Viscoelastic Supports Research Articles

Simulated inter-filament fusion in embedded 3D printing.

In embedded 3D printing (EMB3D), a nozzle extrudes continuous filaments inside of a viscoelastic support bath. Compared to other extrusion processes, EMB3D enables softer structures and print paths that conform better to the shape of the part, allowing for complex structures such as tissues and organs. However, strategies for high-quality dimensional accuracy and mechanical properties remain undocumented in EMB3D. This work uses computational fluid dynamics simulations in OpenFOAM to probe the underlying physics behind two processes: deformation of the printed part due to nearby nozzle motion and fusion between neighboring filaments during printing. Through simulations, we disentangle yielding from viscous dissipation, and we isolate interfacial tension effects from rheology effects, which are difficult to separate in experiments. Critically, these simulations find that disturbance and fusion are controlled by the flow of support fluid around the nozzle. To avoid part deformation, the nozzle must remain far from existing parts during non-printing moves, moreso when traveling next to the part than above the part and especially when the interfacial tension between the ink and support is non-zero. Additionally, because support can become trapped between filaments at zero interfacial tension, the spacing between filaments must be tight enough to produce over-printing, or printing too much material for the designed space. In non-Newtonian fluids, spacings for vertical walls must be even tighter than spacings for horizontal planes. At these spacings, printing a new filament sometimes creates and sometimes mitigates shape defects in the old filament. While non-zero ink-support interfacial tensions produce better inter-filament fusion than zero interfacial tension, interfacial tension also produces shape defects. Slicing algorithms that consider these unique EMB3D defects are needed to improve mechanical properties and dimensional accuracy of bioprinted constructs.

Viscoelastic-Support-Layer-Based Macroscopic Conformal Transfer of van der Waals Materials Compatible with Plasmonic Application.

This study showcases the conformal geometries of van der Waals materials with metallic structures utilizing viscoelastic support layers. Mechanically exfoliated nanometer-thick graphite flakes were transferred onto metal structures with various side slopes using two different polymers: polycarbonate (PC) and polyethylene (PE). We proposed a morphology-based evaluation of the macroscale conformity that can contribute to the selection of a proper support layer. Although both support layers ensured high conformity on the sloped side, the PE layer offered superior conformity on the vertical metal structure. To further investigate the impact of conformal structures, we compared the terahertz transmission changes of a metal bowtie antenna before and after transferring graphite onto the bowtie gap for two distinct conformal structures. The conformity of graphite to the metal gap structure significantly influenced the optical response in the terahertz frequency regime. This suggests that the conformal structuring technique can be leveraged in various terahertz devices composed of metals and van der Waals materials, opening avenues for quantitative analysis in light-matter interactions.

Analytical Solution for Dynamic Response of a Reinforced Concrete Beam with Viscoelastic Bearings Subjected to Moving Loads.

To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam.

Assessment of the Compound Damping of a System with Parallelly Coupled Anti-Seismic Devices

(1) Background: Romanian earthquakes caused severe damage over time to a significant number of constructions, and that is why efforts are being made to make structural systems safer. (2) Methods: For structural systems with protection against seismic actions or vibrational actions that have linear viscous dissipation devices, the requirement to assess the equivalent modal damping rate for the entire functional assembly related to the other dynamic parameters arises. (3) Results: This article presents the analytical development of formulas for the compound damping and circular frequency when anti-seismic devices have different dynamic characteristics and their application in order to solve some real engineering cases of bridges and viaducts in Romania with distinct viscoelastic supports. In support of this idea, some experimental tests on a beam system resting on two different anti-seismic elastic supports highlighted the fact that the compound damping of the system can be calculated with the relations established in this paper, provided that the displacements in the horizontal direction of excitation are in the linear domain. Also, we determined the seismic response considering the Vrancea 1977 accelerogram for critical damping ratios of 5% and 18.5%, and then we obtained the variation in the factor of transmissibility depending on the frequency, in order to highlight the optimized value of the equivalent amortization/damping. (4) Conclusions: In the specific context of Romanian seismicity, seismic isolation through the use of isolators with different characteristics represents an optimal technical solution, and it is also optimal from an economic point of view, with an appropriate level of dynamic isolation obtained.

Lift modeling, load and vibration analysis of Magnus rotors

The method of theoretical combined with numerical simulation is employed to study the lift model and the optimal position of viscoelastic supports for the rotating cylindrical sail (short for Magnus rotor or rotor sail). Initially, using a numerical simulation method to modify the Magnus rotor lift model established based on the Kutta-Joukowski theory obtained a lift/drag model for the rotor. Subsequently, the lift/drag model is utilized as an external load, considering the rotor as a rotating cantilever beam with fixed support at one end. The finite element method is employed to study the vibration characteristics of the drive shaft under external excitation, analyzing the deflection characteristics of the cantilever beam, the stiffness of elastic support, and the span variation on the vibration characteristics of the drive shaft for different cross-sectional radii. Finally, for the investigated large-scale Magnus rotor, a modified lift model and the optimal design position for viscoelastic supports and the dimensions of the drive shaft are provided. Simulation results demonstrate that by appropriately adding viscoelastic supports to the structure, the vibrational deflection of the drive shaft's steady-state response can be significantly suppressed.

Experimental Analysis of an Optimal Designed Multi-DOF Viscoelastic Support for Passive Vibration Control in Rotor Dynamics

Experimental Analysis of an Optimal Designed Multi-DOF Viscoelastic Support for Passive Vibration Control in Rotor Dynamics

The effect of the viscoelastic support and GRPL-reinforced foam material on the thermomechanical vibration response of piezomagnetic sandwich nanosensor plates

This paper investigates the vibration characteristics of a sandwich nanosensor plate composed of piezoelectric materials, specifically barium and cobalt, in the upper and lower layers, and a core material consisting of either ceramic (silicon nitride) or metal (stainless steel) foams reinforced with graphene (GPRL). The study utilized the novel sinosoidal higher-order deformation theory and nonlocal strain gradient elasticity theory. The equations of motion for nanosensor sandwich graphene were derived using Hamilton's principle, considering the thermal, electroelastic, and magnetostrictive characteristics of the piezomagnetic surface plates. These equations were then solved using the Navier method. The core element of the sandwich nanosensor plate can be represented using three distinct foam variants: a uniform foam model, as well as two symmetric foam models. The investigation focused on analyzing the dimensionless fundamental natural frequencies of the sandwich nanosensor plate. This analysis considered the influence of three distinct foam types, the volumetric graphene ratio, temperature variation, nonlocal parameters, porosity ratio, electric and magnetic potential, as well as spring and shear viscoelastic support. Furthermore, an analysis was conducted on the impact of the metal and ceramic composition of the central section of the sandwich nanosensor plate on its dimensionless fundamental natural frequencies. In this context, the use of ceramic as the central material results in a mean enhancement of 33% in the fundamental natural frequencies. In contrast, the incorporation of graphene into the core material results in an average enhancement of 27%. The thermomechanical vibration behavior of the nanosensor plate reveals that the presence of graphene-supported foam and a viscoelastic support structure in the core layer leads to an increase in thermal resistance. This increase is dependent on factors such as the ratio of graphene, porosity ratio of the foam, and parameters of the viscoelastic support. Metal foam or ceramic foam has been found to enhance thermal resistance when compared to solid metal or ceramic core materials. The analysis results showed that it is important to take into account the temperature-dependent thermal properties of barium and cobalt, which are piezo-electromagnetic materials, and the core layer materials ceramics and metal, as well as the graphene used to strengthen the core. The research is anticipated to generate valuable findings regarding the advancement and utilization of nanosensors, transducers, and nano-electromechanical systems engineered for operation in high-temperature environments.

DESIGN OF VISCO-ELASTIC SUPPORTS FOR TIMOSHENKO CANTILEVER BEAMS

The appropriate design of supports, upon which beams are usually placed as structural components in many engineering scenarios, has substantial significance in terms of both structural efficacy and cost factors. When beams experience various dynamic vibration effects, it is crucial to contemplate appropriate support systems that will effectively adapt to these vibrations. The present work investigates the most suitable support configuration for a cantilever beam, including viscoelastic supports across different vibration modes. Within this particular framework, a cantilever beam is simulated using beam finite elements. The beam is positioned on viscoelastic supports, which are represented by simple springs and damping elements. These supports are then included in the overall structural model. The equation of motion for the beam is first formulated in the temporal domain and then converted to the frequency domain via the use of the Fourier Transform. The basic equations used in the frequency domain are utilized to establish the dynamic characteristics of the beam by means of transfer functions. The determination of the ideal stiffness and damping coefficients of the viscoelastic components is achieved by minimizing the absolute acceleration at the free end of the beam. In order to minimize the objective function associated with acceleration, the nonlinear equations derived from Lagrange multipliers are solved using a gradient-based technique. The governing equations of the approach need partial derivatives with respect to design variables. Consequently, analytical derivative equations are formulated for both the stiffness and damping parameters. The present work introduces a concurrent optimization approach for both stiffness and damping. Passive constraints are established inside the optimization problem to impose restrictions on the lower and higher boundaries of the stiffness and damping coefficients. On the other hand, active constraints are used to ascertain the specific values of the overall stiffness and damping coefficients. The efficacy of the established approach in estimating the ideal spring and damping coefficients of viscoelastic supports and its ability to provide optimal support solutions for various vibration modes have been shown via comparative experiments with prior research.

Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic Finite Element Method.

The present work's main objective is to investigate the natural vibrations of the thin (Kirchhoff-Love) plate resting on time-fractional viscoelastic supports in terms of the Stochastic Finite Element Method (SFEM). The behavior of the supports is described by the fractional order derivatives of the Riemann-Liouville type. The subspace iteration method, in conjunction with the continuation method, is used as a tool to solve the non-linear eigenproblem. A deterministic core for solving structural eigenvibrations is the Finite Element Method. The probabilistic analysis includes the Monte-Carlo simulation and the semi-analytical approach, as well as the iterative generalized stochastic perturbation method. Probabilistic structural response in the form of up to the second-order characteristics is investigated numerically in addition to the input uncertainty level. Finally, the probabilistic relative entropy and the safety measure are estimated. The presented investigations can be applied to the dynamics of foundation plates resting on viscoelastic soil.

Stochastic nonlinear eigenvibrations of thin elastic plates resting on time-fractional viscoelastic supports

– The main objective of this work is to investigate natural vibrations of the thin (Kirchhoff-Love) plate resting on time-fractional viscoelastic supports using the Stochastic Finite Element Method (SFEM). The mechanical behavior of the supports is deterministic and is described by the fractional order derivatives of the Riemann-Liouville type. A subspace iteration method in conjunction with the continuation method is the basis of the numerical solution carried out using the displacement formulation of the Finite Element Method. The probabilistic analysis includes independent Monte-Carlo simulation, the semi-analytical approach, and the iterative generalized stochastic perturbation method of the first two probabilistic moments. Moreover, a corresponding relative entropy and the entropy-based reliability index are contrasted with the First Order Reliability Method (FORM). It has been found that the relative entropy for analyzed eigen-vibrations is some interesting alternative to the FORM methodology in reliability assessment.

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

The frequency parameters of an Axially Functionally Graded (AFG) bar for viscoelastic and point mass boundary conditions are studied in this paper. The structures with functionally graded materials under axial loads can be modelled as AFG bars. Those may be considered as support elements with spring and dashpot in the vibration isolation. Keeping the ratio of force frequency and natural frequency at a certain level is ensured to control the natural frequency therefore dynamic amplification factor with different material combinations. Various boundary conditions are attained by changing the spring and damping coefficients of viscoelastic support elements and the ratio of rod mass to tip mass. Researchers assume that the beam material properties in directions of length and thickness change exponentially, individually, or both in their studies. There are a few studies on the AFG rods in the existing studies. Analysis is carried out via the finite element method for the non-dimensional frequency parameters of the bar in MATLAB. The energy equations of the motion are obtained in the frame of axial bar theory considering the material properties of the bar vary longitudinally according to the power-law distribution. The effects of material distribution, spring, damping and tip mass values on the bar's frequency parameters and structural behaviour have been extensively investigated.

Dynamic damping of vibrations of a solid body mounted on viscoelastic supports

The study of the problem of damping vibrations of a solid body mounted on viscoelastic supports is an urgent task. The paper considers the problem of reducing the level of vibrations on the paws of electric machines using dynamic vibration dampers. For this purpose, the paw of electric machines is represented in the form of a subamortized solid body with six degrees of freedom mounted on viscoelastic supports. The aim of the work is to develop calculation methods and algorithms for studying the oscillations of the resonant amplitudes of a solid body mounted on viscoelastic supports. Dynamic oscillation (vibration) damping method consists in attaching a system to the protected object, the reactions of which reduce the scope of vibration of the object at the points of attachment of this system. Applying the D’Alembert principle, the equations of small vibrations of a solid with dampers are derived. For practical calculations, a simplified system of equations was obtained that takes into account only three degrees of freedom. Numerical calculations were carried out on a computer to determine the amplitude-frequency characteristics of the main body. Numerical experiments were carried out using the Matlab mathematical package. Considering that a solid body is characterized by vibration, as a rule, in a continuous and wide frequency range, therefore, dynamic vibration dampers are used to protect a solid body mounted on viscoelastic supports. It was found that when the damper is set at a frequency of 50 Hz, the vibration level at the left end of the frequency interval of rotary motion of the rotor-converter, decreases to 37.5 dB, and at the right end — to 42.5 dB. At a frequency of 50 Hz, the paws do not oscillate. When setting the dampers to a frequency of 51.5 Hz, the maximum vibration level does not exceed 40 dB. The optimal setting of the dampers is within the frequency of 50.60...50.70 Hz, and a two-mass extinguisher is 10–15% more efficient than a single-mass one. Thus, the paper sets the tasks of dynamic damping of vibrations of a solid body mounted on viscoelastic supports, develops solution methods and an algorithm for determining the dynamic state of a solid body with passive vibration of the object in question.

Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam

Non-stationary loading of a mechanical system consisting of a hinged beam and additional support installed in the beam span was studied using a model of the beam deformation based on the Timoshenko hypothesis with considering rotatory inertia and shear. The system of partial differential equations describing the beam deformation was solved by expanding the unknown functions in the Fourier series with subsequent application of the integral Laplace transform. The additional support was assumed to be realistic rather than rigid. Thus it has linearly elastic, viscous, and inertial components. This means that the effect of a part of the support vibrating with the beam was considered such that their displacements coincide. The beam and additional support reaction were replaced by an unknown concentrated external force applied to the beam. This unknown reaction was assumed to be time-dependent. The time law was determined by solving the first kind of Volterra integral equation. The methodology of deriving the integral equation for the unknown reaction was explained. Analytic formulae and results of computations for specific numerical parameters were given. The impact of the mass value on the additional viscoelastic support reaction and the beam deflection at arbitrary points were determined. The research results of this paper can be helpful for engineers in designing multi-span bridges.

Compromised Cranio-Spinal Suspension in Chiari Malformation Type 1: A Potential Role as Secondary Pathophysiology.

In Chiari Malformation Type I (CM1), low-lying tonsils obstruct the cisterna magna at the foramen magnum, thereby compromising the essential juncture between the cranial and spinal compartments. The anatomical obstruction of the cisterna magna inhibits bi-directional CSF flow as well as CSF pulse pressure equilibration between the intracranial compartment and the intraspinal compartment in response to instances of increased intracranial pressure. Less understood, however, are the roles of the spinal cord suspension structures at the craniocervical junction which lend viscoelastic support to the spinal cord and tonsils, as well as maintain the anatomical integrity of the cisterna magna and the dura. These include extradural ligaments including the myodural bridges (MDBs), as well as intradural dentate ligaments and the arachnoid framework. We propose that when these elements are disrupted by the cisterna magna obstruction, tonsillar pathology, and altered CSF dynamics, there may arise a secondary pathophysiology of compromised and dysfunctional cranio-spinal suspension in CM1. We present intraoperative images and videos captured during surgical exposure of the craniocervical junction in CM1 to illustrate this proposal.

Determining experimentally the patterns of the manifestation of the Sommerfeld effect in a ball auto-balancer

This paper proposes an experimental method for studying the Sommerfeld effect in auto-balancers or exciters of resonant vibrations of pendulum, ball, or roller type. The method is based on the processing of signals acquired from analog sensors of rotations and vibration acceleration using regression analysis. The method is tested on a specially designed rotor bench on isotropic viscoelastic supports, which executes spatial motion, and an auto-balancer with one ball. Checking the accuracy of the method using stroboscopic lighting demonstrates the accuracy of determining the speed of rotation of the rotor, ball, oscillation frequency of the rotor, etc. with an error of several hundredths of a percent. When fixing the ball relative to the rotor, a classic inertial vibration exciter is obtained. The rotor has two resonant velocities. The Sommerfeld effect is almost not manifested. With a gradual increase in the frequency of the current, the rotor speed increases monotonously. There is no significant slip or jump in the rotor speed. There are two distinct peaks on the amplitude-frequency characteristic. Therefore, such a vibration exciter is not suitable for the excitation of resonant vibrations. With the free placement of the ball in the oil, the behavior of the system changes significantly in the vicinity of the first resonant velocity. The first narrow resonant peak disappears in the roto. Instead, there is a long, gentle resonant rise. It lasts at a current frequency of 9.4 Hz to 19.3 Hz. The amplitude at the reference point on the resonant rise increases from 0.7 mm to 2.84 mm. Therefore, by changing the frequency of the current, it is possible to smoothly change the amplitude of the rotor oscillations by almost 4 times. The maximum amplitude of rotor oscillations is the same as at the first resonance with a fixed ball. Due to the gentleness of the resonant rise, a freely installed ball itself is a reliable exciter of resonant vibrations

Experimental Study on Magnetic Resonant Coupling AC Magnetic Suspension Considering Electrical Power Transmission

A three-degree-of-freedom AC magnetic suspension system using magnetic resonant coupling was fabricated. The AC magnetic suspension system can produce restoring force without active control. This system is dynamically stabilized by adding indirect damping, which is produced by suspending to the stator with viscoelastic support mechanisms. A non-contact electrical power transmission is achieved simultaneously by magnetic resonant coupling. The structure of magnetic resonant coupling is similar to the structure of the transformer. The magnetic flux path for suspension is combined with that of electrical power transmission. The electric characteristics of the transformer depend on the resistance of a load connecting the secondary circuit. The measured results indicate that the driving frequency needs to be adjusted to achieve stable suspension in relation to the resistance of the load. These characteristics are confirmed experimentally.

Effect of two-parameter partial foundation and viscoelastic supports on free vibration of Terfenol-D layered functionally graded fluid conveying pipe using domain decomposition technique

The purpose of the current research work is to investigate the free vibration control characteristics of a Terfenol-D layered functionally graded fluid-conveying pipe when subjected to partial two-parameter foundation, viscoelastic supports, and multi-span length. The integration of differential quadrature method with domain decomposition and the δ point approach, as well as Terfenol-D layer actuation with viscoelastic supports, distinguishes the current study effort. The equivalent spring stiffness for the two-parameter partial foundation is determined methodically for various elastic soil materials. The effect of varied spans with viscoelastic supports on the stability of fluid conveying pipes is also explored.

Suppression of Filament Defects in Embedded 3D Printing

Embedded 3D printing enables the manufacture of soft, intricate structures. In the technique, a nozzle is embedded into a viscoelastic support bath and extrudes filaments or droplets. While embedded 3D printing expands the printable materials space to low-viscosity fluids, it also presents new challenges. Filament cross-sections can be tall and narrow, have sharp edges, and have rough surfaces. Filaments can also rupture or contract due to capillarity, harming print fidelity. Through digital image analysis of in situ videos of the printing process and images of filaments just after printing, we probe the effects of ink and support rheology, print speeds, and interfacial tension on defects in individual filaments. Using model materials, we determine that if both the ink and support are water-based, the local viscosity ratio near the nozzle controls the filament shape. If the ink is slightly more viscous than the support, a round, smooth filament is produced. If the ink is oil-based and the support is water-based, the capillary number, or the product of the ink speed and support viscosity divided by the interfacial tension, controls the filament shape. To suppress contraction and rupture, the capillary number should be high, even though this leads to trade-offs in roughness and roundness. Still, inks at nonzero interfacial tension can be advantageous, since they lead to much rounder and smoother filaments than inks at zero interfacial tension with equivalent viscosity ratios.

Selection and research of stability of the steady state motions of a single-mass resonance vibromating machine working on the Somerfeld effect

This paper has defined and investigated for stability the steady state modes of motion of a single-mass resonant vibratory machine. The vibratory machine has a platform that is supported by viscoelastic supports. The platform moves rectilinearly translationally. A vibration exciter is installed on the platform. The vibration exciter consists of N identical loads – balls, rollers, or pendulums. The center of mass of each load can move in a circle of a certain radius with a center on the longitudinal axis of the rotor. Each load, when moving relative to the body of the vibration exciter, is exposed to a viscous resistance force. It was established theoretically that with small forces of viscous resistance and any number of loads, the vibratory machine has jamming modes under which the loads that are collected form a conditional combined load and lag behind the rotor. In this case, there are two bifurcation speeds of the rotor. At speeds less than the first bifurcation speed, the vibratory machine has one single (first) jamming mode. When the first bifurcation speed is exceeded, the second and third jamming modes appear. When the second bifurcation speed is exceeded, the first and second jamming modes disappear. The first jamming mode is resonant. In the cases of two or more loads, the vibratory machine also has an auto balancing mode (no vibrations), under which the loads rotate synchronously with the body of the vibration exciter and mutually balance each other. With small forces of viscous resistance, the computational experiment found that odd jamming modes are stable if they are numbered in ascending order of the frequency of load jamming. An auto-balancing mode is stable at the rotor speeds above the resonance. For the onset of a resonant mode of motion of the vibratory machine, it is enough to slowly accelerate the rotor to a speed lower than the second bifurcation speed. The results reported here are applicable in the design of resonant single-mass vibratory machines with inertial vibration exciters of the ball, roller, or pendulum type.

Simulation of a mass-on-belt dynamical model with the Zener viscoelastic support

Mass-on-belt models have been developed for the study of stick–slip. For most cases, a linear spring or the Kelvin–Voigt representation form the connection between the inertial reference frame and the mass. Here, the Zener viscoelastic support was included and the linear stability indicate that adequate parameter combinations enhance the stability zone to cope with higher frictional levels. Nonlinear numerical results show that responses are represented by three-dimensional limit cycles. For several conditions, its stable branches of solution presented hysteresis according to the nondimensional belt speed, where the bistability was described by three-dimensional regions of attraction. The results also indicate that the system may present interactions between limit cycles and fixed points, generating a sequence of period increasing bifurcations.