Viscoelastic Spring Research Articles

Microstructural Simulations of Polymer Composites by a Viscoelastic Spring Lattice Model

AbstractAn improved viscoelastic spring lattice model is used to analyze the mechanical properties of polymer composites containing different microstructures, as exemplified by hydroxyl‐terminated polybutadiene‐based solid propellants. A drop‐on‐demand structural model is programmed using the C language to simulate the real solid propellant microstructure. The results show that increasing the particle content has a positive effect on the tensile strength of the propellant, but is detrimental to the ductility. The increase in particle size decreases the maximum tensile strength of the material, reflecting the importance of the dewetting process in the microstructure analysis. Finally, the model accurately predicts that initial defects have a destructive effect on the mechanical properties of the material.

COMPREHENSIVE ANALYSIS OF ENERGY DISSIPATION IN SOIL-EMBEDDED PILES: AN ANALYTICAL APPROACH

The study delves into a comprehensive examination of the total energy dissipation associated with a pile entrenched in the soil, with the soil being conceptualized as viscoelastic springs. "Dissipation" can be utilized to gauge the decay rate of displacement amplitude over time. Understanding dissipation in piles is pivotal for discerning the pace at which a pile achieves its equilibrium state when exposed to impact or free vibrations. Elevated dissipation levels indicate a swifter attenuation of transient vibrations, a crucial aspect for effective vibration mitigation during significant occurrences such as earthquakes, severe weather conditions, explosions, and impacts. The dispersion relation, reliant on wavenumber and free wave frequency, is derived for the pile-soil system using the Bloch's Floquet theorem. This relation is approached via the free-wave method, where a real wavenumber produces a sequence of complex frequencies. We propose an analytical closed-form expression in this study to forecast the overall dissipation from these complex frequency values. Additionally, we validate the accuracy of the predicted dissipation against a finite element-based numerical model of the soil-pile system. Furthermore, we examine the influence of factors such as material damping, Young's modulus, and shear modulus of the soil on the dissipation characteristics of the pile-soil system.

COMPREHENSIVE ANALYSIS OF ENERGY DISSIPATION IN SOIL-EMBEDDED PILES: AN ANALYTICAL APPROACH

The study delves into a comprehensive examination of the total energy dissipation associated with a pile entrenched in the soil, with the soil being conceptualized as viscoelastic springs. "Dissipation" can be utilized to gauge the decay rate of displacement amplitude over time. Understanding dissipation in piles is pivotal for discerning the pace at which a pile achieves its equilibrium state when exposed to impact or free vibrations. Elevated dissipation levels indicate a swifter attenuation of transient vibrations, a crucial aspect for effective vibration mitigation during significant occurrences such as earthquakes, severe weather conditions, explosions, and impacts. The dispersion relation, reliant on wavenumber and free wave frequency, is derived for the pile-soil system using the Bloch's Floquet theorem. This relation is approached via the free-wave method, where a real wavenumber produces a sequence of complex frequencies. We propose an analytical closed-form expression in this study to forecast the overall dissipation from these complex frequency values. Additionally, we validate the accuracy of the predicted dissipation against a finite element-based numerical model of the soil-pile system. Furthermore, we examine the influence of factors such as material damping, Young's modulus, and shear modulus of the soil on the dissipation characteristics of the pile-soil system.

Eric Ungar and vibration damping

This presentation honors Eric Ungar’s contributions to vibration damping. The classic paper titled “Loss Factors of Viscoelastic Systems in Terms of Energy Concepts,” which he co-authored with Edward Kerwin in 1962, takes center stage. Two significant contributions of the paper deserve detailed discussion. The first is the time dependence of total energy for viscoelastic systems with added mass, which results in ambiguous loss factor definitions off resonance. The second and most important contribution is an equation for the loss factor of a network of ideal viscoelastic springs. This equation reveals that the system loss factor is a weighted average of the loss factors of the viscoelastic springs, where the weights are the total energies in the viscoelastic springs. Next, the value of this work is illustrated by some recent work inspired by the 1962 paper. This recent work, which was published 60 years after the 1962 paper, involves the calculation of loss factors from finite element models of complex structures with viscoelastic elements. The presentation concludes with recollections that celebrate Eric Ungar’s talent in educating and inspiring generations of engineers and researchers. [Work supported by ONR under Grant N00014-22-1-2785.]

Optimal multiple tuned mass dampers for monopile supported offshore wind turbines using Genetic Algorithm

This study investigates the parametric optimization of multiple-tuned mass dampers (MTMDs) deployed along the length of a tower and monopile structure subjected to stochastic wind and wave forces. The structural components, comprising the tower and monopile, are conceptualized as Euler–Bernoulli beams. The interaction with the soil is modeled through viscoelastic springs distributed along the monopile. The rotor nacelle assembly (RNA) and blades are abstracted into a concentrated mass at the tower’s apex. The MTMDs are characterized as spring–mass–dashpot systems strategically positioned at intervals along the tower and monopile. The investigation involves a random vibration analysis under wind and wave loads, employing the Kaimal spectrum for wind and the JONSWAP spectrum for waves. The study focuses on optimizing the TMD parameters using H2 optimization techniques, with the optimization criteria being the minimization of the standard deviation of the tower’s top displacement response. Additionally, meta-heuristic algorithms like the genetic algorithm (GA) are utilized to refine the determination of these optimal parameters. A key aspect of the research includes a parametric study that reveals variations in optimal parameters as the number of TMDs is altered, maintaining a consistent total mass across the MTMDs.

Nonlinear elasticity and short-range mechanical coupling govern the rate and symmetry of mouth opening in Hydra.

Hydra has a tubular bilayered epithelial body column with a dome-shaped head on one end and a foot on the other. Hydra lacks a permanent mouth: its head epithelium is sealed. Upon neuronal activation, a mouth opens at the apex of the head which can exceed the body column diameter in seconds, allowing Hydra to ingest prey larger than itself. While the kinematics of mouth opening are well characterized, the underlying mechanism is unknown. We show that Hydra mouth opening is generated by independent local contractions that require tissue-level coordination. We model the head epithelium as an active viscoelastic nonlinear spring network. The model reproduces the size, timescale and symmetry of mouth opening. It shows that radial contractions, travelling inwards from the outer boundary of the head, pull the mouth open. Nonlinear elasticity makes mouth opening larger and faster, contrary to expectations. The model correctly predicts changes in mouth shape in response to external forces. By generating innervated : nerve-free chimera in experiments and simulations, we show that nearest-neighbour mechanical signalling suffices to coordinate mouth opening. Hydra mouth opening shows that in the absence of long-range chemical or neuronal signals, short-range mechanical coupling is sufficient to produce long-range order in tissue deformations.

Simulation of mechanical properties of HTPB‐based propellant by a viscoelastic spring lattice model

AbstractAn improved lattice spring model extended by viscoelastic part using the Maxwell model was applied to predict the mechanical properties of HTPB‐based solid propellants. The influence of both strain rate and temperature on the maximum elongation of HTPB‐based propellants was quantitatively analyzed by simulating the uniaxial tensile test, as well as the process of crack development during tensile loads. The results show that the maximum elongation of HTPB‐based propellant decreases as a power function along with the linear increase of strain rate. In contrast, the maximum stress increases as a power function. Increasing the temperature linearly, both the maximum stress and the maximum elongation decrease as a power function.

Estimation of the dissipation due to radiation damping for the pile embedded in soil: A closed-form solution

In the present work, the overall energy dissipation of a pile embedded in the soil, modeled as visco-elastic springs, is thoroughly investigated. The term dissipation is used to measure the rate of decay of amplitude of displacement response in the time domain. The estimation of dissipation in piles is necessary to understand how quickly a pile reaches its steady state or equilibrium under dynamic loads or in cases of free vibration, respectively. A higher level of dissipation indicates a shorter duration of transient vibration, which is a deserving trait for vibration mitigation in extreme events, such as earthquakes, storms, blasts, shocks, etc. The dispersion relation which is a function of wavenumber and free wave frequency is obtained for the pile embedded in the soil medium by implementing the generalized form of Bloch’s theorem. The dispersion relationship is solved in the free-wave approach, in which a real wave number yields a set of complex frequencies. For predicting the overall dissipation of the system from the complex frequency values, an analytical closed-form expression is proposed in this paper. Further, the predicted dissipation is validated with a finite element-based numerical model of the soil–pile system.

A generalized Duffing equation with the Coulomb’s friction law and Signorini–type contact conditions

This work provides mathematical and numerical analyses for a spring–mass system, in which Signorini–type contact conditions and Coulomb’s friction law with thermal effects are taken into consideration. The motion of a mass attached to a viscoelastic (Kelvin–Voigt type) nonlinear spring is described by a generalized Duffing equation. Signorini contact conditions are understood as extended complementarity conditions (CCs), where convolution is incorporated, allowing to consider thermal aspects of an obstacle. We prove the existence of global weak solutions for the highly nonlinear differential equation system with all the conditions, based on the regularized differential equation and the normal compliance condition with the standard mollifier. In addition, we investigate what side effects produce higher singularities of contact forces in dynamic contact problems, which is also supported by numerical evidences. Numerical schemes are proposed and then several groups of data are selected for the display of our numerical simulations.

Nonlinear viscoelastic damping in a Poynting oscillator

This work considers a cylindrical rod, acting as a nonlinear viscoelastic spring, with an attached mass that can displace along and rotate about the rod’s axis, thereby inducing an extension and twist in the rod. The coupling between them produces the Poynting effect in the body. The material is modeled by the nonlinear single integral Pipkin–Rogers constitutive equation. The mass has been assumed to be at rest in a long-time equilibrium state and then given a small axial or rotational disturbance and released (plucked). The subsequent motion is governed by a linear Volterra integro-differential equation. For a particular choice of material parameters, analytical expressions for the time-dependent decay of the disturbance are obtained in terms of the extension/torsion coupling, material stiffness, the amount and rate of stress relaxation, and the inertia of the mass. For other choices of material parameters, the results provide insight into how these quantities affect the time-dependent decay. A number of plucking scenarios are treated such as extensional or rotational disturbances from the undeformed state, rotational plucking after a finite axial stretch, and extensional plucking after a finite rotation. Simultaneous rotational and extensional plucking leads to a system of Volterra integro-differential equations whose treatment is deferred to later work.

Spectral element formulation for rock-socketed mono-pile under horizontal dynamic loads

The current study entails a thorough investigation of the dynamic response of a mono-pile foundation in homogeneous soil and varied layered soil–rock conditions under horizontal dynamic loads. A sequence of visco-elastic springs linked along its length represents the mono-pile immersed in elastic half space. The frequency dependent stiffness and damping of a mono-pile foundation embedded in layered elastic half space are developed using spectral element formulation. The variations in stiffness and damping with frequency for various soil–rock systems are demonstrated. The dynamic response characteristics of the pile were found to be influenced by the depth of the rock-socketed pile. The presence of the underlying layer of stiffer layer of rock enhances the overall stiffness of the system. The frequency versus amplitude responses of a mono-pile supported heavy mass block for both horizontal translation and rocking motion are calculated using the stiffness and damping of the mono-pile under various soil rock conditions. The horizontal amplitude of the pile decreases with increasing pile rock socketing depth. The resonant amplitudes for rocking motion increases as the pile’s rock socketing depth increases. Finally, the changes in natural frequency and peak amplitudes with varied pile slenderness ratios are investigated for diverse pile–soil–rock conditions.

Semi-analytical approach for nondestructive test for offshore pipe piles considering soil-pile slippage induced by heavy hammer impact

For the offshore large dimension piles, heavy hammer impact is often utilized as the input of the incident wave of the low strain integrity test, making the slippage at the soil-pile interface inevitable. Also, the significant soil plug effect and the transverse inertia effect associated with the large dimension pipe piles bring severe challenges to the test signal processing. To facilitate signal interpretation, this paper establishes a rigorous saturated seabed-pipe pile-soil plug mathematical model, pioneering the coupling analysis of the soil plug, transverse inertia, and the soil-pile slippage effects, which usually occur simultaneously for offshore pile testings. The soil-pile slippage is realized through distributed linear viscoelastic springs and dashpots. The main findings can be summarized as: 1. The increase of the strength (both stiffness and damping) at the soil-pile interfaces would decrease the amplitudes of the reflected signal. 2. The increases in the wall thickness and the Poisson's ratio of the pile both increase the wave oscillation after the reflected signals. 3. As the degree or the length of the defect increases, the amplitude of the reflected signal of the corresponding defect would increase, whereas the amplitude of the reflected signal at the pile bottom would decrease in the opposite.

Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Analytical description of vibration loads of the complex construction structure is considered as a system of masses connected by means of viscoelastic springs. To take into account the rheological properties of the spring material, the Boltzmann-Volterra principle is used. A mathematical model of the problem under consideration has been developed, which boils down to the solution of a system of nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis. The results are shown as graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Considering the transverse crack as a massless viscoelastic rotational spring, the equivalent stiffness of the viscoelastic cracked beam is derived by Laplace transform and the generalized Dirac delta function. Using the standard linear solid constitutive equation and the inverse Laplace transform, the analytical expressions of the deflection and rotation angle of the viscoelastic Timoshenko beam with an arbitrary number of open cracks are obtained in the time domain. By numerical examples, the bending results of the analytical expressions are verified with those of the FEM program. Additionally, the effects of the time, slenderness ratio, and crack depth on the bending deformations of the different cracked beam models are revealed.

Analysis of parametric instability of a spring-attached pre-twisted beam with viscoelastic end support

This study investigated the parametric instability of a single elastic beam with spring attachment on the top and viscoelastic springs as end supports. The beam considered is pre-twisted with a pin connection at both ends that supports the beam. The analytical solution of the problem is expressed in the matrix form achieved from the implementation of Hamilton’s principle and General Galerkin’s method, from which both static and dynamic stability of the beam can be investigated. The results of various influential dimensionless parameters such as stiffness, mass, length, position of the spring attachment, and stiffness of the viscoelastic springs on both the stabilities are studied. This analysis concluded that the spring attachment on the system leads to substantial contribution in improving the stability. The viscoelastic springs also contribute in upsurging the beam’s stability. Three different profiles of the beam have been considered, and for each profile, three different types of springs have been examined. The results revealed that the beam with parabolic profile and stiffness of the spring attachment with parabolic variation is most effective towards strength-to-weight ratio.

Visco-elastic contact spring in numerical simulations of train – track system vibrations

Abstract: In train – track coupled systems, interaction between subsystems occurs in wheel- rail contact. The most common contact model is perfectly elastic, linearized Hert’z spring. It has wide range of application in numerical simulations. In more detailed interaction models, the energy dissipation in wheel-rail contact is taken into account. There are no known comparisons of these models in the literature, that would indicate the effects of a specific solution application. In this paper, the main purpose is to analyze and compare the effects of two contact models in terms of numerical simulations of train – track vibrations. The reference contact model taken into account is linearized, perfectly elastic Hert’z spring. The second spring, proposed by the authors is enriched with viscous element based on hysteresis damping. Application of both models, and its effects were examined in plane, train – track vibrations simulations with threshold inequality excitation in the middle of the track length. Concluding from the analyzes performed, it was found that viscoelastic contact model application is important, when track stresses and fatigue are being investigated. In addition, it was found that neglecting the damping element in contact model reduces the probability of the wheel – rail contact loss phenomenon, and thus leads to incorrect identification of its occurrence. Keywords: Wheel/rail contact; Hertz contact; Linearized contact spring; Train/track dynamics

Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support

This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.

Bioinspired 3D helical fibers toughened thermosetting composites

Thanks to the special helical structure, natural composites such as shell, wood, and bone have remarkable toughness, strength and damage tolerance. Herein, a bioinspired spiral nylon monofilament/epoxy composite is developed, which is a representative example of helical fiber/thermosetting composites. The relationship between toughness and strength of composites was studied by controlling parameters of the helical fibers. As a result, the impact resistance is regularly increased by the increase of pitch and the decrease of helix fiber angle. With a single-layer addition, the impact toughness of composites is increased by 150% without decreasing the mechanical strength and that is increased by 450% in the case of three-layer addition. The proposed toughening mechanism was verified by finite element analysis and dynamic mechanical analysis, which including 3D stress dispersion, the interlocking fibrous building interface, and energy absorption capacity of viscoelastic spring polymer. Furthermore, the toughness and strength of the composites is improved by 310% in single layer via surface modification of spiral fibers. The introduction of the three-dimensional spiral structure into the composite is demonstrated to be a unique strategy to overcome the trade-off between toughness and strength of high-performance composite materials.

Generalised viscoelastic fibre at small strain

A straight elastic fibre is usually perceived as a one-dimensional structural component, and its similarity with a cylindrical rod makes its concept analogous, if not equivalent with the concept of an elastic spring. This analogy enables this communication to match the one-dimensional response of a relevant viscoelastic fibre with that of a viscoelastic spring and, hence, to describe its one-dimensional behaviour in the light of a new, generalised viscoelastic spring model. The model shares simultaneously properties of an elastic spring and an inelastic damper (dashpot) and this communication is interested on its applicability at small strain only. However, the form of its constitutive equation, which is based on the combined action of an internal energy function and a viscous flow potential, is non-linear as well as differential and, also, implicit in the stress. The model enables a posteriori determination of (i) the manner that the elastic and the inelastic parts of the fibre strain are assembled and form the observed total deformation, (ii) the part of stress that creates recoverable work and the part of stress wasted in energy dissipation, and (iii) the amount of work stored in the material as well as the amount of energy dissipation during the fibre deformation. A detailed analysis is presented for the case that small-strain, steady viscoelastic deformation takes place in a spatially homogeneous manner. This includes a complete relevant solution of the problem of interest and is accompanied by an adequate set of corresponding qualitative numerical results.

Exploration of the Structure–Property Relationship of Polymer‐Based Composites by Monte‐Carlo‐Coupled Viscoelastic Lattice Spring Model

AbstractA viscoelastic lattice spring model is applied to real polymer blend containing strong interaction, i.e., chemical bond, to investigate the structure–property correlation in combination of Monte Carlo method modified by cavity diffusion and bond length fluctuation algorithms. Impacts of inclusion ratio, chemical bonds, chain length, and interface orientation on the mechanical response along with fracture mode are quantified through simulation of uniaxial tensile test. It is confirmed that introduction of strong interaction and prolongation in chain length induces observable reinforcement in global modulus and ultimate tensile strength, respectively, and the amplification is more significant when the interface is parallel to external load.