Infinite Stiffness Research Articles

Vibration attenuation of dual periodic pipelines using interconnected vibration absorbers

Pipelines are crucial elements in various engineering applications. However, unexpected vibrations from different sources can jeopardize the operational performance and potentially damage the piping structures and other connected units. This study explores flexural wave propagation and attenuation characteristics of the pipes supported periodically on a rack. Also, a specific case of a rack with infinite stiffness (simple support) is investigated. The dispersion relations pertinent to pipe rack scenario is obtained through transfer matrix method (TMM) in conjunction with Floquet-Bloch’s theorem, and the accuracy of ensuing band gaps (BGs) are confirmed through finite element (FE) models. Following this, the modal analysis is performed to ascertain the minimum number of unit-cells necessary for the FE model to accurately mimic the attenuation and propagation characteristics of the corresponding infinite structure. The findings indicate that a pipe supported on rack displays resonance and Bragg-type BGs, arising from local resonance and spatial periodicity, respectively, while the pipe on simple support exhibits only Bragg-type BGs. To control low-frequency vibrations in dual pipelines placed on the rack, a novel configuration using interconnected dynamic vibration absorbers (DVAs) is proposed. The DVA consisting of two spring-damper units along with a mass is connected across the center of each span of the two pipelines. The proposed DVA is designed via genetic algorithm-based optimization. It was found that the designed DVA significantly reduces the vibration of the two pipelines. The performance of DVAs improves with an increase in the mass ratio. Additionally, the performance of pipes connected with conventional tuned mass damper (TMD) is evaluated and compared with the proposed DVA. The effectiveness of DVAs is also verified by employing a white Gaussian noise as input. The proposed DVAs are efficient in scenarios involving multiple pipes within a rack, leveraging other pipe’s mass, stiffness, and damping properties to mitigate vibrations in the considered pipes.

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, nonhomogeneous solution. The model is supplemented with bending energies and attractive-interaction energies between nonconsecutively visited pairs of nearest-neighboring sites (contacts). It captures the main features of a semi-flexible polymer subjected to variable solvent conditions. A hierarchical structure of the fractal lattice enabled the determination of the exact recurrence equations for the generating function, through which universal and local properties of the model were studied. An analysis of the recurrence equations showed that for all finite values of the considered energies and nonzero temperatures, the polymer resides in an expanded phase. The critical exponents of the expanded phase are universal and the same as those for ordinary self-avoiding walks on the same lattice found earlier. As a measure of local properties, the mean number of contacts per mean number of steps as well as the persistence length, are calculated as functions of Boltzmann weights associated with bending energies and attractive interactions between contacts. Both quantities are monotonic functions of stiffness weights for fixed interaction, and in the limit of infinite stiffness, the number of contacts decreases to zero, while the persistence length increases unboundedly.

Stability and infinite static stiffness of hydrostatic lead screw compensated with a single-action membrane restrictor

Stability and infinite static stiffness of hydrostatic lead screw compensated with a single-action membrane restrictor

Out-of-plane bending behavior of cross-laminated timber members enhanced with fiber-reinforced polymers

Carbon or basalt fiber-reinforced polymer (FRP) fabrics were bonded to the bottom of three-layer hemlock cross-laminated timber (CLT), aimed at improving its bending performance under out-of-plane loading. The FRP layer effectively enhanced bending strength by up to 23.8% and global bending stiffness with infinite shear stiffness by up to 18.4%. Carbon FRP was stronger and most effective, and combining it with an inner layer of cheaper basalt FRP also effectively reduced cost. Failure was not observed in the FRP layer, while failure at the transverse layer became more significant. Reinforcement of the transverse layer is therefore recommended to better realize the FRP enhancement effect. A predictive model for bearing capacity in bending for CLT with FRP fabric was developed and validated. Predicted bending stiffness results considering the offset of the neutral axis showed a good agreement with experimental results. The results support the application of FRP fabrics for improved bending performance for CLT panels under out-of-plane loading.

Acoustic Response of a Vibrating Elongated Cylinder in a Hydrodynamic Turbulent Flow

The present paper contains the results of the numerical analysis of the interaction between a Newtonian incompressible turbulent flow and a linear elastic slender body, together with the influence of the fluid–structure interaction (FSI) on the noise generation and propagation. The purpose is to evaluate the differences in term of acoustic pressure between the case where the solid body is rigid (infinite stiffness) and the case where it is elastic (finite stiffness). A partitioned and implicit algorithm with the arbitrary Lagrangian–Eulerian method (ALE) is used for the interaction between the fluid and solid. For the evaluation of the turbulent fluid motion, we use a large eddy simulation (LES) with the Smagorinsky subgrid scale model. The equation for the solid is solved through the Lagrangian description of the momentum equation and the second Piola–Kirchoff stress tensor. In addition, the acoustic analogy of Lighthill is used to characterize the acoustic source (the slender body) by directly using the fluid dynamic fields. In particular, we use the Ffowcs Williams and Hawkings (FW-H) equation for the evaluation of the acoustic pressure in the fluid medium. As a first numerical experiment, we analyze a square cylinder immersed in a turbulent flow characterized by two different values of stiffness: one infinite (rigid case) and one finite (elastic case). In the latter case, the body stiffness and mean flow velocity are such that they induce the lock-in phenomenon. Finally, we evaluate the differences in terms of acoustic pressure between the two different cases.

DAE-PINN: a physics-informed neural network model for simulating differential algebraic equations with application to power networks

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. However, deep-learning methods find it very challenging to learn stiff dynamics. In this paper, we develop DAE-PINN, the first effective physics-informed deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE). DAEs are used to model complex engineering systems, e.g., power networks, and present a “form” of infinite stiffness, which makes learning their solution trajectories challenging. Our DAE-PINN bases its effectiveness on the synergy between implicit Runge–Kutta time-stepping schemes (designed specifically for solving DAEs) and physics-informed neural networks (PINN) (deep neural networks that we train to satisfy the dynamics of the underlying problem). Furthermore, our framework (i) enforces the neural network to satisfy the DAEs as (approximate) hard constraints using a penalty-based method and (ii) enables simulating DAEs for long-time horizons. We showcase the effectiveness and accuracy of DAE-PINN by learning the solution trajectories of a three-bus power network.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

Study on the shear concentration in high‐rise buildings with transfer structure and its effects on seismic performance

SummaryThe architectural complexity and multifunctional requirements for modern high‐rise buildings usually lead to the utilization of combined structural systems, which typically consists of shear walls in higher zones while frames–core walls in lower zones. To fulfill reasonable load transfer between the different structural forms, transfer structures are commonly introduced in high‐rise buildings. However, the abrupt conversion in structural form usually causes shear concentration effect in the exterior walls just above the transfer structure, which is particularly vulnerable to seismic loading. In this paper, finite element models based on several types of practical high‐rise buildings were presented and analyzed to simulate the shear concentration effect in exterior walls. It was verified that the assumption of infinite stiffness in transfer structures will lead to underestimation of the shear concentration effect. The local deformations of transfer structures were demonstrated to be a key factor to scale the shear concentration. A scale factor of the shear concentration in the shear walls (SCSF) which can measure the intensity of shear concentration was defined. Parametric studies were carried out to provide insight on the influence factors of shear concentration. The results indicated that the SCSF only related to the difference between the rotation of external walls and center walls. Based on time‐history analysis, the influence of SCSF on the seismic performance of high‐rise buildings with transfer structures was studied. The results indicated that decreasing of SCSF can control the local damage caused by shear concentration, thereby improving the seismic performance of the structure.

Micro-rheology of a particle in a nonlinear bath: Stochastic Prandtl–Tomlinson model

The motion of Brownian particles in nonlinear baths, such as, e.g., viscoelastic fluids, is of great interest. We theoretically study a simple model for such a bath, where two particles are coupled via a sinusoidal potential. This model, which is an extension of the famous Prandtl–Tomlinson model, has been found to reproduce some aspects of recent experiments, such as shear-thinning and position oscillations [R. Jain et al., “Two step micro-rheological behavior in a viscoelastic fluid,” J. Chem. Phys. 154, 184904 (2021)]. Analyzing this model in detail, we show that the predicted behavior of position oscillations agrees qualitatively with experimentally observed trends; (i) oscillations appear only in a certain regime of velocity and trap stiffness of the confining potential, and (ii), the amplitude and frequency of oscillations increase with driving velocity, the latter in a linear fashion. Increasing the potential barrier height of the model yields a rupture transition as a function of driving velocity, where the system abruptly changes from a mildly driven state to a strongly driven state. The frequency of oscillations scales as (v0−v0*)1/2 near the rupture velocity v0*, found for infinite trap stiffness. Investigating the (micro-)viscosity for different parameter ranges, we note that position oscillations leave their signature by an additional (mild) plateau in the flow curves, suggesting that oscillations influence the micro-viscosity. For a time-modulated driving, the mean friction force of the driven particle shows a pronounced resonance behavior, i.e., it changes strongly as a function of driving frequency. The model has two known limits: For infinite trap stiffness, it can be mapped to diffusion in a tilted periodic potential. For infinite bath friction, the original Prandtl–Tomlinson model is recovered. We find that the flow curve of the model (roughly) crosses over between these two limiting cases.

A passive compensated method with hydraulic transmission for static infinite stiffness of thrust bearing

Hydrostatic bearings are a core component of the worktable in heavy duty high-precision machine tools and a non-touch sliding pair composed of oil pads and guideway surfaces. The stiffness of an oil film produced by an oil pad is a key indicator that restricts the manufacturing precision and efficiency of machine tools. This paper presents a novel oil pad. It can withstand the impact of any step load in the designed range and always maintain the load position to only change in the submicron level. Therefore, the pad has the advantages of infinite stiffness and submicron precision stability. The pad performances were verified by the tests, and the theoretical, simulation and experimental results were highly consistent with one another.

Numerical Simulation of Unreinforced Masonry Buildings with Timber Diaphragms

Though flexible diaphragms play a role in the seismic behaviour of unreinforced masonry buildings, the effect of the connections between floors and walls is rarely discussed or explicitly modelled when simulating the response of such buildings. These flexible diaphragms are most commonly timber floors made of planks and beams, which are supported on recesses in the masonry walls and can slide when the friction resistance is reached. Using equivalent frame models, we capture the effects of both the diaphragm stiffness and the finite strength of wall-to-diaphragm connections on the seismic behaviour of unreinforced masonry buildings. To do this, we use a newly developed macro-element able to simulate both in-plane and out-of-plane behaviour of the masonry walls and non-linear springs to simulate wall-to-wall and wall-to-diaphragm connections. As an unretrofitted case study, we model a building on a shake table, which developed large in-plane and out-of-plane displacements. We then simulate three retrofit interventions: Retrofitted diaphragms, connections, and diaphragms and connections. We show that strengthening the diaphragm alone is ineffective when the friction capacity of the wall-to-diaphragm connection is exceeded. This also means that modelling an unstrengthened wall-to-diaphragm connection as having infinite stiffness and strength leads to unrealistic box-type behaviour. This is particularly important if the equivalent frame model should capture both global in-plane and local out-of-plane failure modes.

Design and Analysis of an Aerostatic Pad Controlled by a Diaphragm Valve

Because of their distinctive characteristics, aerostatic bearings are particularly suitable for high-precision applications. However, because of the compressibility of the lubricant, this kind of bearing is characterized by low relative stiffness and poor damping. Compensation methods represent a valuable solution to these limitations. This paper presents a design procedure for passively compensated bearings controlled by diaphragm valves. Given a desired air gap height at which the system should work, the procedure makes it possible to maximize the stiffness of the bearing around this value. The designed bearings exhibit a quasi-static infinite stiffness for load variation ranging from 20% to almost 50% of the maximum load capacity of the bearing. Moreover, the influence of different parameters on the performance of the compensated pad is evaluated through a sensitivity analysis.

Evaluation of noise transfer path contributions using virtual springs with infinite stiffness

Transfer path analysis (TPA) is a process that can identify the priorities for a variety of possible paths from a noise and vibration source to an output. To reduce noise response, efficient transfer paths for the transmission and isolation of noise need to be identified. This study proposes a novel TPA method that is based on a dynamic substructuring model, which uses the frequency response function (FRF) information of a base system to evaluate the effect of increasing stiffness at the measurement points, without actually modifying the stiffness. In the proposed method, a spring with infinite stiffness is added to a specific transfer path among a variety of possible paths; this addition is tantamount to eliminating the specific path. Thus, the virtual spring helps to reduce the contribution of the specific path significantly. This method is easier to implement and is more applicable than existing TPA methods (i.e., classical TPA and operational TPA). This is because it does not require part removal or the correlation information among signals. To verify the feasibility of the FRF-based contribution analysis method, it was applied to a road noise phenomenon. The test results show that the proposed method can be applied to the TPA of suspension linkages and vehicle body.

Effect of interfacial stiffness on the stretchability of metal/elastomer bilayers under in-plane biaxial tension

Flexible electronic devices are often subjected to large and repeated deformation, so that their functional components such as metal interconnects need to sustain strains up to tens of percent, which is far beyond the intrinsic deformability of metal materials (~1%). To meet the stringent requirements of flexible electronics, metal/elastomer bilayers, a stretchable structure that consists of a metal film adhered to a stretchable elastomer substrate, have been developed to improve the stretch capability of metal interconnects. Previous studies have predicted that the metal/elastomer bilayers are much more stretchable than freestanding metal films. However, these investigations usually assume perfect bonding between the metal and elastomer layers. In this work, the effect of the metal/elastomer interface with a finite interfacial stiffness on the stretchability of bilayer structures is analyzed. The results show that the assumption of perfect interface (with infinite interfacial stiffness) may lead to an overestimation of the stretchability of bilayer structures. It is also demonstrated that increased adhesion between the metal and elastomer layers can enhance the stretchability of the metal layer.

Resonant periodic solutions in regularized impact oscillator

We use a perturbation approach to prove the occurrence of asymptotically stable periodic solutions in a bilinear oscillator whose one spring has nearly infinite stiffness. This leads to a singularly perturbed problem where the classical theory does not apply.

Contribution of FE and FFT-based methods to the determination of the effective elastic and conduction properties of composite media with flat inclusions and infinite contrast

Homogenization theory is increasingly applied to coupled phenomena, i.e. when different physical processes have to be modeled in order to correctly describe a system. The reason is that this methodology provides the means to propose a consistent morphological description of the system irrespective of the different phenomena involved, which is deemed to be physically sound. Here, we perform numerical simulations of both mechanical and transport processes in a linear context, so as to identify the best homogenization scheme out of five classical ones. The goal is to eventually apply the result to cracked rocks, which present complex structures, but this study is restricted to the case of parallel disks in an otherwise isotropic matrix. Since cracks in rocks present a vanishing stiffness but an infinite conductivity with respect to the rock, both types of contrast will be considered, and the reverse cases as well (infinite stiffness and vanishing conductivity) for the sake of completeness.After detailing the motivations behind this work, the theoretical background necessary to derive all the analytical estimates is laid down. The derivations given are somewhat improved over previously published ones, and the framework is extended to deal with vanishing as well as infinite contrast. The methodology is explained for the 3D numerical simulations, and the results are presented and discussed. Two different numerical strategies have been used: an FEM software and an FFT-based code. This allows to lessen potential biases of a particular method, and increases the credibility of the results. All in all, the differential scheme is identified as the best fit, which confirms the results of previous studies, but this time in several different cases.

Vibration frequencies and mode shapes of CCFF rectangular plates simply supported at the free corner. Application to large vibration amplitudes.

The linear flexural vibration of a thin isotropic rectangular plate simply supported at the free corner has been investigated by the symplectic superposition method by Rui.Li and al. The purpose of the present study was to establish the efficiency of the Rayleigh-Ritz method (RRM) applied to similar plate problems. Due to its numerical and systematic character, the RRM has many practical advantages compared to the classical laborious analytical approaches and can be extended to investigate the case of geometrically nonlinear vibrations. The trial plate functions used were obtained as products of beam functions with appropriate end conditions in each direction and the point support was modeled by a translational spring with an infinite stiffness. Different cases have been dealt with corresponding to different edge conditions, different aspect ratios, and for several modes. The comparisons made of the solutions obtained with the known solutions of isotropic rectangular plates with one or more point supports show a satisfactory agreement. The nonlinear vibration of various plates with a with point support at one corner have been also examined. The backbone curves based on the SMA have been calculated by Matlab code. The systematic and straightforward method presented can be readily extended to plates with inside point corners.

Development of a novel boring tool with anisotropic dynamic stiffness to avoid chatter vibration in cutting: Part 1: Design of anisotropic structure to attain infinite dynamic stiffness

This paper presents a novel design method of the anisotropic structure to attain infinite dynamic stiffness to avoid chatter vibration in boring operations. Because a long and slender tool is used for boring operations, the stiffness of the tool holder is likely to decrease, resulting in low chatter stability. Although it is difficult to improve the stiffness of the boring holder itself, the nominal dynamic stiffness for the cutting process can be improved by designing an appropriate anisotropy in the dynamic stiffness of the boring tool. In this study, we formulate a theoretical relationship between the mechanical structural dynamics and chatter stability in boring operation and present the basic concept of tool design with anisotropic structure. In the actual tool design, ideal anisotropy may not be realized because of the influence of design error. Therefore, an analytical study was conducted to clarify the influence of the design error on the vibration suppression effect. Analytical investigations verified that the similarity of the frequency response functions in the modal coordinate system and the design of the compliance ratio according to the machining conditions are important. Furthermore, we designed a boring tool with an anisotropic structure which can achieve the proposed anisotropic dynamics. The frequency response function was evaluated utilizing FEM analysis. The estimated anisotropic dynamics of the proposed structure could significantly improve the nominal dynamics for boring operations.

Improvement of the Performance-Based Seismic Design Method of Cable Supported Bridges with the Resilient-Friction Base Isolation Systems

In areas of civil engineering, the resilient friction base isolator (R-FBI) system has been used due to its enhanced isolation performance under seismic excitations. However, because nonlinear behavior of the R-FBI should be reflected in seismic design, effective stiffness (Keff) of the R-FBI is uniformly applied at both peak ground acceleration (PGA) of 0.08 g and 0.154 g which use a multimodal response spectrum (RS) method analysis. For rational seismic design of bridges, it should be required to evaluate the dynamics of the R-FBI from in-field tests and to improve the seismic design procedure based on the performance level of the bridges. The objective of this study is to evaluate the dynamics of the R-FBI and to suggest the performance-based seismic design method for cable-supported bridges with the R-FBI. From the comparison between the experiments’ results and modal shape analyses, the modal shape analyses using primary (Ku) or infinite stiffness (fixed end) showed a great agreement with the experimental results compared to the application of Keff in the shape analysis. Additionally, the RS or nonlinear time history method analyses by the PGA levels should be applied by reflecting the dynamic characteristics of the R-FBI for the reasonable and efficient seismic design.

Determination of Effective Damping of Elastic Mechanism Vibrations of Balanced Manipulator by Electric Drive

Research results of electric drive using capability determination are presented for vibrations damping of elastic mechanisms of ShBM-150M type manipulator. Symbolic expressions are listed for calculation of rational speed controller’s parameters in electric drive coordinates subordinate regulation system providing minimal vibration amplitude of torque in elastic transmission and executive mechanism speed. Comparison of effective damping of manipulator lift elastic vibrations was completed tuning motor speed controller with standard recommendation about infinite stiffness transmissions and rational controller’s parameters