Foundation Parameters Research Articles

Modal analysis of plates resting on elastic foundation based on the first-order shear deformation theory and finite element method

This paper investigates the free vibration characteristics of plate structures supported by a Pasternak elastic foundation, utilizing the first-order shear deformation theory (FSDT). FSDT simplifies the plate theory by considering only first-order shear deformation, enhancing formulation simplicity. Additionally, employing plate theory reduces computational complexity, as 2D models entail fewer degrees of freedom compared to their 3D counterparts. The finite element method (FEM) with 8-node quadrilateral element is employed for computational analysis, implemented using MATLAB. First, a comparison is made with some existing data to show the accuracy and reliability of the research. Numerical examples are then presented of the influence of the effects of thickness variation, foundation parameters and boundary conditions on frequency are investigated. The results show that the method converges very fast and reliability when compared to other research findings. The results of the research can be applied to many different engineering applications related to plates resting on elastic foundation.

A Design Review for Biomedical Wireless Power Transfer Systems with a Three-Coil Inductive Link through a Case Study for NICU Applications

This paper outlines a design approach for biomedical wireless power transfer systems with a focus on three-coil inductive links for neonatal intensive care unit applications. The relevant literature has been explored to support the design approach, equations, simulation results, and the process of experimental analysis. The paper begins with a brief overview of various power amplifier classes, followed by an in-depth examination of the most common power amplifiers used in biomedical wireless power transfer systems. Among the traditional linear and switching amplifier classes, class-D and class-E switching amplifiers are highlighted for their enhanced efficiency and straightforward implementation in biomedical contexts. The impact of load variation on these systems is also discussed. This paper then explores the basic concepts and essential equations governing inductive links, comparing two-coil and multi-coil configurations. In the following, the paper discusses foundational coil parameters and provides theoretical and experimental analysis of both two-coil and multi-coil inductive links through step-by-step measurement techniques using lab equipment and addressing the relevant challenges. Finally, a case study for neonatal intensive care unit applications is presented, showcasing a wireless power transfer system operating at 13.56 MHz for powering a wearable device on a patient lying on a mattress. An inductive link with a transmitter coil embedded in a mattress is designed to supply power to a load at distances ranging from 4 cm to 12 cm, simulating the mattress-to-chest distance of an infant. the experimental results of a three-coil inductive link equipped with a Class-E power amplifier are reported, demonstrating power transfer efficiency ranging from 75% to 25% and power delivery to a 500 Ω-load varying from 340 mW to 25 mW over various distances.

Effects of new nonlinear curvature models and non-local elasticity on buckling investigation of FG tapered nano-beams locating on elastic foundations

New nonlinear curvature models are proposed to show their effects on the compressive critical buckling load on functionally graded (FG) tapered nano-beams locating on elastic foundations in the presence of non-local elasticity. Fourth and fifth orders finite difference methods (bvp4c and bvp5c) are applied on the governing differential equation which is a highly non-linear, due to curvature and has variable coefficients, due to properties. Dimensional analyses have been applied on the governing system together with the problem conditions to produce their dimensionless forms. For different considered parameters, the critical buckling load is computed using the eigenvalue theorem. The effects of nonlinear curvature, variable Young modulus, variable moment inertia and foundation parameters are studied and displayed in tables and figures. The stability and convergence of the present solution are tested using more than one strategy as: comparison with available results, comparison between bvp4c and bvp5c with different mesh intervals and tolerances of truncation errors. These comparisons show that, the new curvature model affects the critical buckling with different ratios depending on variability of properties and foundation parameters. The new results show that the nonlinear curvature model reduces the critical buckling load in comparison with the classical linear model, which, leads to decreasing in factor of safety in design of structures. The new results show that the design of structures will be influenced with the new reduction of the compressive critical buckling load, since it may affect the factor of safety in design of structures. The new results can lead, generally, to more reduction of critical buckling load for large or small input parameters and it will affect other critical values such that frequencies. The introduced Tables and Figures of the present problem with comparisons of previously exact, analytical and numerical works establish the higher accuracy and stability of current findings using bvp4c or bvp5c with preferable of the later. This study is related to some practical applications such as aeronautical and structural engineering.

A meshfree formulation for size-dependent thermal buckling and post-buckling behaviour of porous microplates on elastic foundation subjected to localized heating

The semi-analytical framework is developed for in-plane thermal stresses within the microplates under localized heating. Localized heating is modelled using Fourier Series expansions over the complete domain of the plate. These stresses within the plate are estimated after solving the in-plane thermoelasticity problem using Airy's stress approach. Utilizing these stresses, present work also studies the buckling and post-buckling behaviour of a porous metal foam microplate resting on Winkler and Pasternak elastic foundations. The plate is modelled using Reddy's third-order shear deformation theory (TSDT) and von Kármán geometric nonlinearity, and the size-dependent effects are included using the modified strain gradient theory (MSGT). Galerkin's weighted residual method converts the partial differential equations (PDEs) into algebraic equations. The post-buckling equilibrium path is obtained using the modified Newton-Raphson method. The mode shapes of the microplate for the various configurations of the plate with different boundary conditions due to localized thermal loading are plotted. Also, these mode shapes are compared with the mode shapes of the microplate due to in-plane mechanical loading. The parametric effect of porosity, elastic foundation parameters, thickness of plate, size of plate, boundary conditions and loading concentrations on the buckling and post-buckling behaviour of the plate is studied.

On the Applications of a New Advanced PEPFG Mathematical Model for HTM Dynamic Behavior of SDF Sandwich Plates

Considering the crucial role of the flexoelectricity phenomena (the electrical polarization–strain gradient coupling) in the mechanical behavior of different structures on the micro/nanoscale, this paper is derives the motion equations of a size-dependent flexoelectric (SDF) sandwich plate to study its hygro-thermo-mechanical (HTM) dynamic behavior. The model is a three-layer microplate including a porous exponential and power–law functionally graded (PEPFG) mid-layer, and two flexoelectric face sheets. The whole structure is under hygrothermal loading and the Vlasov foundation serves as the stand for the structure. Then, Hamilton’s principle and modified couple stress theory (MCST) are implemented to derive the motion equations. The new PEPFG utilization besides evaluating the impact of the length scale parameter, hygrothermal loading, materials composition, porosity, foundation parameter, and boundary conditions on the normalized natural frequency (NNF) of such an SDF sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes NNF and stiffness reduction in the model. Furthermore, among all considered boundary types, simply supported and clamped refer to the lowest and the highest NNFs, respectively. This paper serves as a good source to provide a better understanding of the dynamic response of high stiffness-to-weight ratio structures to different variable variations.

Nonlinear thermo-mechanical static stability analysis of FG-TPMS shallow spherical shells

An analytical solution for the nonlinear static stability problem of functionally graded triply periodic minimal surface (FG-TPMS) shallow spherical shells is studied in the current research for the first time. Three common TPMS structures including Primitive (P), Gyroid (G), and I-graph and Wrapped Package-graph (IWP) with three models of functionally graded porosity distribution along the thickness are considered. The shallow spherical shells (shallow SSs) are subjected to combined thermo-mechanical loadings and rested on a nonlinear elastic foundation. The fundamental formulas are expressed based on the higher-order shear deformation theory (HSDT) and von Kármán's geometrical nonlinearities. Employing the Ritz energy minimization method, the explicit relationship between load and deflection is derived. Subsequently, the static stability behavior of FG-TPMS shallow SSs is investigated. Numerical illustrations are investigated to show the superior thermo-mechanical load-carrying performance of the FG-TPMS SSs compared to corresponding isotropic structures of the same weight. The significant effects of geometric parameters, nonlinear elastic foundation parameters, and the type of FG-TPMS structures on the nonlinear static stability behavior of shallow SSs are further considered.

An analytical modelling of free vibration in porous FG-CNTRC plate resting on elastic foundations

This paper presents an analytical investigation of the vibrations of porous functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate resting on elastic foundations. The plates are reinforced with randomly oriented straight carbon nanotubes, featuring four distinct reinforcement distribution patterns along the thickness. Material properties of the porous FG-CNTRC are graded along the thickness, with both symmetric and asymmetric porosity distributions considered. Utilizing high-order shear deformation theory (HSDT), the equations of motion are derived from Hamilton’s energy principle, and Navier’s method is employed for the solutions. The simply supported plate is assumed to rest on Winkler/Pasternak elastic foundations. The study examines the effects of various parameters, including CNT volume fractions, CNT distribution patterns, thickness ratio (a/h), aspect ratio (a/b), porosity coefficient, and elastic foundation parameters, on the dimensionless frequency parameter.

Research on the vertical compressive bearing characteristics of offshore wind power steel pipe piles

In the absence of a comparison of static load test results for large-diameter steel pipe piles at home and abroad, optimize the design parameters based on the test pile results to guide later construction. This paper is based on the pile foundation design calculation method of API specification, as well as the relationship between the t-z, Q-z, p-y curve modes suggested by this specification, vertical ultimate bearing capacity, and stratum parameters. The conclusions and results obtained are limited to pile foundation calculations using API specifications. Analyze and back-analyze the results of static load tests on large-diameter steel pipe piles, and verify the pile foundation parameters. Combined with the data obtained from the test pile tests, analyze the stratum parameters to guide the optimization design of pile foundations in the construction drawing design stage of the offshore wind farm expansion project.

Thermal vibration analysis of bi-directionally stepped porous functionally graded plates with segment-specific material property variation supported by Kerr foundation

This paper presents a comprehensive analysis of the nonlinear dynamic response of stepped rectangular plates made of functionally graded porous material (FGPM), supported by the Kerr foundation, in a thermal environment. A novel analytical framework is developed to explore geometric and material variations. The study investigates structural variations in plate thickness with abrupt changes in uni- or bi-directional orientations, examining both single and double stepped thickness profiles. Material properties vary with thickness, featuring distinct horizontal discontinuities across plate segments. Porosity distributions, both even and uneven, are addressed using modified mixture rules. Nonlinear kinematic relationships are established using Reddy’s third-order shear deformation plate theory and von Kármán’s nonlinear geometric assumptions, with equations of motion solved via Galerkin’s technique. This improved model effectively addresses non-continuous thickness variation through integral calculus, enhancing computational efficiency. Validation is achieved by comparing outcomes with published literature and Finite Element Analysis (FEA). The study investigates the influence of material properties, elastic foundation, boundary conditions, and geometric parameters on the free vibration and nonlinear behaviors of the plates. Some of the key findings include: increasing the thickness of the stepped segment significantly heightens the fundamental frequency while reducing vibrational amplitudes; optimizing the location of the stepped segment directly impacts the plate’s fundamental frequency and vibrational amplitudes; and as the load factor increases, the difference between linear and nonlinear deflection becomes evident. Therefore, accurate FGPM stepped plate design requires incorporating nonlinear terms in the strain–displacement relationships. Suggestions for future model modifications are also discussed, contributing to advancements in structural design and analysis.

Nonlocal strain gradient-based nonlinear vibration analysis of nonlinear FG three-phase HJCNT/MWCNT/epoxy composite microbeam resonators using a modified micromechanical model

This paper aims to study nonlinear dynamic behavior of functionally graded (FG) three-phase composite microbeam resonators made of an epoxy matrix and two reinforcements namely multi-walled carbon nanotubes (MWCNTs) and hetero-junction carbon nanotubes (HJCNTs). The effective mechanical properties of the composite microbeam are obtained using the modified Halpin-Tsai micromechanical model. The microbeam surrounding medium is simulated using a two-parameter elastic foundation. The von-Karman’s geometric nonlinearity relations are incorporated and the equations of motion are derived based on the nonlocal strain gradient Euler–Bernoulli beam model. A new closed-form analytical solution is obtained using the homotopy perturbation method. The effects of vibration amplitude, nanofiber volume fraction, nanofiber distribution pattern, small-scale parameters and the foundation parameters on the nonlinear frequency and deflection of the FG three-phase composite microbeams are studied in detail. The findings of the paper are valuable for researchers in the field of microbeam resonators.

Sagittal spinal alignment measurements and evaluation: Historical perspective

Spinal alignment analysis play an important role in evaluating patients and planning surgical corrections for adult spinal deformity. The history of these parameters is relatively short with the first parameter, the Cobb angle, introduced in 1948 as part of an effort to improve scoliosis evaluation. New developments in the field were limited for nearly 30 years before better imaging technology encouraged new theories and later data about spinal alignment and the relationship between the spine and pelvis. These efforts would ultimately contribute to the creation of foundational spinal alignment parameters, including pelvic incidence, pelvic tilt, and sacral slope. By the 1990s, spinal alignment had become a sustained area of investigation for spinal surgeons and researchers. Novel alignment parameters have since been introduced as our knowledge has evolved and has allowed for valuable research that demonstrates the clinical and surgical value of alignment measurement. This manuscript will explore the history of spinal alignment analysis over the decades.

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Electro-mechanical vibration characteristics of imperfect sandwich FG piezoelectric honeycomb nanoplates resting on Kerr foundation

This study presents an innovative analytical approach to examine the electro-mechanical vibration characteristics of sandwich nanoplates featuring a honeycomb core and two surface layers composed of imperfect piezoelectric functionally graded (FG) material, incorporating porosities, atop a Kerr elastic foundation. Utilizing nonlocal elasticity theory and four-variable refined plate theory (HSDT-4), we account for nanoscale effects and model the electric potential variation across the piezoelectric layer thickness as a combination of cosine and linear variations satisfying Maxwell's equation. The proposed method's novelty lies in its comprehensive analysis of the interplay between porosity, elastic foundation parameters, material properties, geometrical dimensions, external voltage, and nonlocal parameters on the free vibration frequency of these nanostructures. Numerical simulations validate the model's reliability and assess the significant impacts of these factors. Our findings contribute to the optimization of nanostructural designs for advanced engineering applications, highlighting the method's added value in predicting the behavior of imperfect piezoelectric FG honeycomb nanoplates.

The Effect of Hyperelasticity and Nonlinearity on the Dynamic Behaviors of Hyperelastic Functionally Graded Beams on Nonlinear Elastic Foundation

Hyperelastic functionally graded materials have a wide range of application prospects in soft robotics and biomedical fields. This paper investigates the nonlinear free and forced vibrations of a hyperelastic functionally graded beam (HFGB) based on higher-order shear deformation beam theory. The geometrical nonlinearity is considered by using the von-Kármán’s nonlinear theory. The three-material-parameter free energy function named as Ishihara model is employed to characterize the hyperelastic material. The power-law gradient form along the thickness direction is adopted. The HFGB is resting on the elastic foundation. The Winkler, Pasternak and nonlinear stiffness coefficients are considered. The time-harmonic external force is applied to the HFGB. The nonlinear governing equations for the vibration of the HFGB are derived by using Hamilton’s principle, and are subsequently transformed into ordinary differential equations via Galerkin’s method. The nonlinear free vibration and primary resonance of the HFGB are investigated analytically by employing the extended Hamiltonian method and multiple scales method, respectively. The results indicate that the power-law index, slenderness ratio, material properties, and elastic foundation parameters have significant influences on the nonlinear frequency of free vibration as well as the frequency–response and force–response curves of forced vibration. The phase plane method is employed to analyze the system’s stability states under various excitation amplitudes. The relative error between the results of the current computational model and the published literature is less than 0.1 percent.

A novel dynamic stiffness matrix for the nonlocal vibration characteristics of porous functionally graded nanoplates on elastic foundation with small-scale effects

The present paper deals with the development of a dynamic stiffness matrix to evaluate the free vibration response of functionally graded nanoplate (FG-nP) resting on the Winkler-Pasternak elastic foundation. The complete mathematical modeling of the dynamic stiffness matrix for nanostructures is given for the first time. The equation of motion for rectangular FG-nP plates supported on an elastic foundation is derived using Hamilton’s principle in conjunction with nonlocal elasticity theory. The non-local theory is incorporated to account for the size effect in the small-scale plate. The effective material property of the porous FG-nP has been calculated using three recently developed models of porosity. The developed dynamic stiffness matrix is solved using the Wittrick-Williams algorithm to extract the natural frequencies of the FG-nP. The variation of natural frequencies with the change of numerical values, such as nonlocal parameter, aspect ratio, elastic foundation parameters, and porosity volume fraction is analyzed. The validity and accuracy of the results are confirmed through comparison with the available literature. The use of non-local theory in dynamic stiffness analysis is shown to be effective in predicting the natural frequency of the FG-nP on a Winkler-Pasternak elastic foundation, providing new insights into the dynamic behavior of small-scale structures.

Three-dimensional hygro-thermo-mechanical bending analysis of anisotropic skewed parallelogram plates on a tri-parameter foundation using a wavelet method

In the paper, a brand-new three-dimensional hygro-thermo-mechanical bending model of anisotropic skewed parallelogram plates with extreme skew angle in large deformation supported by a tri-parameter nonlinear elastic foundation is proposed. By investigating the mutual coupled interaction of hygrothermal effects between in-plane distribution and thickness variation, nine kinds of spatially analytical hygrothermal fields in parallelogram domain are established by analyzing the Dirichlet, Neumann and Robin thermal boundary conditions of sinusoidally induced heat conduction at top and bottom surfaces. With coordinate transformation in oblique system considering the Von Kármán membrane strains, the highly coupled and strongly nonlinear governing partial differential equations have been derived. A wavelet solving procedure has been developed with the convergence process validated and precision of obtained solutions verified in good accordance with published results. Parametric studies have been carried out to investigate the large-deflection behavior of simply supported or clamped skew plates on Winkler–Pasternak foundation under combined mechanical and hygrothermal loads. The influence of skew angle, material orthotropy and foundation contact nonlinearity is examined, which reveals the geometrically nonlinear responses of plates are highly affected by large oblique angle, principle orientation of material orthotropy and foundation parameters.

Investigation of moving load-induced vibrations in layered functionally graded Terfenol-D beams: a differential quadrature method and analytical approach

The paper investigates the potential of the full-sinusoidal Fourier series as a solution form for the deflection of layered functionally graded beams associated with smart actuators, drawing on the fundamental principles of classical Fourier series theory. The current method simplifies the difficult beam problem to a set of linear algebraic equations by using the Duhamel integration technique and the orthogonality of the trial function. The study takes into account generalized boundary conditions and moving forces, which are seldom discussed in previous research. Under the action of a moving load, the boundary value problem for a functionally graded beam integrated with Terfenol-D is efficiently addressed using the approach of combined differential and integral quadrature. The generalized boundary conditions may be easily achieved by adjusting the stiffness of the restraining springs. The significant agreement between the differential quadrature solution and the Fourier series solution underlines the efficiency and accuracy of both methods. Furthermore, the influences of various crucial physical characteristics on the natural frequencies and the essential flow velocities are explored, including boundary stiffness, foundation parameters, and geometric parameters.

Frequency Analysis of Asymmetric Circular Organic Solar Cells Embedded in an Elastic Medium under Hygrothermal Conditions

This research represents the first theoretical investigation about the vibration behavior of circular organic solar cells. Therefore, the vibration response of asymmetric circular organic solar cells that represent a perfect renewable energy source is demonstrated. For this purpose, the differential quadrature method (DQM) is employed. The organic solar cell is modeled as a laminated plate consisting of five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. This cell is rested on a Winkler–Pasternak elastic foundation and assumed to be exposed to various types of hygrothermal loadings. There are three different kinds of temperature and moisture variations that are taken into account: uniform, linear, and nonlinear distribution throughout the cell’s thickness. The displacement field is presented based on a new inverse hyperbolic shear deformation theory considering only two unknowns. The motion equations including hygrothermal effect and plate–foundation interaction are established within the framework of Hamilton’s principle. The DQM is utilized to solve these equations. In order to ensure the accuracy of the proposed theory, the present results are compared with those reported by other higher-order theories. A comprehensive parametric illustration is conducted on the impacts of different parameters involving the geometrical configuration, elastic foundation parameters, temperature, and moisture concentration on the deduced eigenfrequency of the circular organic solar cells.

Environmental Microvibration Analysis Method for Vibration Isolation Research in High-Precision Laboratories

Environmental microvibrations, often originating from unidentified sources, pose a significant challenge for predicting and controlling their complex wave fields, potentially leading to measurement errors of sensitive instruments in high-precision laboratories and impacting the accuracy of experimental outcomes. Therefore, investigating effective control measures for environmental microvibrations under passive conditions is key to addressing such engineering issues. This paper presents a finite element analysis method tailored to address environmental microvibrations in the absence of apparent sources. This method involves obtaining the vibration time history at specific ground surface points through field measurements and combining the Rayleigh wave velocity attenuation character with depth at the center frequencies of one-third octave bands within the 1–100 Hz frequency range; the vibration time history at any depth in the soil is calculated. These calculated vibrations are then applied as input loads to the corresponding nodes on one boundary of the foundation–soil model, serving as the source of environmental microvibrations. The predicted results are compared with measured data and the empirical point source input method, indicating that this approach is more precise and efficient, providing valuable reference for the prediction and analysis of environmental microvibrations. In addition, utilizing this method, the study examines the effects of pile foundation parameters such as the pile length, burial depth, and concrete baseplate thickness on the vibration isolation performance of environmental microvibrations, providing guidance for designing pile foundation isolation.

Three-dimensional elastoplastic post-buckling analysis of porous FG plates resting on Winkler/Pasternak foundation using meshless RRKPM

This paper presents a three-dimensional (3D) analysis of the elastoplastic post-buckling behavior of porous functionally graded (FG) plates resting on Winkler/Pasternak foundations under uniaxial and biaxial in-plane loadings using an enhanced meshless approach. The principle of virtual work is used to derive the governing equations, and 3D nonlinear Green–Lagrange strains are considered. Plastic deformation is modeled employing the Prandtl–Reuss flow law and the isotropic hardening von Mises criterion. A novel meshless radial basis reproducing kernel particle approach is used to obtain the discretized system of equations. The Newton–Raphson method, coupled with the arc-length technique, is used to compute post-buckling paths of porous FG plates. Numerical assessments show that post-buckling paths are significantly influenced by porosity parameter, porosity distribution, foundation parameters, material gradient, plate thickness, loading ratio, and boundary conditions (BCs).