to simulate real construction scenario. One of the frames has been tested as a bare frame, and the second one has been retrofitted with conventional steel braces designed to undergo in‐plane buckling. The size of the brace has been selected based on the result of a nonlinear time history analysis of representative low‐ to mid‐rise open‐ground storey RC buildings. Post‐installed chemical anchors have been utilized to connect the steel braces to the narrow RC frame members following the outcomes of an experimental investigation by the same authors. Local‐level retrofitting by steel jacketing using adhesives has been designed and utilized on columns and beams to achieve the desired seismic response. The seismic performance of the retrofitted frame has been compared with the bare frame in terms of strength, stiffness, ductility, energy dissipation and hysteretic damping. The tests provide insight into the role of the plinth beam, effect of RC slab on the strong‐column weak‐beam aspect and the achievement of the desirable hinge mechanism through a precise design and detailing of global and local level retrofitting technique.

A compliant helical structure to amplify inertia for nonlinear vibration absorption

The vibration absorption is a passive approach for vibration control by attaching a secondary vibration system to realize the energy transfer and dissipation. To generate a sufficient inertial force, vibration absorbers need to introduce large additional mass, and thus the engineering applications are limited. In this study, a novel compliant structure is proposed with the inertial amplified through a helical movement, and the structure is adopted for nonlinear vibration absorption. The dynamic equations of the absorber are established based on the Lagrange equation, characterizing the nonlinear characteristics arising from the large deformation of the structure and the nonlinear kinetic relationship between the translation and the rotation. Amplitude-frequency responses of the absorber under different excitations are solved using the harmonic balance method and the arc-length continuation method. A rotation-inertial dominant absorber (RIDA) and a translation-inertial dominant absorber (TIDA) are fabricated with the same helical structure while different mass distributions and experiments are performed to validate the nonlinear characteristics and vibration absorption effects. It is observed that both RIDA and TIDA demonstrate effective vibration absorption performances., RIDA introduces smaller additional mass than TIDA. The proposed helical structure absorbers exhibit combined nonlinearities of softening stiffness and displacement-dependent inertia and damping, demonstrating resonance shifting and jump phenomena. With an increasing excitation amplitude, the vibration absorption efficiency decreases and then increases.

Nonlinear response of very high frequency contour mode resonators

We explore the source of nonlinearities in Aluminum Nitride (AlN) Contour Mode Resonators (CMRs) operating in the Very High Frequency (VHF) range. We demonstrate that the red-shift of the resonance frequency found in VHF CMRs when the input RF power increases is due to nonlinear stiffness appearing from self-heating, and variable damping due to geometric nonlinearities. Moreover, we find a linear relationship between the variable damping coefficient and the resonator quality factor (Q). Such nonlinear mechanisms are modeled using a spring-mass-damper physical system and, in the electrical domain, a modified Butterworth-Van Dyke (MBVD) circuit where the nonlinear stiffness and variable damping are captured by a charge-dependent motional capacitor and a charge-dependent motional resistor, respectively. Detailed guidelines are provided to accurately analyze nonlinear CMRs using full-wave numerical simulations based on a finite-element method. Such simulations allow us to isolate the influence of each independent nonlinear mechanism and establish a relation between variable damping and geometric nonlinearities. Circuit and full-wave numerical simulations are in good agreement with measured data from fabricated 225 MHz CMRs exhibiting different Q. Finally, we exploit nonlinearities in high-Q CMRs to generate frequency combs at the MHz range opening the door to new exciting applications in telecommunication and sensing.

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Performance enhanced magnetic negative stiffness eddy-current damper: Numerical simulation and experimental investigation

Passive negative stiffness dampers (NSDs) possess significant advantages and promising application prospects in the field of structural vibration control. NSDs with high energy dissipation capability are desired to satisfy the vibration mitigation requirements for large-scale engineering structures, such as high-rise buildings and long-span bridges. However, in practical applications, due to the constraints of mounting space and additional weight, the negative stiffness and damping coefficient of existing NSDs are generally not very large and with poor adjustability. To overcome these limitations, this study develops a novel magnetic negative stiffness eddy-current damper (MNSECD) with enhanced overall performance. This damper consists of a magnetic negative stiffness system (MNSS), a multi-layer-plate-type eddy-current damping system (ECDS) in parallel, and a bidirectional ball screw transmission system. Firstly, different magnetic arrays are designed to optimize the magnetic fields of the MNSECD, and to enhance its magnetic negative stiffness and eddy-current damping without adding extra dimensions and weight. Subsequently, the electromagnetic finite-element models (FEMs) of the MNSECD are established to precisely simulate its magnetic negative stiffness and eddy-current damping forces, and these models are further utilized to elucidate the enhancement mechanism of different magnetic arrays. Finally, based on the numerical simulation results, the best performing magnetic array is selected respectively for the ECDS and MNSS systems to carry out experimental studies on a small-scale prototype. Numerical and experimental results indicate that the selected magnetic array for the MNSS proves highly effective in enhancing the magnetic negative stiffness of the MNSECD, while the selected magnetic array for the ECDS also demonstrates superior effectiveness in enhancing the eddy-current damping of the damper. These findings suggest that the novel MNSECD can be readily used in the vibration control of large-scale engineering structures.

HSC-RSW with laterally installed XADAS dampers: Seismic performance

This study investigates the seismic behavior of high-strength concrete (HSC) rocking shear walls (RSW) equipped with X-shape Adding Damping and Stiffness (XADAS) dampers installed perpendicular to the wall via brackets. Unlike previous studies where dampers are integrated along the wall length, this research leverages the advantages of HSC to minimize sectional dimensions while employing laterally installed XADAS dampers to enhance the cyclic response, yielding flag-shaped hysteresis curves. The alignment angle of the XADAS dampers is also considered a crucial variable in assessing the overall seismic performance of the proposed HSC-RSW system. A novel constructional approach using brackets to install lateral XADAS dampers is implemented. Post-tensioning (PT) forces are applied as consistent axial strains in cables, achieved through predefined cable support displacements. A macro-FEM model is developed to validate the chosen experimental reference test and is subsequently used for further parametric studies. The parametric studies indicate that increasing concrete compressive strength (CCS) enhances the self-centering capability by reducing RSW strains and facilitating rocking. Additionally, incorporating XADAS dampers into the system improves energy dissipation, with a zero-degree alignment angle identified as optimal. Notably, the modeled HSC-RSW systems exhibit limited drift capacity (less than 2 %) compared to normal strength concrete (NSC)-RSW systems, where wall toes are conventionally prone to crushing.

Enhancing the stability and efficiency of the advanced concrete structures surrounded by an auxetic foundation

This study delves into the vibrational characteristics of concrete annular plates reinforced with graphene oxide powders (GOP), underpinned by an innovative auxetic-elastic foundation. By applying Hamilton’s principle, the governing dynamic equations are meticulously derived, incorporating the effects of internal forces and GOP geometrical properties. The Differential Quadrature Method (DQM) is utilized to solve these equations, providing a robust and efficient numerical approach for analyzing the system’s complex dynamic behavior. GOP reinforcement significantly enhances the mechanical properties of the concrete plates, yielding improved stiffness and superior damping capabilities. The auxetic-elastic foundation, known for its unique property of becoming thicker perpendicular to the applied force, plays a pivotal role in altering the vibrational response of the system. The study meticulously examines the influence of this foundation on the system’s vibrational behavior, highlighting its potential to enhance performance under varying operational conditions. A comprehensive analysis is conducted to understand the effects of different boundary conditions on the vibrational characteristics of the reinforced concrete annular plates. The results underscore the importance of integrating advanced materials like GOP and innovative foundation designs in optimizing structural components. This study provides valuable insights into the design and application of reinforced concrete structures, emphasizing the effectiveness of GOP reinforcement and auxetic-elastic foundations in enhancing vibrational performance. These findings offer a significant contribution to the field of structural engineering, paving the way for future innovations in the design of resilient and efficient structural systems.

Vibration serviceability assessment of ribbon-shaped large-span footbridge at high altitudes under wind-pedestrians coupling effects

Large-span footbridges have low structural stiffness, light deadweight and small damping and thus are prone to significant vibration under the wind-pedestrian coupling effect. Fast and accurate calculation of structural dynamic response is the key to vibration serviceability assessment of footbridges. This study proposed a method of vibration serviceability assessment considering wind-pedestrian coupling for the ribbon-shaped large-span footbridge at high altitudes. The simulated crowd load and wind load were obtained through theoretical derivation and wind tunnel tests. A refined numerical model was developed to analyze the dynamic response of a large-span footbridge under wind-pedestrian coupling. The peak acceleration of the footbridge under different cases was statistically analyzed for an empirical formula, and the serviceability assessment of the footbridge was realized based on the fitting formula. The results revealed that the dynamic response of the footbridge under wind-pedestrian coupling was larger than that under one type of load alone. The dynamic response under the coupling effect was not equal to the linear superposition of the dynamic response in the case of one load. The closer the excitation frequency is to the natural frequency of the structure, the larger the dynamic response of the structure is, and the superposition of multiple modes occurs.

Modeling Torsional Stiffness and Damping of Liquid Slosh in Spacecraft Diaphragm Tanks

This study presents a pendulum-based empirical model of liquid slosh in spacecraft diaphragm tanks. Diaphragm torsional stiffness and effective damping are predicted within a range of lateral excitation frequency typical of launch or on-orbit operations. A pendulum-analog model with two primary slosh modes is extracted from diaphragm tank slosh data corresponding to steady-state triaxial force measurements at the support points of the tank under sinusoidal excitation. The approach leads to repeatable and accurate determination of pendulum model parameters. A gradient-based algorithm and a procedure for setting initial conditions for optimal parameter estimation are proposed to predict the liquid slosh forces and torques acting on the tank as frequency response functions of apparent mass and apparent mass moment. The pendulum models were assessed by comparing model-predicted force/torques with measurements, showing good agreement (1–5% prediction error in the time domain) under most test conditions (fill level, excitation amplitude, and frequency). An empirical model of the stiffness and damping is also proposed for the tested range of operational conditions. Because of the nonlinear nature of liquid slosh behavior in a diaphragm tank, both the stiffness and damping are local values for a given set of test conditions.

Bamboo-inspired lightweight, mechanically-stable and vibration-damping structural members for engineering applications

After millions of years of natural evolution, bamboo stems have formed exquisite variable cross-section hollow multi-node structures that are lightweight, tough, and stable. Bamboo is difficult to break and damage from the roots under dynamic loads, providing an important reference for te biomimetic design of lightweight components. This paper investigates the structural characteristics and variation patterns of bamboo stems and subsequently proposes an imitation bamboo stem structure design strategy for engineering structural members, namely, imitation bamboo double-jointed columns (IDJC). We establish a macro scale finite element model to predict the mechanical properties and failure modes of the IDJC under cyclic bending loads, and validate the model using experimental and analytical methods. The simulation and experimental results show that compared with traditional double-jointed columns (DJC), the weight of the IDJC is reduced by 41.7 %. Under bending load, the compressive stress of each section is approximately equal, reducing stress concentration, and increasing bending resistance. The strength to weight ratio of IDJC is 1.96 times that of DJC, indicating lightweight and high-strength characteristics. The stiffness degradation, energy dissipation, and damping and vibration reduction performance of the IDJC were also evaluated. The results showed that compared with the DJC, the stiffness degradation rate of the IDJC decreased by 6.87 times, the energy dissipation rate increased by 1.07 times, and the damping and vibration reduction performance improved by 48.40 %, reflecting a high stability and robust vibration reduction performance. The results demonstrate the potential application of biomimetic structures for the development and design of resource-rich, low-carbon, and sustainable bamboo for bamboo engineering members with excellent performance and functionality. Biomimetic structures have great potential in replacing nonrenewable structural materials in the fields of civil engineering and transportation.

Seismic performance evaluation of adjacent structures connected with negative stiffness and inerter-based dampers

Seismic performance evaluation of adjacent structures connected with negative stiffness and inerter-based dampers

Analytical Investigation of Performance of Passive Negative Stiffness Damper in Two-Cable Hybrid Network

Analytical Investigation of Performance of Passive Negative Stiffness Damper in Two-Cable Hybrid Network

Self-centering of steel braced frames equipped with Fe-SMA TADAS dampers

This study proposes a novel triangular added damping and stiffness (TADAS) damper that uses the shape memory effect of iron-based shape memory alloy (Fe-SMA) to provide a self-centering system to recover the initial shape of a structure after significant inelastic deformation induced by nonlinear response of fused elements, without the need for difficult and expensive replacement procedures of conventional TADAS systems. Unlike most studies which consider simplified uniaxial behavior of Fe-SMAs, the present non-linear finite element simulations cover the full 3D material non-linearity of Fe-SMA component based on the SMA constitutive law to capture both flexural and shear behavior in various coupled thermomechanical loadings, including the mechanical loading/unloading, the heating, and the final cooling (as the recovering process). Simulations performed on a one-bay steel frame for different drift ratios reveal that although the dissipation energy of the new device is at most 10% less than the ordinary one, it enjoys the self-centering property to recover the initial shape of the frame before loading, showing that the proposed damper is an effective alternative to ordinary TADAS yielding dampers to achieve the self-centering characteristics.

New deterministic model for calculating mesh stiffness and damping of rough-surface gears considering elastic–plastic contact and energy-dissipation mechanism

For a long time, meshing parameter calculations and dynamic modeling of gear systems have assumed smooth tooth surfaces, disregarding the impact of actual three-dimensional (3D) microscopic topography. Based on elastic–plastic contact and energy-dissipation mechanisms, this work developed a comprehensive deterministic model that integrates 3D rough surface modeling, reconstruction, and contact analysis, for calculating the time-varying mesh stiffness (TVMS) and mesh damping (TVMD) of deterministic rough-surface gears. Distinct from fractal and statistical models, the deterministic model analyzes deterministic, real 3D rough surfaces rather than simple surfaces defined by a few parameters. Utilizing stochastic process theory, different-topography surfaces are obtained using height and spatial features and reconstructed employing watershed algorithm and ellipsoidal asperity fitting. Subsequently, a deterministic elastic–plastic contact model based on equivalent rough curved-surface contact is constructed, emphasizing local contact states and energy dissipation for calculating contact stiffness (CS) and damping (CD) of gears. Accordingly, a meshing characteristics analysis model is established for calculating TVMS, TVMD, and load sharing ratio (LSR). Experimental validation and comparisons with several statistical and gear contact models demonstrate the effectiveness, reliability, and superiority of the proposed deterministic model. Multi-parameter impact analysis reveals small Sq (meaning low roughness Sa) and Ssk and high load correlate with increased CS and TVMS, while CD and TVMD depend on their interaction and hardness. Overall, by bridging the micro-surface topography and macro-meshing parameters, our model provides essential insights for the design and manufacturing of high-performance gear to reduce vibration and noise.

Damping effects of a stay cable attached with a viscous damper and a high damping rubber damper considering cable bending stiffness and damper support flexibility

To mitigate cable oscillations in cable-stayed bridges, a common approach involves using a strategically positioned viscous damper near the cable’s anchorage and bridge deck. However, for longer cables, this method may be insufficient due to installation constraints. In such cases, supplementing the damping system with a high-damping rubber (HDR) damper near the cable’s anchorage point on the bridge tower becomes imperative to enhance the cable’s damping ratio. Conventional designs often overlook crucial factors like viscous damper support stiffness and stay cable bending stiffness when integrating dampers into cable-stayed structures. This study presents findings on achieving an effective damping ratio in stay cables by using both a viscous damper and an HDR damper, considering the influence of viscous damper support stiffness and stay cable bending stiffness. The results indicate that the combined deployment of these dampers achieves a damping efficiency approximately equivalent to the sum of their individual effects. Importantly, decreased viscous damper support stiffness significantly affects the damping effectiveness, leading to a rapid decline in the stay cable’s damping ratio. While stay cable bending stiffness also influences the damping ratio, its impact is relatively less pronounced than that of viscous damper support stiffness. The study outcomes enable a more accurate prediction of the achievable damping ratio for a stay cable with additional components, considering both damper support stiffness and stay cable bending stiffness. Furthermore, the study explores parameters of both the viscous damper and HDR damper, such as the viscous coefficient, loss coefficient, HDR damper stiffness, and damper placement, evaluating their influence on the first damping ratio of the stay cable. The survey results provide valuable insights for determining optimal parameters for both dampers, maximizing the damping efficiency of cable-stayed bridges.

Column-based programmable damper for impact protection and vibration suppression of jacket structures

Steel jacket structures subjected to environmental impacts exhibit severe dynamic responses, potentially causing local fatigue failure, plastic damage, and even catastrophic collapse. Therefore, a structure with adjustable stiffness and large damping is ideal for coping with complex environmental loads and dissipating kinetic energy. A novel programmable damper was designed by connecting N-layer coupling elements composed of a linear spring, wire ropes, and an asymmetric column. Analytical models for the elastic buckling behavior of the damper were derived and mutually verified with finite element analysis (FEA). Based on the analytical models, the dependence of the mechanical responses of the damper on the number of elements and the spring stiffness was investigated for design guidance. The results indicate that the N-layer damper has 2N different stiffnesses, and the total dissipation capacity increases by approximately 2.6N times compared with a single asymmetric column. For potential applications, the dynamic decay responses of representative jacket structures assembled with the damper were simulated using the FE software ABAQUS combined with user-defined-material (UMAT) code, which demonstrated that the programmable damper is an advanced device that simultaneously achieves adjustable stiffness and significant damping.

A study of controlling the transverse vibration of a beam-plate system by utilizing a nonlinear coupling oscillator

In the engineering field, prolonged exposure of complex structures to high-strength vibration environments can lead to various engineering challenges. This underscores the importance of effectively managing the vibration of complex structures. Given the extensive utilization of beams and plates in the construction of intricate structures, this study incorporates a nonlinear coupling oscillator into the beam-plate system and formulates a vibration analysis model for this system. The governing equations of the system are derived theoretically and solved numerically using the Galerkin truncation method. This study focuses on the operational modes of the nonlinear coupling oscillator based on accurate numerical results. Meanwhile, the influence of parameters belonging to the nonlinear coupling oscillator on the transverse vibration responses of the beam-plate system is systemically studied. Upon meticulous examination of the numerical results, the operational states of the nonlinear coupling oscillator encompass the normal vibration suppression mode and the quasi-periodic vibration suppression mode. The alteration in the linear elastic coupling stiffness of the beam-plate system impacts the effectiveness of vibration suppression in the nonlinear coupling oscillator. This influence stems from the fact that changes in the linear elastic coupling stiffness directly affect the nonlinear forces exerted on the beam-plate system within a nonlinear coupling oscillator. Within a feasible range, the nonlinear stiffness and viscous damping can be chosen as the adjustable parameters for the nonlinear coupling oscillator to regulate the vibration of the beam-plate system by adjusting the motion mass of the nonlinear coupling oscillator, which presents a challenge. The appropriate utilization of the nonlinear coupling oscillator demonstrates favorable control effectiveness in managing the transverse vibration of the beam-plate system. The study presented in this work offers a method to simultaneously control the vibration of each component within beam-plate coupling systems.

Bowstring-type inerter negative stiffness damper for vibration control of slender towers

The difficulty of practical installation restrains the application of tuned damping devices in the high-performance vibration control of slender towers. In order to address this issue, a novel Bowstring-type Inerter Negative Stiffness Damper (BINSD) is proposed. The BINSD is composed of an inerter-negative-stiffness-dashpot system connected between the tower and a mass block (or a massless node) located on a vertical prestressed cable like a bowstring. In order to determine the multiple optimal parameters of the proposed BINSD, analytical parametric optimizations are investigated for the following three aspects. Firstly, the optimal tuning frequency and damping ratios are obtained via an analytical approach considering H∞ and H2 norms. Secondly, the optimal negative stiffness is determined by balancing the static and dynamic performances, particularly for practical excitations with mixed static and dynamic components (such as wind). Thirdly, the optimal installation height is analytically derived to fulfil a least negative stiffness criterion, which leads to an economic realization in practice. Finally, the effectiveness of the presented BINSD and corresponding optimal design approaches is numerically validated by the wind- and seismic- induced vibration control cases of a wind turbine tower. The proposed optimal design approaches lead to a high-performance, economic, and feasible design of BINSD.