Porous Beams Research Articles

Nonlinear dynamics of contact interaction porous size-dependent Euler-Bernoulli beams resonators with clearance: Numerical analysis of the stability problem

In this study, a new mathematical model is developed to study the contact interactions of nano- and micro-electro-mechanical (NEMS/MEMS) beam resonators. The structural elements are considered as porous, size-dependent Euler-Bernoulli beams subjected to a variable transverse load. The beams resonators are located one above the other with minimal clearance. The analysis includes interactions between beams of both linear elastic and physically nonlinear materials, following the approach of Professor B. Ya. Kantor. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. Hamilton's principle is applied to derive new size-dependent equations of motion together with the corresponding boundary and initial conditions. This study presents a new approach to the analysis of the chaotic dynamics of the contact interaction of porous, size-dependent Euler-Bernoulli beams. They are considered as systems with an "almost" infinite number of degrees of freedom. This innovative approach uses Principal Component Analysis (PCA) and Wavelet Analysis to filter out noise from signals. In addition, different beam interaction scenarios are classified including static Euler and Rayleigh instabilities as well as interactions between Koning-Taub and Richtmeyer-Meshkov instabilities. A significant discovery of this investigation is the chaotic behaviour of nonlinear vibrations during the contact interaction of these closely positioned beams. This demonstrates the complex dynamics involved in these high technology mechanical systems.

Free Vibration of Axially Loaded Functionally Graded Porous Cracked Beams

This study employed a method of analysis to examine the free oscillation behavior of functionally graded (FG) porous-cracked beams under axial loads and varied boundary conditions. The cracked beam system was composed of interconnecting beam segments kept together by massless rotating springs. Based on the Timoshenko beam theory (TBT) or Euler–Bernoulli theories (EBT), each segment was sectionally flexible. Using a power-law function, mechanical features were expected to gradually change along with the height of the beam. Two different pore distributions, even and uneven, were also explored. Subsequently, Hamilton’s theory was used to derive the equations of kinematic motion for FG-cracked porous beams, and the transfer matrix (TMM) approach was used to get the determinantal equation. A parametric analysis was performed to evaluate how cracks, porosity distribution, slenderness ratio, volume fraction index, boundary conditions, and axial load affect the dynamic characteristics of FG beams. The results revealed that the suggested analytical approach provided several findings that were similar to the existing analytical outcomes in the literature. Moreover, the computer analysis demonstrated that porosity, especially when there were cracks, significantly affected the eigenfrequencies of FG beams. Hence, this study opened the door for possible applications in a variety of engineering settings by offering some crucial insights into the complex dynamics of FG porous-cracked beams.

An isogeometric formulation for free vibration and buckling analyses of FG graphene platelets-reinforced porous beams based on a two-variable shear deformation theory

An isogeometric formulation for free vibration and buckling analyses of FG graphene platelets-reinforced porous beams based on a two-variable shear deformation theory

The effects of gradient index, aspect ratio, porosity, and boundary conditions on the buckling behavior of functionally graded porous beams: A k-out-of-n system reliability analysis

Functionally graded materials are a class of multifunctional materials that exhibit spatial variation in composition and microstructure. This deliberate variation is designed to effectively manage and manipulate changes in thermal, structural, or functional qualities within the material. The current study explores the system reliability of functionally graded porous beams (FGPB) subjected to buckling, focusing on the interplay of gradient index (0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10), aspect ratio (5, 10, 15, 20, 25, 30 and 35), porosity index (0, 0.1 and 0.2) and boundary conditions (simply supported, clamped–clamped and clamped-free), with a particular emphasis on the k-out-of-n system reliability assessment, employing three distinct methods such as Evolutionary, GRG Non-linear, and Lagrangian. The results show the system's sensitivity to changes in distribution parameters, with the Lagrangian method being the most robust and stable. The 10-out-of-12 system reliability analysis demonstrates that aspect ratio and even porosity distribution are reliable, while uneven porosity is not. This study enhances structural reliability analysis in FGPBs, enhancing system reliability considerations and paving the way for further advancements in structural reliability analysis.

Novel Kuhn-Tucker conditions for vibration analysis in a functionally graded porous beam using the R-program

Functionally graded materials provide a flexible and individualized strategy for material design, allowing for optimization of properties and performance for particular purposes. The investigation considers the effects of simply supported (SS), clamped-clamped (CC) and clamped-free (CF) configurations. The study examines the vibration characteristics of bi-directional functionally graded porous beams (BDFGPB) using the third-order shear deformation theory, considering both even and uneven porosity conditions. The Hamilton method is used to derive equilibrium equations for beams, which are then solved using the Kuhn-Tucker technique and R-program. The BDFGPB's validity was verified by comparing it with open literature, revealing deviations of 3.19%, 1.25%, and 2.15% in non-dimensional natural frequency for SS, CC and CF boundary conditions. Furthermore, as the porosity index increases, the dimensionless natural frequency decreases, reducing beam stiffness and rigidity. This study demonstrates that porosity plays a critical role in the design of modern structures, as its ratio greatly impacts their performance and responsiveness.

Novel Kuhn–Tucker conditions with R-program to analyze the buckling of a functionally graded porous beam

Novel Kuhn–Tucker conditions with R-program to analyze the buckling of a functionally graded porous beam

Static and dynamic behaviour of sandwich beams with porous core: Experiment and moving least squares mesh-free analysis

In this paper, the static and dynamic behaviour of sandwich beams with porous core are numerically analyzedand validated by experimental tests. The beam consists of a thick porous core with a uniform porosity distribution over its domain and two outer face layers. For the theoretical study, the virtual work principle is employed to derive the governing equation. A one-dimensional (1D) mesh-free approach, associated with the moving least squares Hermite interpolation, is developed to approximate the primary variable fields and discretize the governing equation. Additionally, a simple transformation method is applied to create Kronecker delta property of constructed shape functions, straightforwardly facilitating the imposition of the boundary condition, similar to the finite element method without additional techniques. The accuracy of the computational method is subsequently verified against previous literature. For the experimental tests, various mechanical responses, such as the natural frequency, static deflection, and deflection-time history of a cantilever porous sandwich beam consisting of cemboard faces and a concrete core with Expanded Polystyrene are measured and compared with the theoretical prediction. The outcomes of this study can be valuable for the design of sandwich beams with porous core.

Free vibrations of functionally graded porous hanging and standing cantilever beams

The free oscillations of a functionally graded (FG) porous vertical cantilever beam in the frame work of Euler–Bernoulli beam theory is investigated. The beam is subjected to the gravity-load and the properties of the FG material such as the modulus of elasticity and the density are supposed to change through the thickness of the beam according to power-law relations. The equation of motion is derived using Newton’s second law. The Numerical Chebyshev collocation method is utilized to determine the transverse frequencies of the FG porous hanging and standing cantilever Euler–Bernoulli beams. A parametric study is conducted to determine the effects of various factors such as the transverse functionally graded index, the porosity factor, and the elastic and the mass density ratios on the natural frequencies and the mode shapes of the FG porous vertical hanging and standing cantilever thin beams under their self-weight. The accuracy of the proposed numerical method is evaluated through comparisons of the frequencies obtained from the present approach with those available in previous literature. In general, it was observed that the elastic ratio has a softening impact on the frequencies except for the fundamental frequency which remains constant as the elastic ratio increases. Moreover, the porosity parameter and the power-law index may have a softening or hardening impact on the frequencies, and the behavior of these frequencies depends on the values of the elastic and the mass density ratios.

Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section

Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section

Nonlinear forced vibration investigation of the sandwich porous FGM beams with viscoelastic core layer

Nonlinear forced vibration investigation of the sandwich porous FGM beams with viscoelastic core layer

Combined effect of temperature dependent material properties and boundary conditions on non-linear thermal stability of porous FG beams

Combined effect of temperature dependent material properties and boundary conditions on non-linear thermal stability of porous FG beams

Analysis of Natural Frequencies in Non-uniform Cross-section Functionally Graded Porous Beams

Analysis of Natural Frequencies in Non-uniform Cross-section Functionally Graded Porous Beams

Explicit Formulas for the Deformation of Chiral Porous Circular Beams in Gradient Thermoelasticity

Chirality and porosity are characteristic properties of nanostructured materials. Their effects on the mechanical behaviour of structural elements, such as shells, plates and beams, cannot be disregarded. In this paper, we study the thermoelastic deformation of a chiral porous circular beam loaded with an axial force and torque. The beam is also under the action of a constant temperature field. The analytical solution is obtained using the results established in a paper recently published by the Author within the context of the strain gradient theory proposed by Papanicopolous. In the constitutive equations, the chirality is introduced by a material constant parameter and the porosity is described by means of a scalar function. Displacements, microdilatation function, and stress and strain fields are expressed in explicit form and in terms of engineering constants. Explicit formulas of the stiffness of chiral porous circular beams are presented and the effects of right and left chirality are discussed.

Analysis of Stress Distribution in a Curved Functionally Graded Porous Beam Using the Unified Shear Deformation Theory

Using unified shear deformation theory (USDT) and a modified power law, the current study examines bending properties of two-dimensional functionally graded curved porous beam. In order to improve accuracy, this method incorporates equilibrium equations, potential energy, and the idea of a neutral surface. The analysis uses a boundary conditions, namely simply supported . A functionally graded beam composed of metal and ceramic with both even and unequal porosity is modeled. The formulation takes into account the symmetrical material gradation, which guarantees alignment between the geometrical and physical neutral surfaces. A displacement-based formulation and energy concepts are used, which leads to a more thorough and accurate beam analysis. This approach effectively regulates the constant changing of material characteristics in FGMs, takes into consideration higher-order shear deformation effects, and does away with the requirement for shear correction factors. As a result, it improves structural behavior predictions, which makes USDT very useful for advanced material applications. The equilibrium equations for the beams are derived using the Hamilton technique and solved with the Kuhn-Tucker conditions.

Wave propagation in beams with functionally graded porosity distribution under highly transient axial and transverse impacts

Recent advances in the manufacturing process provide a possibility of fabricating a new generation of porous materials denoted by functionally graded porous materials (FGPM). This paper aims to present a time domain analysis of wave propagation through the porous structures with functionally graded porosity distribution, which has not been completely studied before. For this purpose, the beams with different functionally graded porosity distributions subjected to both axial and transverse tip impact loads with a high-frequency content are investigated. The shear deformable cantilevered functionally graded porous beams with various porosity distributions through the beam thickness are studied. The governing differential equations are derived using the Hamiltonian principle based on the Timoshenko beam theory. A locking-free first-order shear deformable beam element is used to derive the finite element formulation of the equations. The Newmark time integration method is used to perform a time domain analysis of the equations of motion and to investigate the transient response of the beams. The axial and transverse wave propagation characteristics through functionally graded (FG) porous beams are found using time domain analysis of the results. Deflection and velocity time histories of the tip and each point of the beam, reflection time, and variation of support reactions are obtained. The influences of the porosity magnitude and porosity distribution on the wave propagation characteristics and overall time responses are investigated. The results reveal that porosity distribution has a significant effect on the wave amplitude, wave speed, and reflection from the boundary. Also, this study can help in a better understanding of porous structures' behavior subjected to high-transient impact loads in different engineering applications.

Mechanical properties prediction and design of curved beams by neural network

It is known that curved beams are used widely in vibration isolation and noise reduction. The curved beam can show bistable, negative stiffness and other mechanical characteristics in the compression process through design. The preflex beam absorbs energy during the multi-state jump process and can recover its initial configuration after undergoing loading and unloading, so it is an ideal energy absorb component. In this paper, preflex beams are designed and the mechanical properties are studied and predicted by neural network. Firstly, a large number of finite element models for sinusoidal preflex beams are built by using Python randomly selected the parameters of beams. Secondly, the dataset corresponding to the parameters of the beams and mechanical properties is established. The variation trend of mechanical properties such as initial stiffness, force threshold, negative stiffness and total absorbed energy with the change of structural parameters and the sensitivity of structural parameters to the above mechanical indexes are obtained. Thirdly, by substituting the data set into the artificial neural network, the trained neural network can predict the mechanical properties of the beams within the allowable error range. At last, a new type of preflex beam with porous section is proposed in order to optimize the specific absorbed energy of the preflex beam. After data screening and optimization, the specific absorbed energy of the porous preflex beam is increased by 15.56 % compared with the beam whose section without porous. The results obtained show that the data-driven method can greatly shorten the structural design time and expand the design space. This study will provide a theoretical basis for the wider application of preflex beams in engineering field.

A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams

The free vibration and buckling behaviours of 2D-FG porous microbeams are explored in this paper utilizing the Quasi-3D beam deformation theory based on the modified couple stress theory and a Differential Quadrature Galerkin Method (DQGM) systematically, as a combination of the Differential Quadrature Method (DQM) and the semi-analytical Galerkin method, which has used to reduce computational cost for problems in dynamics. The governing equations are obtained using the Lagrange’s principle. The mass and stiffness matrices are calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The matrices are expressed in a similar form to that of the Differential Quadrature Method by introducing an interpolation basis on the element boundary of the Galerkin method. The sampling points are determined by the Gauss-Lobatto node method. The influence of the thickness-to-material length scale parameter (MLSP) on the nondimensional natural frequencies and nondimensional critical buckling loads of 2D-FG porous microbeams are investigated, along with the effects of the boundary condition, aspect ratio and gradient index. The results are validated with literature to establish the accuracy of the procedure described. This work will provide a numerical basis for the design of FG microstructures in the field of micromechanics. These results can be applied to the engineering design of porous FG microstructures.

Analytical modelling of a multifunctional heterogeneous beam-bending analysis

Pores have a crucial role in shaping the features of functionally graded materials. If the distribution of pores is permitted to gradually rise from the outside inwards towards the center, many more features can be incorporated. A shear shape function is used to analyze the bending response of a two-directional functionally graded porous beam (FGPB), which can be considered a multifunctional heterogeneous material while accounting for both even as well as uneven porosity distributions. The power law is adapted to modify the material properties of FGPB through out the length and thickness dimensions. The notion of virtual displacements is applied when establishing equilibrium equations in FGPB. The Navier method is applied to clamped-clamped, clamped-free boundary conditions and simply supported boundary conditions to offer solutions to FGPB. The proposed methodology is supported by the numerical results of functionally graded beams from earlier studies. The dimensionless deflections and stresses under study are affected by gradient exponents, porosities, and aspect ratios.

New Enriched Beam Element for Static Bending Analysis of Functionally Graded Porous Beams Resting on Elastic Foundations

New Enriched Beam Element for Static Bending Analysis of Functionally Graded Porous Beams Resting on Elastic Foundations

Efficient buckling and post-buckling analysis of porous FG sandwich beams by new RPIM-HOCM mesh-free approach

The main purpose of this paper is to analyze buckling and post-buckling behavior of porous functionally graded (FG) beams and sandwich beams using a new efficient optimal mesh-free high order algorithm. The proposed solver combines mesh-free approach based on radial point interpolation method with high order continuation method (RPIM-HOCM). It is assumed that the FG beam and FG layers of sandwich beam are made from a mixture of ceramic and metal such that bottom surface of the plate is metal-rich, whereas top surface is ceramic-rich. So, constitutive equation as well as material properties are considered to change smoothly and gradually in the thickness direction via a mathematical relationship distribution. Non-linear strong form of the beam buckling problem which is based on the first-order shear deformation theory (FSDT) is derived using the virtual displacements theorem. The proposed coupling (RPIM-HOCM) is presented and validated firstly by comparing obtained numerical results with those computed using a reference algorithm. Then, RPIM-HOCM solver is used to investigate the effect of power-law index, porosity distribution, span-to-height ratio, boundary conditions and skin-core–skin thickness ratio on critical buckling load and post-buckling behavior.