Viscoelastic Plate Research Articles

Multi-scale optimization design of viscoelastic damping sandwich plate

Aiming at the optimization design problem of viscoelastic damping sandwich plate under the background of lightweight, a multi-scale optimization design method is proposed to realize the collaborative optimization design of viscoelastic damping sandwich plate in both macro and micro scales. It is assumed that the viscoelastic damping material is microscopically composed of 3D periodic unit cells. The effective constitutive matrix of the unit cell is derived using the homogenization method. The topology optimization model is established, and sensitivity analysis is conducted. The iteration of the design variables is realized by the Optimization Criterion (OC) method. Several numerical examples are presented to demonstrate the effectiveness of the proposed multi-scale optimization method. In-depth discussions are given for the impact of optimization objectives and volume fractions on the design results. The results show that the optimized configuration on both scales are dependent on the objective mode. The macroscopic optimal layout is affected by the microscopic volume fraction, while the change in macroscopic volume fraction has little effect on the microscopic optimal configuration. The dynamic characteristics of the viscoelastic damping sandwich plate are improved significantly through multi-scale optimization design.

Blow-Up of Solutions in a Fractionally Damped Plate Equation with Infinite Memory and Logarithmic Nonlinearity

In this article, we consider the dynamics of a viscoelastic plate equation with internal fractional damping, a nonlinear logarithmic source, and infinite memory effects. The existence of a local weak solution is shown effectively through the framework of semigroup theory. Furthermore, we show that the blow-up in finite time of the local solution may occur under specific conditions and is demonstrated within the development of a suitable Lyapunov functional. Our result offers an insight into the challenges presented by this class of equations and their relevance to physical systems.

LSTM-based neural network architecture for predicting the nonlinear dynamic behavior of functional gradient viscoelastic porous plates

LSTM-based neural network architecture for predicting the nonlinear dynamic behavior of functional gradient viscoelastic porous plates

Sensitivity of Lamb waves in viscoelastic polymer plates to surface contamination.

Detecting surface contamination on thin thermoformed polymer plates is a critical issue for various industrial applications. Lamb waves offer a promising solution, though their effectiveness is challenged by the strong attenuation and anisotropy of the polymer plates. This issue is addressed in the context of a calcium carbonate (CaCO3) layer deposited on a polypropylene (PP) plate. First, the viscoelastic properties of the PP material are determined using a genetic algorithm inversion of data measured with a scanning laser vibrometer. Second, using a bi-layer plate model, the elastic properties and thickness of the CaCO3 layer are estimated. Based on the model, the sensitivity analysis is performed, demonstrating considerable effectiveness of the A1 Lamb mode in detecting thin layers of CaCO3 compared to Lamb modes A0 and S0. Finally, a direct application of this work is illustrated through in-situ monitoring of CaCO3 contaminants using a straightforward inter-transducer measurement.

Formulation of the extended plane wave expansion for in‐plane and out‐of‐plane vibrations in viscoelastic phononic thin plates under a constant temperature field

AbstractIn this study, we develop an extended plane wave expansion method to determine the complex elastic band gaps for both in‐plane and out‐of‐plane vibrations in a viscoelastic phononic crystal (PnC) thin plate model under a constant temperature field. The periodic structure of the thin plate comprises a unit cell (UC) consisting of an epoxy matrix and circular steel inclusions. In this configuration, we consider the viscoelastic effects described by the generalized Maxwell model arising from the epoxy matrix. Furthermore, we incorporate thermal effects in the UC, accounting for the linear dependence of the Young's modulus on the temperature of the epoxy matrix, assuming the absence of heat flow in the dimensions of the UC. We present a band structure illustrating the displacement of the real and imaginary parts of the complex band structure for evanescent waves arising from the viscoelastic PnC thin plate, considering both in‐plane and out‐of‐plane vibrations.

Modeling of shear wave propagation in piezo-viscoelastic microbeam over quadratic heterogeneous viscoelastic plate with sliding contact

Abstract This study analyzes the phase and attenuation dynamic behavior of piezo-viscoelastic microbeam overlying quadratic heterogeneous viscoelastic plate under sliding contact. Using the Kelvin-Voigt model, the material properties of the system are assumed to be viscoelastic. Maxwell’s relations are used to incorporate the electric potential function. The solutions for both media are derived separately by solving the second-order hyperbolic differential equation using the method of separation of variables and asymptotic expansions of Bessel functions. The system of linear homogeneous equations is obtained by applying admissible boundary conditions to determine fundamental physical quantities. The key contribution of the current work is demonstrating the influence of dissipation factors, sliding contact, micro-length, heterogeneity, and thickness ratio parameters on shear wave propagation. The micro-length effect is found to suppress the attenuation of shear waves through the analysis and discussion of the dispersion and attenuation curves.

Stability/instability analysis of advanced nanocomposite-reinforced bridge asphalt mixtures at low temperatures: Verification of the results via AI-driven approach

This study investigates the stability/instability analysis of advanced nanocomposite-reinforced bridge asphalt mixtures under low-temperature conditions, incorporating a fractional viscoelastic plate model for more accurate simulation of time-dependent material behavior. The nanoclay reinforcement is introduced into the asphalt matrix to enhance its mechanical properties, particularly improving the stiffness and thermal stability, which are critical for the long-term performance of bridge structures. The fractional viscoelastic plate formulation captures the complex viscoelastic behavior of the reinforced asphalt at low temperatures, where traditional models may fall short in accounting for the intricate time-dependent response of the material. The stability/instability analysis is conducted to assess the behavior of the nanocomposite asphalt mixtures under varying temperature conditions. The analysis identifies critical conditions leading to structural instability, ensuring the durability of bridge decks exposed to severe thermal environments. The results are validated using an AI-driven approach, leveraging machine learning algorithms to model the response of the nanocomposite asphalt mixtures more effectively. The AI model is trained using experimental data and computational simulations, with hyperparameters, such as learning rates, neural network architectures, and optimization techniques carefully selected to optimize prediction accuracy. The findings offer valuable insights into the performance of nanoclay-reinforced asphalt mixtures for bridge applications, with the AI-driven verification enhancing the reliability and applicability of the proposed models in practical engineering scenarios.

Bending analysis of viscoelastic plates according to the Reissner’s theory using meshless local Petrov–Galerkin method and hereditary integral formulation

Purpose The purpose of this study is to apply the Meshless Local Petrov–Galerkin (MLPG) method to solve the bending problems of linear viscoelastic plates, considering Reissner’s theory.Design/methodology/approachThe weak formulation for the set of equations that govern Reissner’s plate theory is implemented in conjunction with the integral formulation applied to viscoelastic constitutive expressions. A meshless method based on the Moving Least Squares (MLS) approximation is considered in the numerical implementation. The final equation system is assembled by adopting simple and efficient schemes for numerical integration, considering a simplified formulation through centralization of the local interpolation domains and Gaussian quadrature at the same field point. The results obtained are compared with available solutions to demonstrate the efficiency of the proposed formulation.FindingsThe hereditary integral approach proved to be the most general way to analyze the viscoelastic problem, especially when applied together with the modified scheme for numerical integration. In addition, the variable changing technique is demonstrated to be an efficient formulation for solving shear-locking effects in thin plate problems.Originality/valueThe differential of the present study is related to the manner in which the properties of linear viscoelastic materials are considered in the formulation. Although most authors consider this point through the application of the correspondence principle, the present study works with a hereditary integral formulation. In addition, the variable changing technique is applied to solve the shear-locking effects, and an alternative approximation technique is considered to speed up the numerical integration process.

Impact response of fractionally damped rectangular plates made of viscoelastic composite materials

The paper aims to find dynamic response of fractionally damped rectangular viscoelastic plates under low-velocity impact of a mass. The general fractional (Rubbery, Transition and Glassy) RTG model for the plate material was considered. First, the governing equation of the plate is derived and solved. Next, using the modified Hertz contact law, the governing integral equation of the problem in terms of indentation is derived and solved. Finally, relation between indentation and impact force is discretized and using the Mittag-Leffler function, history of impact force is obtained. The work is validated by comparison of the results with some particular cases and available experimental data.

Global and exponential attractors for viscoelastic Kirchhoff plate equation with memory and time delay

In this paper, we consider the viscoelastic Kirchhoff plate equation with memory and time delay. Under appropriate conditions on the real numbers and , we prove the existence of a compact global attractor with finite fractal dimension through a stabilizability estimate. Additionally, we demonstrate the existence of a fractal exponential attractor. To the best of our knowledge, these findings are novel for for this system.

Non-homogeneity effect on the vibration of the rectangular visco-elastic plate subjected to the linear temperature effect with quadratic thickness variation in both directions

The present work investigates the effect of non-homogeneity on the vibration of a rectangular visco-elastic plate. The plate is subjected to linear temperature variation in the x-direction with quadratic thickness variation in both directions. The quadratic variation has been considered in the material density of the plate only along the x-axis, and it is assumed that non-homogeneity transpires because of this variation. The governing differential equation is solved using the Rayleigh-Ritz technique. All four edges of the plate should be clamped to drive the frequency equation. Deflection and time period have been evaluated for several combinations of values of the thermal constant, constant of nonhomogeneity, taper constants, and length-to-width ratio (aspect ratio) for the first two vibrationmodes of the clamped plate. The results presented are compared with those found in the literature.

Existence of Solutions for a Viscoelastic Plate Equation with Variable Exponents and a General Source Term

The subject of this study is a nonlinear viscoelastic plate equation with variable exponents and a general source term. Through the application of the Faedo–Galerkin approximation method and a fixed point theorem under appropriate assumptions, we proved the existence of weak solutions.

Numerical analysis of nonlinear Volterra integrodifferential equations for viscoelastic rods and plates

Numerical analysis of nonlinear Volterra integrodifferential equations for viscoelastic rods and plates

Global sensitivity analysis of damped sandwich plates using sparse polynomial chaos expansions

The present article aims at performing a global sensitivity analysis of modal properties of a frequency dependent viscoelastic sandwich plate. The latter are evaluated using a finite element model relying on Kirchhoff theory for the elastic faces and the Mindlin-Reissner approach for the viscoelastic layer. The plate’s characteristics are considered as random variables following log normal laws. Sparse polynomial chaos expansions are employed to evaluate Sobol’s indices. For high damping, the resonant frequencies and loss factors turn to be sensitive to the elastic face properties, while in the weak damping case they are mostly affected by the viscoelastic model parameters.

On the Method for Solving the Problem of Ice Cover Deformation under an Arbitrary Moving Load

Introduction. The development of the polar areas of the World Ocean and the need to solve various problems associated with a large number of freezing inland water bodies issue new challenges for science. These challenges include the problem of studying the behavior of ice cover when exposed to various types of loads. Of great interest is the consideration of problems about the action of a moving load on the ice cover. A moving load simulates the effect of moving vehicles on ice. However, in papers devoted to the above problems, cases of load movement along a straight-line trajectory are considered. The objective of this research is to develop a method for studying the behavior of ice cover under the action of a load moving arbitrarily.Materials and Methods. The article proposes a method for solving the problem of the action of a force moving along an arbitrary trajectory on the ice cover of a reservoir of finite depth. The problem amounts to solving a system of two differential equations. The first of them models the behavior of the ice cover, and it is the equation of vibrations of a viscoelastic plate. The second equation simulates the behavior of fluid in a state of potential flow, and it is Laplace's equation. To solve the system of differential equations, integral transformations in time, space and variables were used. The resulting solution was expressed through an iterated integral, which was calculated using numerical methods.Results. The development and implementation of the method resulted in solving the problem of the movement of a concentrated force along an ice cover according to an arbitrary law. At the same time, studies were carried out on the behavior of displacements and stresses in the ice cover depending on the speed and acceleration of the movement of the vertical load, on the depth of the reservoir, and on the viscoelastic properties of ice. In addition, the distribution of the velocity vector of fluid particles along the depth of the reservoir was calculated.Discussion and Conclusion. The proposed method is very effective for solving problems of moving loads acting on the ice cover of a reservoir of finite depth. It provides solving problems about the action of a load moving along an ice cover along a complex trajectory. The results obtained can be used to calculate the stress and displacement of the ice cover during the laying of ice roads or the construction of airfields on the ice.

Automated Shape Correction for Wood Composites in Continuous Pressing

The effective and comprehensive utilization of forest resources has become the theme of the global “dual-carbon strategy”. Forestry restructured wood is a kind of wood-based panel made of wood-based fiber composite material by high-temperature and high-pressure restructuring–molding, and has become an important material in the field of construction, furniture manufacturing, as well as derivative processing for its excellent physical and mechanical properties, decorative properties, and processing performance. Taking Medium Density Fiberboard (MDF) as the recombinant material as the research object, an event-triggered synergetic control mechanism based on interventional three-way decision making is proposed for the viscoelastic multi-field coupling-distributed agile control of the “fixed thickness section” in the MDF continuous flat-pressing process, where some typical quality control problems of complex plate shape deviations including thickness, slope, depression, and bump tend to occur. Firstly, the idea of constructing the industrial event information of continuous hot pressing based on information granulation is proposed, and the information granulation model of the viscoelastic plate shape process mechanism is established by combining the multi-field coupling effect. Secondly, an FMEA-based cyber granular method for diagnosing and controlling the plate thickness diagnosis and control failure information expression of continuous flat pressing is proposed for the problems of plate thickness control failure and plate thickness deviation defect elimination that are prone to occur in the continuous flat-pressing process. The precise control of the plate thickness in the production process is realized based on event-triggered control to achieve the intelligent identification and processing of the various types of faults. The application test is conducted in the international mainstream production line of a certain type of continuous hot-pressing equipment for the production of 18 mm plate thickness; the synergistic effect is basically synchronized after 3 s, the control accuracy reaches 30%, and the average value of the internal bond strength is 1.40, which ensures the integrity of the slab. Practical tests show that the method in the actual production is feasible and effective, with detection and control accuracy of up to ±0.05 mm, indicating that in the production of E0- and E1-level products, the rate of superior products can reach more than 95%.

Nonlinear dynamic response and damping performance of the viscoelastic composite core-based sandwich plates subjected to blast load

Nonlinear dynamic response and damping performance of the viscoelastic composite core-based sandwich plates subjected to blast load

A numerical investigation of longitudinal wave for thermo-acoustoelastic effects on fluid-embedded in two viscoelastic layer plates at higher temperatures

Ultrasound has become indispensable for inspecting complex structures due to its efficient propagation in both liquids and solid materials. Extensive research has been conducted across various domains, encompassing wave behavior, structural interactions, material dispersion due to heterogeneity, propagation characteristics near boundaries, defect detection, and signal processing. In this context, longitudinal waves are particularly favored for examining thick components exhibiting surface defects or thermal gradients across their depth. In our current work, we employed a numerical approach based on the Transfer Matrix Method (TMM) to model ultrasound signals backscattered under normal incidence by a multilayer structure immersed in water. This method involves representing each layer using a quadrupole formalism that combines stresses and velocities. Simultaneously, we harnessed the thermodynamic equation for aqueous solutions and Fourier’s law to derive the expression for the thermo-acoustic coefficient of longitudinal waves within a fluid embedded between two parallel immersed plates, enabling precise control of the fluid temperature over a range from 0 °C to 700 °C. In the time domain, we evaluated the ultrasonic parameters of a fluid exposed to a temperature range from 0 to 700 °C. This evaluation was supported by a variety of multilayer structures designed to ensure the accurate processing of backscattered signals. These structures were excited by longitudinal waves, with a central frequency fixed at 5 MHz. The results obtained emphasize the sensitivity of longitudinal waves to temperature variations and reveal the presence of wave dispersion induced by temperature fluctuations. In order to investigate this dispersion, we conducted an extensive study of ultrasonic longitudinal wave propagation across a range of excitation frequencies from 2 to 12 MHz. This study encompassed the calculation of phase and group velocities, as well as the corresponding attenuation. The results confirm the relevance of our research to various applications and highlight the complex interaction between longitudinal wave dispersion and temperature variations.

Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach

Asymptotic modeling of viscoelastic thin plates and slender beams, a unifying approach

Wave resistance of slender body in unsteady motion under an ice sheet

The paper is devoted to the theoretical study of the rectilinear unsteady movement of a slender body in a liquid near the free surface and an ice sheet. Water is an ideal incompressible liquid, and the motion of the liquid is potential. The ice cover is modeled by a floating viscoelastic plate. The viscoelastic properties of ice are described using the Kelvin–Voigt model. A slender body of a given shape in the liquid flow is modeled by the flow of the source-sink system. Various modes of body movement are considered: acceleration, deceleration, movement at a given speed. The effect of the ice sheet, acceleration and deceleration of the body on its wave resistance is analyzed. It is obtained that unsteady modes of motion (acceleration and deceleration) significantly affect the wave resistance of a slender body. Motion with low initial acceleration makes it possible to reduce amplitude of the first-time hump of wave resistance. During body deceleration to a full stop, the curve of wave resistance has an oscillations. Reduction of deceleration coefficient results in decrease of oscillation amplitude of wave resistance curve. The presence of the ice cover smoothes the hump of wave resistance during acceleration and reduces the number of oscillations and their amplitude during deceleration.