Poroelastic Plate Research Articles

State-Spatial Viewpoint of Stress in Thermally Postbuckled and Nonlinearly Bent FG Saturated Poroelastic Circular Plates

A dimensionless discrete state-space mathematical model is proposed for stress analysis of an axially-symmetric saturated poroelastic circular plate being loaded by temperature rise of one of the flat faces. Computation of stress by means of this model is free from a need for differentiation. The curves of thermal postbuckling, thermal nonlinear bending, radial stress, circumferential stress and resultant radial force have been achieved by means of six state-space variables and differential quadrature procedure. The effects of loading temperature, boundary conditions, porosity, pore distribution and fluid pore pressure on the thermal post buckling and nonlinear bending phenomena have been investigated. The critical postbuckling thermal load has been determined by means of a numerical algorithm that does not converge to trivial solution because it starts from a relatively great numerical thermal load. Contrary to the governing equation in usual form, the governing equations in state space together with the state equations equalize the number of the governing assembled difference equations and that of the unknowns, and eventually do not require to apply the so-called auxiliary extra boundary conditions at the nodes adjacent to the boundary nodes. As another advantage, in state-spatial viewpoint, there is not any necessity for computing the coefficients of derivatives with order higher than unity.

Small-amplitude waves in a floating poroelastic plate forcing by vertical pitching plate

The linear two-dimensional problem of flexural-gravity waves generated by an oscillating rigid plate build-in a floating poroelastic plate is studied. The problem is coupled. The plate deflections and the hydrodynamics loads are determined at the same time. The liquid under the poroelastic plate is inviscid and incompressible. Dynamics of the floating plate is described by a thin elastic plate equation. Porosity of the floating plate is taken into account only through the liquid flux into the plate. The velocity of the inflow is assumed to be governed by Darcy's law being proportional to the hydrodynamic pressure at the plate/liquid interface. Two cases of the oscillating rigid plate with and without its part in the liquid are considered. The problems are solved by the Fourier transform method for non-zero porosity and by the vertical mode method for elastic plates with zero porosity. The deflection and strain distributions are analyzed depending on the excitation frequency and the porosity. Two models of floating plate porosity, where the hydrostatic pressure is included into Darcy's law (Zavyalova's model) and excluded (Meylan's model), are compared. Plate porosity induces damping to the system. It is shown that the damping rate is non-monotonic with respect to the plate porosity.

Hydroelastic analysis of wave diffraction by multiple flexible porous plates

The study investigates the phenomenon of wave diffraction by multiple poroelastic plates in infinitely deep water using the two-dimensional linearized potential theory. The study focuses on numerically computing the reflection and transmission coefficients using Galerkin approximations specifically designed for two nonidentical vertical poroelastic plates. By varying the separation lengths, porosity, and flexural rigidity of the plates, the study explores the hydrodynamic quantities associated with the wave-plate interaction. These quantities are then represented graphically to visualize their behavior under different conditions. The results of the study show that the flexural rigidity of the porous plates has a significant effect on wave reflection and transmission. The correctness of the method used in the study is confirmed by comparing the results available in the literature. Overall, the study provides valuable insights into the behavior of waves interacting with multiple poroelastic plates and highlights the importance of considering the flexural rigidity of the plates in such systems. The numerical approach used in the study can also be applied to other similar problems and can provide a useful tool for predicting the behavior of waves in complex systems.

Bending wave at the edge of a thermally affected functionally graded poroelastic plate

This study examines the propagation characteristics of flexural edge waves in a functionally graded poroelastic plate within a thermal environment. A transversely isotropic, functionally graded porous material plate supported by a Pasternak elastic foundation is introduced to analyze the dynamics of bending edge wave. Kirchhoff plate theory and Moore–Gibson–Thomson (MGT) thermoelasticity theory are introduced to study the displacement field and the temperature distributions on the plate respectively. Seven different porosity models are tested in this study to compare edge wave behavior in different porous structures. It is found that the decay’s constant for edge wave propagation depends implicitly on frequency and wave number for each of the seven cases. The dispersion relation is derived using the plane harmonic wave propagating along the free edge of the plate. On analyzing the model, it is evident that waves exhibit a cut-off frequency due to an elastic foundation, dependent only on the Winkler modulus. The impact of various parameters, such as porosity and temperature, on the traveling edge wave is illustrated numerically and discussed in terms of their physical behavior.

Thermo-elastodynamic study of the nanocomposite circular sector plates exposed to swift thermal shock

Owing to ruinous effects of thermal shocks on the nanocomposite structures, this study scrutinizes the thermal shock resistance of the poroelastic nanocomposite circular sector plates in the scheme of elasticity theory and application of the harmonic differential quadrature approach (HDQA). Due to the fact that the related studies published priorly were just able to predict the response of the simply-supported plates, the current research would be considered as the first study on the transient thermal shock response of the above-mentioned plates with fully-clamped boundary conditions. To determine the system’s time-dependent response, differential equations are translated to the Laplace domain. Then, the modified declaration of the Dubner and Abate’s technique is exploited to derive the time realization of the system’s response from the Laplace domain. The validation procedure of the current analysis is performed by comparing the outcomes with those claimed in the published researches. In order to clearly assess the system’s shock resistance against the abrupt thermal load, effect of various parameters such as thermal relaxation time (TRT), different scattering models and volume fraction of the nano reinforcement, boundary conditions, intensity of the shock, poroelastic properties of the nanocomposite, and radius to thickness ratio of the sector plate on the thermo-elastodynamic response of the system are investigated. It is revealed that the sensitivity of the system’s response to increase of TRT subsides when TRT is over an upper bond.

Layerwise formulation of poroelastic composite plate under pre-buckling and thermal shock loading

The present article scrutinizes the coupled time-variant poro-thermoelasticity behavior of functionally-graded graphene reinforced (FG-GPLR) composite plates embedded in an elastic foundation, intending to provide innovative solutions to preserve operating mechanisms toward harmful impacts of thermal shock load. The nanocomposite plate is initially stressed in three different orientations and subjected to thermal shock loading. The temperature distribution is acquired by employing the celebrated energy balance equation. The analytical solving approach is utilized for differential motion equations of the system based upon substitution of the equivalent Fourier series expansion for each state variable. Eventually, mapping the structure's response from Laplace to the time domain is carried out by a modified version of the celebrated Dubner and Abates' approach. Convergence of the outcomes regarding time is monitored and certified. The acquired results record the impact of varied parameters like length to thickness ratio of the structure, distribution pattern, and weight-content of GPL on the coupled time-variant poro-thermoelastic response of the FG-GPLR composite plate. One of the main conclusions of this survey is that increasing the weight-content of GPL in the way of locating more GPL near the upper and bottom surface of the plate applies enhancing impacts on the system's resistance against detrimental consequences of thermal shocks.

Innovative statistical approach on graphical optimization and closed-form dynamic response of the poroelastic nanocomposite sandwich structure

Present research with the aid of multivariate analysis of variance explores the closed-form dynamics of the poroelastic nanocomposite sandwich plate. Additionally, graphical optimization of the system’s vibration by proper adjusting the involved parameters is provided by employing response surface methodology. p-value and F-value tests are executed to determine the contribution percentage of each parameter on the dynamics of the structure. The nanocomposite face-sheets are made of graphene-platelets reinforced polymer. The main relations governing the dynamics of the initially stressed sandwich system are defined in the background of theory known as linear poroelasticity. Bidirectional format of discrete singular convolution approach (2D-DSCA) is employed in order to determine the design-points’ dynamic performance. Validity of the applied solution procedure is tested through comparison with the outcomes of the first-rate articles. In this research, it is revealed that the graphical optimization is a reliable way to determine the proper adjustment of the parameters for achieving the optimum vibration performance. Moreover, it is observed that the aspect ratio of the plate is the most decisive factor in the free oscillation response of the sandwich plate compared with other factors whose influence are examined in the present article including GPL’s weight-fraction, GPL’s dispersion patterns, in-plane initial stresses, and the poroelasticity coefficient.

High-order SAFE computation of reflection and transmission coefficients for functionally-graded poroelastic plates

This paper aims at studying the ultrasound response of a functionally-graded and anisotropic porous elastic layer surrounded by a fluid in the frequency domain. Based on Biot’s theory in a planar configuration, a semi-analytical high-order finite element method was proposed for computing the reflection and transmission coefficients of a plane wave with oblique incidence to the interface between the fluid and poroelastic layer. Two approximation techniques were investigated: (i) spectral element approximation; and (ii) isogeometric approximation. A numerical study was performed on the ultrasound response of bone materials with different depth-varied profiles of porosity showing high effectiveness of the proposed high-order methods.

Axisymmetric nonlinear behavior of functionally graded saturated poroelastic circular plates under thermo-mechanical loading

In functionally graded saturated poroelastic circular plates with immovable simply supported and clamped rims, the axisymmetric nonlinear bending under transverse thermo-mechanical loading has been parametrically studied and compared with the axisymmetric postbuckling and nonlinear bending under thermal loading. Based on the classical plate theory, Love–Kirchhoff hypotheses and Sander’s assumptions, the general coupled nonlinear radial and transverse equilibrium equations, central continuity, symmetry and boundary conditions has been derived in ordinary and state-spatial forms. The corresponding difference equations have been achieved by using the generalized differential quadrature method. The equations have been assembled and numerically solved by using the Newton–Raphson iterative algorithm. The effects of the mechanical and thermal loads, pore distribution type, porosity parameter, Skempton’s coefficient, and thickness and boundary condition type on the behavior of the deflection, whether caused by thermo-mechanical bending, thermal postbuckling, or thermal bending, have been investigated in detail. From the parametric study, a novel quantity determining bending behavior has been found. The axisymmetric themo-mechanical nonlinear bending deflection is inversely and nonlinearly proportional to thermal load when the quantity is greater than a critical value and is nonlinearly proportional to thermal load when the quantity is less than a critical value. It was verified that the plate behavior complies with the general rules known for FG saturated poroelastic circular plates and with those known for metal–ceramic functionally graded circular plates whose governing equations are mathematically analogous to those of the current research.

Semi-analytical IGA-based computation of wave dispersion in fluid-coupled anisotropic poroelastic plates

Understanding dispersion relations and wave mode shapes is vital in nondestructive control of dynamic behaviors of poroelastic composites. In the framework of semi-analytical finite element (SAFE) method, this paper presents two numerical approaches so-called semi-analytical isogeometric Galerkin (SAIGA-G) and semi-analytical isogeometric collocation (SAIGA-C) for computing dispersion of guided-waves in anisotropic poroelastic plates immersed in acoustic fluids. Biot’s theory was used for describing the dynamic behavior of anisotropic poroelastic material. Assuming the structures is homogeneous along its axial direction, the Non-Uniform Rational B-splines (NURBS) was successfully employed in procedures using isogeometric Galerkin and collocation methods. The numeral studies showed that the SAIGA-G method using high continuity NURBS basis allowed to significantly improve the accuracy as well as the convergence rate of the wave dispersion solutions in compared with the conventional SAFE method, which used Lagrange basis functions. Otherwise, the SAIGA-C method was shown to have similar performance in terms of accuracy to the SAFE method.

Weak solutions for a poro-elastic plate system

ABSTRACT We consider a recent plate model obtained as a scaled limit of the three-dimensional Biot system of poro-elasticity. The result is a ‘2.5’-dimensional linear system that couples traditional Euler–Bernoulli plate dynamics to a pressure equation in three dimensions, where diffusion acts only transversely. We allow the permeability function to be time dependent, making the problem non-autonomous and disqualifying much of the standard abstract theory. Weak solutions are defined in the so-called quasi-static case, and the problem is framed abstractly as an implicit, degenerate evolution problem. Utilizing the theory for weak solutions for implicit evolution equations, we obtain existence of solutions. Uniqueness is obtained under additional hypotheses on the regularity of the permeability function. We address the inertial case in an appendix, by way of semigroup theory. The work here provides a baseline theory of weak solutions for the poro-elastic plate and exposits a variety of interesting related models and associated analytical investigations.

Mathematical Model of Fluids Motion in Poroelastic Snow-ice Cover

The dynamics of a snow-ice cover is considered within the theory of poroelasticity. The snow-ice cover is modeled by a three-phase medium consisting of water, air and ice. The governing equations are the equations of mass conservation for each phase with phase transitions, the equations of conservation of phase momentum in the form of Darcy’s law, the equation of conservation of momentum of the whole system, the rheological equation for porosity and the equation of heat balance of snow. In the full formulation the liquid and air pressures are functions of the temperature and the corresponding densities, and the viscosity and compressibility coefficients of ice are functions of the temperature. The problem of two-dimensional nonstationary filtration of water in a thin poroelastic ice plate is considered in the model case. The solution is obtained in quadratures

The Response of a Poroelastic Ice Plate to an External Pressure

The response of a poroelastic ice cover to an external load is considered. The ice cover is modeled by a thin poroelastic floating plate within the linear theory of hydroelasticity. The porosity parameter is defined as the coefficient of proportionality of the velocity of liquid penetration into the plate and hydrodynamic pressure. The fluid under the plate is inviscid and incompressible. The flow caused by the ice deflection is potential. The external load is modeled by a localized smooth pressure. The two-dimensional problem of waves caused by a periodic external pressure on a floating porous-elastic plate is considered. The profiles of the generated waves are calculated for a given oscillation frequency of the amplitude of the external pressure. It was found that taking porosity into account leads to damping of oscillations in a distance from the external load

Multilayered Poroelasticity Interacting with Stokes Flow

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 25 November 2020Accepted: 13 August 2021Published online: 01 November 2021Keywordsporoelasticity, fluid-poroelastic structure interaction, poroelastic plate, multilayered poroelasticity, well-posednessAMS Subject Headings74F10, 76S05, 74L15, 34A01, 74K20Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher: Society for Industrial and Applied MathematicsCODEN: sjmaah

A Theoretical Study on the Transient Morphing of Linear Poroelastic Plates

Abstract Based on their shape-shifting capabilities, soft active materials have enabled new possibilities for the engineering of sensing and actuation devices. While the relation between active strains and emergent equilibrium shapes has been fully characterized, the transient morphing of thin structures is a rather unexplored topic. Here, we focus on polymer gel plates and derive a reduced linear model to study their time-dependent response to changes in the fluid environment. We show that independent control of stretching and bending deformations in stress-free conditions allows to realize spherical shapes with prescribed geometry of the mid-plane. Furthermore, we demonstrate that tensile (compressive) membrane stresses delay (accelerate) swelling-induced shape transitions compared to the stress-free evolution. We believe that these effects should be considered for the accurate design of smart systems and may contribute to explain the complexity of natural shapes.

On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate.

A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics.

Many problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poro-elastic plates in two dimensions. Such boundary conditions, namely the varying physical parameters and coupled thin-plate equation, present a considerable challenge to current methods. The new method is fast, accurate and flexible, with the ability to compute expansions in thousands (and even tens of thousands) of Mathieu functions, thus making it a favourable method for the considered geometries. Comparisons are made with elastic boundary element methods, where the new method is found to be faster and more accurate. Our solution representation directly provides a sine series approximation of the far-field directivity and can be evaluated near or on the scatterers, meaning that the near field can be computed stably and efficiently. The new method also allows us to examine the effects of varying stiffness along a plate, which is poorly studied due to limitations of other available techniques. We show that a power-law decrease to zero in stiffness parameters gives rise to unexpected scattering and aeroacoustic effects similar to an acoustic black hole metamaterial.

Effect of concentration dependence of viscosity on squeeze film lubrication

Abstract The influence of concentration of solute particles on squeeze film lubrication between two poroelastic surfaces has been analyzed using a mathematical model. Newtonian viscous fluid is considered as a lubricant whose viscosity varies linearly with concentration of suspended solute particles. Convection-diffusion model is proposed to study the concentration of solute particles and is solved using finite difference method of Crank–Nicolson scheme. An iterative procedure is used to get the solution for concentration, pressure and velocity components in film region. It has been observed that load carrying capacity decreases as the concentration of solute particles in the fluid film decreases. Further, the concentration of suspended solute particles decreases as the permeability of the poroelastic plate increases and these results may be useful in understanding the mechanism of human joint.

Enhancement of acoustic absorption of a rigidly backed poroelastic plate with periodic elliptic inclusions

Perfect acoustic absorption is an important issue for a lot of applications. In this paper, a rigidly backed poroelastic plate with periodic elliptic inclusions is proposed to achieve perfect acoustic absorption at low frequencies by using the finite element method (FEM) with the porous material considered as fluid and solid materials. The absorption of the acoustic energy in such a composite plate resulting from viscous and thermal losses is enhanced by the resonances of the inclusions and energy trapping between the upper part of the poroelastic plate and the inclusion at low frequencies. The influence of the geometry, the incidence angle and the material properties on the absorption coefficient are investigated in detail. Our results show that increasing the major axis of the inclusion, the first absorption peak is pushed to lower frequencies and its value is first increased upto one and then it is decreased. The major axis is the most important parameter to tune the absorption peak, when the thickness is not changed. Once the major axis is determined, perfect acoustic absorption persists even if other parameters are changed. The reported results pave the way for the design of absorption devices which could be used to solve the major issue of noise control.

Vibration analysis of tapered circular poroelastic plates with radially graded porosity using pseudo-spectral method

Attractive properties of Functionally Graded (FG) porous materials (porous materials with functionally graded porosity) are of special interest to engineers and researchers to design and develop improved mechanical properties in a wide range of aerospace, biomedical, civil, mechanical and vehicle engineering applications. This paper aims to use First-order Shear Deformation Theory (FSDT) and investigate free vibration of tapered circular porous plates with graded open-cell porosity as a new lightweight and basic structural element. Plates with both constant and linear symmetric thickness variations about the mid-plane of the circular plate are studied. FG-Internal-Solid, FG-External-Solid and Uniform porosities are also introduced as three types of porosity distributions through the radial direction of the circular plate. The equations of motion are derived using Newton's second law with simply supported and clamped end conditions. A pseudospectral method is used to numerically solve the equations of motions. The influences of thickness variation profiles, boundary conditions and types of porosity on the vibrational properties of tapered circular plates are also investigated in detail.