Viscoelastic Structures Research Articles

A novel frequency-labeled adaptive sparse grid collocation method for uncertainty quantification of the frequency response of general viscoelastic damping structures

In this paper, a frequency-labeled adaptive sparse grid collocation (FL-ASGC) method is proposed to study the uncertainty quantification (UQ) of the frequency response of general viscoelastic damping structures. The advantage of the proposed method is that, on the one hand, it has a good approximation ability for both smooth and non-smooth responses so that it can robustly predict the variability of frequency responses under various damping levels. On the other hand, by evaluating the contribution of each interpolation node to the response at all frequencies, it can adaptively select samples and their accompanying analysis frequency domains, thereby minimizing the computational costs of probabilistic surrogate modeling. To obtain the deterministic solution of each sample, the layer-wise finite element method combined with the direct frequency response (DFR) method is employed. Two numerical examples with different damping materials are provided to test the proposed method. Uncertainties that obey normal distribution in material and geometry are considered. The results show the proposed method can accurately, efficiently, and robustly predict the variability of the frequency response of general viscoelastic damping structures.

Application of finite element method in ultrasonic guided waves testing technique

Ultrasonic guided waves have the ability of long-distance nondestructive testing for defects in waveguide structures, and have been one of the hotspots in the field of nondestructive testing for many years. Finite element method (FEM) has the ability to calculate various complex dynamics problems and has become an important tool in the research of ultrasonic guided wave testing technique. Considering the hot issues in the research, a brief review of the relevant FEM is proposed. The development of FEM and its application in the excitation and reception of guided waves under multi-physical coupled field mechanism, the propagation characteristics of guided waves in linear elasticity and viscoelastic structures and nonlinear ultrasonic guided waves are introduced. Finally, the research emphasis and development direction of the relevant FEM in the future is prospected based on the research trend of ultrasonic guided wave testing technique.

A fractional Maxwell approach for the shock response of viscoelastic oscillator

Viscoelastic damping structures under shock loading with variable amplitude and frequency are always in the multifactorial dynamic state, of which the shock response is obviously different from that under low strain rate. In order to accurately describe the impact mechanical properties of viscoelastic damped materials, a fractional order Maxwell model (FMM) is constructed. To verify the adopted model, the dynamic experiments for different strain rates (1800 s-1, 2500 s-1, 3500 s-1 and 4000 s-1) are performed by SHPB system. The experimental stress-strain curves should be divided into three stages: the linear stage, the strain-softening stage and the strain-hardening stage. As increase with the strain rate, the peak strain, the peak stress and the curvature of the curve in strain-softening stage increase, and the hardening effect in the strain-hardening stage tends to stronger, demonstrating a distinct strain rate effect in viscoelastic damped materials. The reason is that as increase of the strain rate, the action time of external loading gets closer to the relaxation time of the molecular chain segment, indicating the apparent strain rate-dependence of molecular slip and friction. The comparisons are made between the models of FMM, fractional Kelvin-Voight, ZWT and Ogden considering the strain rate-dependent. As a fractional-order model, FMM model has the minimum mean of RMSE 0.460 among the four models. The results indicate that FMM model could accurately describe the impact mechanical behavior characteristics of viscoelastic materials in a wider range of strain rate with comprehensive superiority of higher fitting precision, fewer parameters and clear physical meaning.

Dynamic response of viscoelastic multiple-core sandwich structures

This work focuses on the free and forced vibrations of sandwich beams and plates hosting an arbitrary number of damping cores. A fractional derivatives Zener-type model is adopted for representing the frequency-dependent viscoelastic behaviour, along with conventional series developments. The structural models are formulated within an established variable kinematics approach, which enables to investigate the role of specific assumptions and to identify the most accurate model at a least number of degrees of freedom. Approximate solutions are found by a computationally efficient Ritz method that allows to take into account any type of boundary conditions. Modal loss factors and damped eigenfrequencies are obtained from a complex eigenvalue problem, for which a modal strain energy approach or a complex eigensolution can be employed. Frequency responses can be computed by a direct approach or by elementary modal projection algorithms. Results are reported for conventional and innovative sandwich configurations. Different modelling and solution strategies are compared and the role of transverse normal deformation of the mechanically weak viscoelastic plies is particularly emphasised.

Dynamic Response of the Newton Voigt–Kelvin Modelled Linear Viscoelastic Systems at Harmonic Actions

The variety of viscoelastic systems and structures, for the most part, is studied analytically, with significant results. As a result of analytical, numerical and experimental research, which was conducted on a larger variety of linear viscoelastic systems and structures. We analyzed the dynamic behavior for the viscoelastic composite materials, anti-vibration viscous-elastic systems consisting of discrete physical devices, road structures consisting of natural soil structures with mineral aggregates and asphalt mixes, and mixed mechanic systems of insulation of the industrial vibrations consisting of elastic and viscous devices. In this context, the compound rheological model can be schematized as being V−(E|V) type of the Newton Voigt–Kelvin model with inertial excited mass, applicable to linear viscoelastic materials.

Effect of frequency dependence on the seismic performance of linear viscoelastic base-isolated structures

The purpose is to address two issues arising from the frequency dependence of viscoelastic (VE) isolation bearings implemented in base-isolated structures (BIS): (i) how the frequency dependence affects the structural response; and (ii) which method is appropriate for the VE BIS. Effects of the frequency dependence on the absolute acceleration transmissibility are analyzed based on a two-degree-of-freedom system. Three generic algorithms: (i) constant-parameter approximation (CPA), (ii) mode superposition iteration, and (iii) modified rational polynomial approximate (RPA) are used to calculate the seismic responses. Effects of the frequency dependence on the seismic responses of the VE BIS subjected to the historic earthquakes are numerically analyzed through a five-story frame structure. The results show that the frequency dependence of the stiffness can broaden the absolute acceleration transmissibility curve of the VE BIS. The seismic responses in general are underestimated when the frequency dependence is not well considered, and the response errors are influenced by the frequency dependence, excitation characteristics and structural dynamic property. The RPA method takes into account the frequency dependence of VE isolation bearings completely through the rational polynomial model. The CPA and mode superposition iteration methods can only consider frequency dependence effect partially, and the mode superposition iteration method performs better.

Predicting delayed instabilities in viscoelastic solids.

Determining the stability of a viscoelastic structure is a difficult task. Seemingly stable conformations of viscoelastic structures may gradually creep until their stability is lost, while a discernible creeping in viscoelastic solids does not necessarily lead to instability. In lieu of theoretical predictive tools for viscoelastic instabilities, we are presently limited to numerical simulation to predict future stability. In this work, we describe viscoelastic solids through a temporally evolving instantaneous reference metric with respect to which elastic strains are measured. We show that for incompressible viscoelastic solids, this transparent and intuitive description allows to reduce the question of future stability to static calculations. We demonstrate the predictive power of the approach by elucidating the subtle mechanism of delayed instability in thin elastomeric shells, showing quantitative agreement with experiments.

Modal identification of cylindrical shell with high damping using reduction method focusing on symmetry of mode shape

The viscoelastic structures such as tires have high damping characteristics, so that resonance peaks do not appear clearly and they are difficult to identify the existence of modes in the high frequency region. Previous studies have proposed methods that make it easier to understand modes. In that method, the number of modes are reduced by using the fact that the basis function of the mode shape of the cylindrical structure can be expressed by a periodic function. However, a large number of measurement points are placed on the structure and data is collected, so the workload of the experiment is large. In this study, we conducted a numerical experiment of the mode reduction method using some measurement point data for the purpose of reducing the workload, and evaluate the influence on the identification accuracy. As a result, it was confirmed that the identification results of the natural frequency and the structural damping coefficient had sufficient accuracy even if some measurement points were used.

Spatial natural vibrations of viscoelastic axisymmetric structures

Spatial natural vibrations of viscoelastic axisymmetric structures

Static and Dynamic Analysis of Viscoelastic Structure

Generally, the incremental superposition method is used to analyze the stress and deformation of viscoelastic structures. In the calculation, the total time is divided into several intervals. It is assumed that the internal stress remains unchanged in each time interval. The creep deformation generated in this period is taken as the initial strain at the next moment, and the displacement increment is solved according to the elastic problem together with the load, and the total displacement is obtained gradually by superposition. In the study of this method, the integral constitutive relation is used in most cases, and the relaxation modulus is expressed by Prony series. Therefore, the convolution can be expressed by recursion formula, and the memory can be greatly reduced.

Spatial natural vibrations of viscoelastic axisymmetric structures

Spatial natural vibrations of viscoelastic axisymmetric structures

Uncertainty propagation of frequency response of viscoelastic damping structures using a modified high-dimensional adaptive sparse grid collocation method

Uncertainty propagation (UP) of the frequency response is essential for the robust design of viscoelastic damping structures. One challenge in solving this problem is enormous computation cost from the UP analysis. This paper aims to develop a novel computational effective method based on the combination of the adaptive sparse grid collocation (ASGC) method and the high dimensional model representation (HDMR) technique to evaluate the variability of the frequency response of viscoelastic damping structures. First, a well-validated layer-wise finite element method is employed to model the viscoelastic damping structures. The direct frequency response (DFR) method is utilized to calculate the response. Then, a modified adaptive strategy using expectation increments as the sampling indicator is proposed for cost-effective sparse grid construction. Lastly, high dimensional model representation (HDMR) technique is introduced to address the difficulty in moderate and high random dimensional situations. Two numerical examples are provided to assess the performances of the proposed method. Variations in constitutive parameters of viscoelastic material and thicknesses of the viscoelastic layer are considered. Numerical results show that, compared to the original high-dimensional ASGC method and Monte Carlo Simulation (MCS), the proposed method accurately predicts the variability of frequency responses and significantly improves the computational efficiency.

Software package of mathematical modeling and structure for solving the dynamics problems of structurally-inhomogeneous shell structures

On the basis of the principle of modularity, an algorithm and software package for dynamic calculation of structurally-inhomogeneous multiply connected shell units that are the elements of hydro-technical structures are developed in the paper. The purpose of the module is to carry out certain transformations of the initial (source) information into a unique result. The development prospects of construction of various hydro-technical structures, aircraft, rocket and space machinery, shipbuilding, chemical engineering and many other branches of modern technology are characterized by a complication of design decisions in projecting and calculation of objects that present multiply connected spatial shell structures subjected to static and dynamic effects. Multiply connected structures, (such as hydro-technical structures), usually include a wide range of elastic and visco-elastic deformable elements with significantly different rheological properties in the form of blocks of plate stacks, tubular, cylindrical and prismatic shell structures of complex geometry, with attached masses, various types of reinforcement, supports, containing a large number of elastic and visco-elastic couplings with significantly different functions of heredity. Obviously, the search for exact analytical solutions to dynamic problems for structurally inhomogeneous visco-elastic shell structures is doomed to failure, the only possibility of engineering implementation is to build numerical and numerical-analytical algorithms with the subsequent use of modern computers. The solution to dynamic problems involves a numerical simulation of the stress-strain state (SSS) of the structures under consideration.

Dynamic stability of viscoelastic orthotropic shells with concentrated mass

Viscoelastic thin-walled structures such as plates, panels and shells, with mounted objects in the form of additional masses are widely used in modern technology. The role of such additional masses is often played by longitudinal and transverse ribs, tie-plates and fixtures. When designing such structures, it is relevant to study their dynamic behavior depending on the mass distribution, viscoelastic and inhomogeneous properties of the material, etc. In this paper, the dynamic stability of a viscoelastic shell carrying concentrated masses is considered, taking into account the nonlinear and inhomogeneous properties of the material. A mathematical model of the problem is described by a system of integro-differential equations in partial derivatives. With the Bubnov-Galerkin method, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations. To solve the resulting system with the Koltunov-Rzhanitsyn singular kernel, a numerical method based on the use of quadrature formulas is applied. The effect of the viscoelastic and inhomogeneous properties of the shell material, location, and the amount of concentrated masses on stability is studied.

Variable separation method for solving boundary value problems of isotropic linearly viscoelastic bodies

The availability of accurate methods to mathematically model and predict the behavior of viscoelastic structures under mechanical, thermal and other loads remains a critical issue in different fields ranging from construction engineering to aerospace. Methods to calculate elastic structures are well developed; however, considering that viscoelastic properties require significant effort, we have developed and tested a new analytical method to solve boundary problems of isotropic linearly viscoelastic bodies. According to the proposed algorithm, to find the solution for a linear viscoelasticity boundary problem, we must replace the elastic constants with some functions of time and then numerically or analytically calculate the stress–strain state of the structure at any moment of its loading history. As a result of the theoretical justification of the proposed method, carried out in three independent ways, identical expressions of effective modules are obtained. The obtained results, as well as testing on solutions to several problems, allow us to conclude that the new analytical method is applicable to the calculation of the stress–strain state of viscoelastic bodies.

Stress analyses of viscoelastic three-dimensional beam-like structures with low- and high-order one-dimensional finite elements

The mechanical responses of viscoelastic structures are evaluated by using finite beam elements based on different kinematical assumptions. The governing equations related to the structural theories are obtained with the Carrera Unified Formulation. The viscoelastic constitutive law is expressed in an integral form, which relates the viscous moduli with the strain rate. The solution of the governing equations is obtained in the Laplace domain and then transformed in the time domain through a numerical inversion procedure. The numerical simulations are performed on slender, squat, isotropic, and orthotropic beams in order to examine the actual differences between the results obtained with low-order theories and the refined models. The current results are validated with classical and higher-order solutions available in the literature. Moreover, comparisons between the equivalent-single layer and the layer-wise approach are reported and discussed.

Asymmetrical Velocity Distribution in the Drag-Reducing Channel Flow of Surfactant Solution Caused by an Injected Ultrathin Water Layer

Although the turbulent intensity is suppressed in the drag-reducing channel flow by viscoelastic additives, the mean velocity distribution in the channel flow is symmetrical and tends to be similar to the laminar flow. In the study of near-wall modulation of the drag-reducing flow with an injected ultrathin water layer, an asymmetrical mean velocity distribution was found. To further investigate this phenomenon and the underlying cause, an experiment was carried out with the water injected from a porous channel wall at a small velocity (~10−4 m/s) into the drag-reducing flow of surfactant solution. The instantaneous concentration and flow fields were measured by using planar laser-induced fluorescence (PLIF) and particle imaging velocimetry (PIV) techniques, respectively. Moreover, analyses on turbulent statistical characteristics and spatial distribution of viscoelastic structures were carried out on the basis of comparison among various flow cases. The results showed that the injected ultrathin water layer under present experimental conditions affected the anisotropy of the drag-reducing flow. The characteristics, such as turbulence intensity, showed the zonal feature in the wall-normal direction. The Reynolds shear stress was enhanced in the near-wall region, and the viscoelastic structure was modified severely due to the redistributed stress. These results may provide experimental supports for the near-wall modulation of turbulence and the exploration of the drag-reducing mechanism by viscoelastic additives.

General Homogenised Formulation for Thick Viscoelastic Layered Structures for Finite Element Applications

Viscoelastic layered surface treatments are widely used for passive control of vibration and noise, especially in passenger vehicles and buildings. When the viscoelastic layer is thick, the structural models must account for shear effects. In this work, a homogenised formulation for thick N-layered viscoelastic structures for finite element applications is presented, which allows for avoiding computationally expensive models based on solids. This is achieved by substituting the flexural stiffness in the governing thin beam or plate equation by a frequency dependent equivalent flexural stiffness that takes shear and the properties of the different layers into account. The formulation is applied to Free Layer Damping (FLD) and Constrained Layer Damping (CLD) beams and plates and its ability to accurately compute the eigenpairs and dynamic response is tested by implementing it in a finite element model and comparing the obtained results to those given by the standard for the application—Oberst for the FLD case and RKU for the CLD one—and to a solid model, which is used as reference. For the cases studied, the homogenised formulation is nearly as precise as the model based on solids, but requires less computational effort, and provides better results than the standard model.

A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics

To overcome the long wavelength and time limits of classical elastic theory, this paper presents a fractional nonlocal time-space viscoelasticity theory to incorporate the non-locality of both time and spatial location. The stress (strain) at a reference point and a specified time is assumed to depend on the past time history and the stress (strain) of all the points in the reference domain through nonlocal kernel operators. Based on an assumption of weak non-locality, the fractional Taylor expansion series is used to derive a fractional nonlocal time-space model. A fractional nonlocal Kevin–Voigt model is considered as the simplest fractional nonlocal time-space model and chosen to be applied for structural dynamics. The correlation between the intrinsic length and time parameters is discussed. The effective viscoelastic modulus is derived and, based on which, the tension and vibration of rods and the bending, buckling and vibration of beams are studied. Furthermore, in the context of Hamilton’s principle, the governing equation and the boundary condition are derived for longitudinal dynamics of the rod in a more rigorous manner. It is found that when the external excitation frequency and the wavenumber interact with the intrinsic microstructures of materials and the intrinsic time parameter, the nonlocal space-time effect will become substantial, and therefore the viscoelastic structures are sensitive to both microstructures and time.

Stiffness-Damping Matching Modelling for Vibration Isolation System of Roadheader ECB

The electronic control box (ECB) is a key and precise component of a roadheader. The vibration of the ECB is an increasingly prominent issue as the machine capacity grows. In order to promote the isolation effect of the ECB, a whole-body vibration model considering the cutting effect is derived, based upon which the stiffness-damping matching strategy for the ECB isolator is acquired. For engineering application, the tubular constrained damping isolator (TCDI) is developed based on the constrained damping theory and the matching strategy. The theoretical results show that the isolation effect of the ECB isolator strengthens as the stiffness coefficients decline and the damping coefficients increase. The configurations with larger rear stiffness coefficients and larger front damping coefficients could lead to a better vibration control effect. The experiment results indicate that the TCDI exhibits a greater capability of isolating the impact excitation than the traditional E-type isolator, thus verifying the whole-body vibration model for the roadheader and the matching strategy for the ECB isolator. This research can provide theoretical and practical references for the investigation of the dynamic behaviour of complex viscoelastic structures.