Beam Thickness Research Articles

Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect

In this paper, based on the extended dielectric theory, Euler beams theory and von Karman’s geometric nonlinearity, a nonlinear FGM piezoelectric microbeam model is established with flexoelectric effect. The governing equations, initial conditions and boundary conditions are obtained by applying Hamilton’s principle and then solved by combining the differential quadrature method (DQM) and iteration method. The innovation of this paper is to construct a nonlinear forced vibration model of piezoelectric microbeams. The coupling response between the inverse flexoelectric effect and the inverse piezoelectric effect is investigated. Various effects are examined, including the functional gradient index m and transverse distributed load q affecting the distribution of electric potential. Results indicated that the functional gradient index m, beam thickness h, and span-length ratio L/h have a significant impact on the dimensionless deflection of the FGM microbeam. The influence of the flexoelectric effect on dimensionless deflection increases with the decrease of scale. In addition, transverse load q and the functional gradient index m also have a significant impact on the distribution of electric potential. This paper will provide useful theoretical guidance for the design of micro-sensors and micro-actuators.

First Principles Variational Formulation and Analytical Solutions for Third Order Shear Deformable Beams with Simple Supports using Fourier Series Method

The Fourier series method for solving bending problems of third-order shear deformable beams (TSBD) is presented in this paper. The theory accounts for transverse shear deformation and is suitable for moderately thick beams. Transverse shear stress-free conditions are valid at the beam surfaces for TSDB. The field equations are two coupled ordinary differential equations in terms of two unknown displacement functions – transverse deflection w(x) and warping function For simply supported ends considered, the loading and unknown functions w(x) and are represented in Fourier series that satisfies the boundary conditions. The problem is reduced to a system of algebraic equations in terms of the Fourier coefficients wn and which is solved to obtain wn and Axial and transverse displacements fields, axial bending stress and transverse shear stress are then determined for the cases of point load at midspan, uniformly and linearly distributed loads over the span. The results are identical with previous results obtained by other scholars who used Ritz variational methods and other mathematical tools. For moderately thick beams under uniform load with l/h = 4, the results obtained for is 0.516% greater than the exact result by Timoshenko and Goodier while for thick beams under uniform load with l/h = 2, the result for is 1.96% greater than the exact result by Timoshenko and Goodier. Similar acceptable variation was obtained for for beams under linearly distributed load with the variations being less than 2% for l/h = 2. However, unacceptable variations of 68.37% were found for in thick beams under point load, for l/h = 2.0. The variation for however reduced to 12.513% for moderately thick beams under point load for l/h =4.

Extending the Natural Neighbour Radial Point Interpolation Meshless Method to the Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core

This work investigates the mechanical behaviour of sandwich beams with cellular cores using a multiscale approach combined with a meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The analysis is divided into two steps, aiming to analyse the efficiency of NNRPIM formulation when combined with homogenisation techniques for a multiscale computational framework of large-scale sandwich beam problems. In the first step, the cellular core material undergoes a controlled modification process in which circular holes are introduced into bulk polyurethane foam (PUF) to create materials with varying volume fractions. Subsequently, a homogenisation technique is combined with NNRPIM to determine the homogenised mechanical properties of these PUF materials with different porosities. In this step, NNRPIM solutions are compared with high-order FEM simulations. While the results demonstrate that RPIM can approximate high-order FEM solutions, it is observed that the computational cost increases significantly when aiming for comparable smoothness in the approximations. The second step applies the homogenised mechanical properties obtained in the first step to analyse large-scale sandwich beam problems with both homogeneous and functionally graded cores. The results reveal the capability of NNRPIM to closely replicate the solutions obtained from FEM analyses. Furthermore, an analysis of stress distributions along the beam thickness highlights a tendency for some NNRPIM formulations to yield slightly lower stress values near the domain boundaries. However, convergence towards agreement among different formulations is observed with mesh refinement. The findings of this study show that NNRPIM can be used as an alternative numerical method to FEM for analysing sandwich structures.

Energy absorption of auxetic honeycomb with graded beam thickness based on Bezier curve

In order to improve the energy absorption and lightweight of the structure, a novel auxetic honeycomb with graded beam thickness based on Bezier curve (BZH) is proposed on the basis of the double arrow negative Poisson ratio honeycomb. The finite element model of BZH under axial compression is established, and its accuracy is verified by experiments. Compared with a honeycomb of uniform beam thickness (DUH) of the same mass, the thickness of the beam becomes thicker in the middle and thinner on both sides, which causes the BZH to produce more plastic hinges when compressed, and the energy absorption is increased by 12 %. By parameter analysis of beam thickness distribution trend, the mechanical properties of BZH can be effectively controlled. A theoretical model of BZH under quasi-static compression is also established and the BZH configuration is optimized by proxy modeling technique and NSGA-II algorithm. The results show that the SEA of the optimized structure is increased from 5.23 kJ·kg-1 to 6.17 kJ·kg-1, and the energy efficiency is reduced from 3.44 kN to 2.96 kN. Therefore, auxetic honeycomb with graded beam thickness based on Bezier curve has great potential in the field of energy absorption.

Nanodosimetric investigation of the track structure of therapeutic carbon ion radiation part 1: measurement of ionization cluster size distributions

At the Heidelberg Ion-Beam Therapy Center, the track structure of carbon ions of therapeutic energy after penetrating layers of simulated tissue was investigated for the first time. Measurements were conducted with carbon ion beams of different energies and polymethyl methacrylate (PMMA) absorbers of different thicknesses to realize different depths in the phantom along the pristine Bragg peak. Ionization cluster size (ICS) distributions resulting from the mixed radiation field behind the PMMA absorbers were measured using an ion-counting nanodosimeter. Two different measurements were carried out: (i) variation of the PMMA absorber thickness with constant carbon ion beam energy and (ii) combined variation of PMMA absorber thickness and carbon ion beam energy such that the kinetic energy of the carbon ions in the target volume is constant. The data analysis revealed unexpectedly high mean ICS values compared to stopping power calculations and the data measured at lower energies in earlier work. This suggests that in the measurements the carbon ion kinetic energies behind the PMMA absorber may have deviated considerably from the expected values obtained by the calculations. In addition, the results indicate the presence of a marked contribution of nuclear fragments to the measured ICS distributions, especially if the carbon ion does not cross the target volume.

A peridynamic formulation for planar arbitrarily curved beams with Timoshenko–Ehrenfest beam model

In this study, a peridynamic formulation is proposed for analysis of planar arbitrarily curved beams. Assumptions of Timoshenko–Ehrenfest beam model are considered such that linear kinematic relations are described by displacements of the beam axis and rotation of the cross-section. Equilibrium conditions and boundary conditions are derived by means of the principle of virtual work. Then, peridynamic functions are constructed, and incorporated with equilibrium conditions to develop a peridynamic formulation. Several examples are exhibited to examine the performance of the proposed formulation in some regards, i.e., numerical accuracy, convergence properties, and locking effects. It is delineated that the proposed formulation provides a good level of precision for the analysis of relatively thick beams. However, membrane and shear locking effects are present in the analysis of slender beams, and peridynamic functions of higher polynomial degree can be used to mitigate these unfavorable effects.

Lamina Cribrosa Microstructure in Nonhuman Primates With Naturally Occurring Peripapillary Retinal Nerve Fiber Layer Thinning.

The lamina cribrosa (LC) is hypothesized to be the site of initial axonal damage in glaucoma with the circumpapillary retinal nerve fiber layer thickness (RNFL-T) widely used as a standard metric for quantifying the glaucomatous damage. The purpose of this study was to determine in vivo, 3-dimensional (3D) differences in the microstructure of the LC in eyes of nonhuman primates (NHPs) with naturally occurring glaucoma. Spectral-domain optical coherence tomography (OCT) scans (Leica, Chicago, IL, USA) of the optic nerve head were acquired from a colony of 50 adult rhesus monkeys suspected of having high prevalence of glaucoma. The RNFL-T was analyzed globally and in quadrants using a semi-automated segmentation software. From a set of 100 eyes, 18 eyes with the thinnest global RNFL-T were selected as the study group and 18 eyes with RNFL-T values around the 50th percentile were used as controls. A previously described automated segmentation algorithm was used for LC microstructure analysis. Parameters included beam thickness, pore diameter and their ratio (beam-to-pore ratio [BPR]), pore area and shape parameters, beam and pore volume, and connective tissue volume fraction (CTVF; beam volume/total volume). The LC microstructure was analyzed globally and in the following volumetric sectors: quadrants, central and peripheral lamina, and three depth slabs (anterior, middle, and posterior). Although no significant difference was detected between groups for age, weight, or disc size, the study group had significantly thinner RNFL than the control group (P < 0.01). The study group had significantly smaller global and sectoral pore diameter and larger BPR compared with the control group. Across eyes, the global RNFL-T was associated positively with pore diameter globally. BPR and CTVF were significantly and negatively associated with the corresponding RNFL-T in the superior quadrant. Global and sectoral microstructural differences were detected when comparing thin and normal RNFL-T eyes. Whether these LC differences are the cause of RNFL damage or the result of remodeling of the LC requires further investigation. Our findings indicate structural alterations in the LC of NHP exhibiting natural thinning of the RNFL, a common characteristic of glaucomatous damage.

Deriving Ritz formulation for the Static Flexural Solutions of Sinusoidal Shear Deformable Beams

This paper presents the Ritz variational method for the static bending analysis of sinusoidal shear deformable beams. The theory accounts for transverse shear deformation and satisfies transverse shear stress-free conditions at the top and bottom surfaces of the beam. The total potential energy functional for the thick beam bending problem is formulated and minimized using a Ritz procedure. The problem considered simply supported boundary conditions and two cases of loading – uniformly distributed load over the span and point load at the center. The function is a function of two unknown displacement functions constructed in terms of unknown generalized displacement parameters and shape functions that satisfy the boundary conditions. Ritz minimization of the functional is used to find the generalized displacement parameters and then the displacements w(x) and The displacements and stresses are found for the loading distributions considered. It is found that the results obtained agree remarkably well with the exact results obtained using the theory of elasticity. The differences between the present results and the exact solutions are less than 0.3% for maximum transverse displacement for both cases of loading considered. For uniform load over the beam, the result for l/t = 10 is 0.112% greater than the exact solution. For the point load at the center, the result for l/t = 10 is 4.468% greater than the exact solution. The increased difference in the point load case is due to the singular nature of the point load problem.

Potential of Non-Contact Dynamic Response Measurements for Predicting Small Size or Hidden Damages in Highly Damped Structures.

Vibration-based structural health monitoring (SHM) is essential for evaluating structural integrity. Traditional methods using contact vibration sensors like accelerometers have limitations in accessibility, coverage, and impact on structural dynamics. Recent digital advancements offer new solutions through high-speed camera-based measurements. This study explores how camera settings (speed and resolution) influence the accuracy of dynamic response measurements for detecting small cracks in damped cantilever beams. Different beam thicknesses affect damping, altering dynamic response parameters such as frequency and amplitude, which are crucial for damage quantification. Experiments were conducted on 3D-printed Acrylonitrile Butadiene Styrene (ABS) cantilever beams with varying crack depth ratios from 0% to 60% of the beam thickness. The study utilised the Canny edge detection technique and Fast Fourier Transform to analyse vibration behaviour captured by cameras at different settings. The results show an optimal set of camera resolutions and frame rates for accurately capturing dynamic responses. Empirical models based on four image resolutions were validated against experimental data, achieving over 98% accuracy for predicting the natural frequency and around 90% for resonance amplitude. The optimal frame rate for measuring natural frequency and amplitude was found to be 2.4 times the beam's natural frequency. The findings provide a method for damage assessment by establishing a relationship between crack depth, beam thickness, and damping ratio.

Variable angle tow-steered fibres based rotating composite beam with rotary oscillations – Parametric excitation/instability analysis

This study is concerned with the stability analysis for various vibrational motions of tow-steered variable angle fibres based composite rotating beam with time varying speed. The formulation combines a higher order theory introducing sine function along with finite element methodology. It satisfies the plane stress condition in width direction of beam. The displacement kinematics are generic in the sense it includes various possible vibrational motions like chord and flap wise motions, torsional and axial vibration behaviours. The equilibrium equations for the proposed problem evolved adopting virtual dynamic work are then transformed into the equations of Mathieu-Hill type considering time varying harmonic rotational speed. Using Bolotin’s procedure coupled with C1 continuity-based beam element, the parametric resonance zones along with boundary limits are numerically evaluated. The eigenvalue type of solution methodology applied for the detailed study is validated for accuracy and computational efficiency against the time domain dynamic response analysis. Based on in-depth analysis, dynamic instability characteristics in terms of resonance range and origin of instability of composite beam subjected to the chord and flap wise, torsional and axial motions are studied considering curvilinear fibre path angles, beam cross section, hub radius, thickness ratio and mean rotary speed.

Reliability analysis of output electrical response performance of multi-state flexoelectric structures under single and multiple failure modes

This paper proposes a reliability model of flexoelectric beams in the electrical open and short circuit states when different failure modes and the multiple failure modes of the output electrical response performances are considered, respectively. The reliability indices of the flexoelectric beams in the two circuit states can be defined based on the output electrical response models. Sequentially, the importance sampling (IS) and the mixed importance sampling (IS) methods are respectively used to calculate the reliability of the flexoelectric beams in single and multiple failure modes. The reliability results of the flexoelectric beams are verified by comparing them with the results of the Monte Carlo Simulation (MCS). The numerical results show that the flexoelectric beam is entered into a relatively safe and reliable state when the critical value of the open circuit voltage of 0.235 V and the thickness of the flexoelectric beams of 1 mm are considered as well as the length-thickness ratio of 20.

Flexural performance of functionally graded UHPFRC-NSC beams

This paper presents an experimental and numerical study on the flexural performance of Functionally Graded Reinforced Concrete (FGRC) beams using Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) with Normal-Strength Concrete (NSC). The experimental results were used to examine the applicability of the codes’ predictions of flexural capacity adopted in ACI 318-2019, EC-2, and ECP-203-2020. The flexural design recommendations of AFGC-2013, JSCE-2008, and KCI-2012 were also examined. The experimental program involved ten simply supported beams with identical cross-sectional dimensions and two different tensile reinforcement ratios (ρl = 1.38 % and 5.68 %). FGRC beams consisting of UHPFRC (with fcu = 174.3 MPa) and NSC (with fcu = 45.8 MPa) were tested under four-point bending. The layer of UHPFRC was positioned either in the utmost compression region or in both the compression and tension regions. The experimental results revealed that the FGRC beams exhibited strength and ductility comparable to those of pure UHPFRC beams but at a significantly reduced cost. When UHPFRC layers constituted 66.7 % of beam thickness, the FGRC beams were capable of carrying 97.4 % of the load sustained by a full UHPFRC beam, while for UHPFRC layers constituted 40 % of beam thickness the FGRC beam carried 77.5 % of that of a full UHPFRC beam. Increasing ρl% from 1.38 % to 5.68 % in the tested specimens led to a considerable enhancement in the flexural capacity. The sectional analysis conducted in accordance with the recommendations of AFGC-2013, JSCE-2008, and KCI-2012 showed precise predictions of the flexural strength in both UHPFRC and FGRC beams, while the flexural strength calculated using the equations adopted in the studied codes gave conservative estimations. The proposed numerical model displayed a high level of agreement with the experimental findings of the studied FGRC beams.

Sensor-Enhanced Thick Laminated Composite Beams: Manufacturing, Testing, and Numerical Analysis.

This study investigates the manufacturing, testing, and analysis of ultra-thick laminated polymer matrix composite (PMC) beams with the aim of developing high-performance PMC leaf springs for automotive applications. An innovative aspect of this study is the integration of Fiber Bragg Grating (FBG) sensors and thermocouples (TCs) to monitor residual strain and exothermic reactions in composite structures during curing and post-curing manufacturing cycles. Additionally, the Calibration Coefficients (CCs) are calculated using Strain Gauge measurement results under static three-point bending tests. A major part of the study focuses on developing a properly correlated Finite Element (FE) model with large deflection (LD) effects using geometrical nonlinear analysis (GNA) to understand the deformation behavior of ultra thick composite beam (ComBeam) samples, advancing the understanding of large deformation behavior and filling critical research gaps in composite materials. This model will help assess the internal strain distribution, which is verified by correlating data from FBG sensors, Strain Gauges (SGs), and FE analysis. In addition, this research focuses on the application of FBG sensors in structural health monitoring (SHM) in fatigue tests under three-point bending with the support of load-deflection sensors: a new approach for composites at this scale. This study revealed that the fatigue performance of ComBeam samples drastically decreased with increasing displacement ranges, even at the same maximum level, underscoring the potential of FBG sensors to enhance SHM capabilities linked to smart maintenance.

Powder Bed Fusion Techniques in Metal 3D Printing: A Review

The use of 3D printing (additive manufacturing) with metal has grown significantly in demand recently, greatly reducing the time and expense required to produce complex interconnected metal components. This method minimizes material wastage, facilitates material recycling, and eliminates the need for support materials. Among the various Metal Additive Manufacturing techniques, Powder Bed Fusion (PBF) processes stands out as the most prevalent for manufacturing parts. Within the realm of PBF, electron beam melting technique, selective laser sintering technique, and selective laser melting technique are the primary methods employed. Selective laser melting and selective laser sintering operate without the need for any special conditions, unlike EBM, which necessitates a vacuum environment. Regarding the choice of materials, laser melting/sintering processes are suitable for almost all types of metals except those which surpasses beam melting capabilities. While electron beam melting is constrained to a few materials such as titanium alloys, cobalt and chromium alloys, and nickel alloys, whereas selective laser melting and sintering allows for a broad range of materials, including iron and steel alloys. However, electron beam melting exhibit the ability to process brittle materials that would typically be challenging for melting and sintering through laser. Nevertheless, the ductility, yield testing, and ultimate testing of materials created through EBM are inferior to those processed by laser methods. Although all PBF techniques excel at creating complex structures, finishing products to have a smooth surface directly over a rough surface remains a subject of ongoing research. To attain suitable mechanical properties such as hardness, tensile strength, and endurance, critical process factors include power of laser or beam, speed for scanning, density for powder bed, thickness of laser or beam, and material characteristics. Inadequate material selection coupled with incorrect process settings can lead to issues such as porosity, slag formation, and other flaws.

Investigation of Delamination Characteristics in 3D-Printed Hybrid Curved Composite Beams.

This study focuses on understanding the impact of different material compositions and printing parameters on the structural integrity of hybrid curved composite beams. Using the continuous filament fabrication technique, which is an advanced fused deposition modelling process, composite curved beams made of short carbon and various continuous fibre-reinforced nylon laminae were fabricated and subjected to four-point bending tests to assess their delamination characteristics. The results show that the presence of five flat zones in the curved region of a curved beam achieves 10% and 6% increases in maximum load and delamination strength, respectively, against a smooth curved region. The delamination response of a curved composite beam design consisting of unidirectional carbon/nylon laminae is superior to that of a curved beam made of glass fibre/nylon laminae, while the existence of highly strengthened glass fibre bundles is alternatively quite competitive. Doubling the number of continuous fibre-reinforced laminae results in an increase of up to 36% in strength by achieving a total increase in the beam thickness of 50%, although increases in mass and material cost are serious concerns. The hybrid curved beam design has a decrease in the maximum load and the strength by 11% and 13%, respectively, when compared with a non-hybrid design, which consists of some type of stronger and stiffer nylon laminae instead of short carbon fibre-reinforced conventional nylon laminae. Two-dimensional surface-based cohesive finite element models, which have a good agreement with experimental results, were also established for searching for the availability of useful virtual testing. The results from this study will greatly contribute to the design and numerical modelling of additively manufactured hybrid composite curved beams, brackets, and fittings.

Development and Investigation of a Grasping Analysis System with Two-Axis Force Sensors at Each of the 16 Points on the Object Surface for a Hardware-Based FinRay-Type Soft Gripper.

The FinRay soft gripper achieves passive enveloping grasping through its functional flexible structure, adapting to the contact configuration of the object to be grasped. However, variations in beam position and thickness lead to different behaviors, making it important to research the relationship between structure and force. Conventional research using FEM simulations has tested various virtual FinRay models but replicating phenomena such as buckling and slipping has been challenging. While hardware-based methods that involve installing sensors on the gripper and the object to analyze their states have been attempted, no studies have focused on the tangential contact force related to slipping. Therefore, we developed a 16-way object contact force measurement device incorporating two-axis force sensors into each of the 16 segmented objects and compared the normal and tangential components of the enveloping grasping force of the FinRay soft gripper under two types of contact friction conditions. In the first experiment, the proposed device was compared with a device containing a six-axis force sensor in one segmented object, confirming that the proposed device has no issues with measurement performance. In the second experiment, comparisons of the proposed device were made under various conditions: two contact friction states, three object contact positions, and two object motion states. The results demonstrated that the proposed device could decompose and analyze the grasping force into its normal and tangential components for each segmented object. Moreover, low friction conditions result in a wide contact area with lower tangential frictional force and a uniform normal pushing force, achieving effective enveloping grasping.

Investigating the bending and buckling behaviors of composite porous beams reinforced with carbon nanotubes and graphene platelets using a TRPIM path following mesh-free approach

The aim of the present work consists in investigating the nonlinear behavior of porous beams reinforced with graphene platelets (GPL) and supported carbon nanotubes (CNT), termed functionally graded graphene platelets reinforced composite beam (FG-GPLRC) and functionally graded nanotube carbon reinforced composite beam (FG-CNTRC), respectively. Notably, the distribution of GPL/CNT is explored in both uniform and non-uniform patterns across the beam's thickness. What sets this research apart is its utilization of a refined beam model as enhanced FSDT incorporating nonlinear shear terms which is a crucial advancement in accurately capturing the post-buckling response in certain boundary conditions, a feature lacking in the existing FSDT literature. Innovatively, the post-buckling load-deflection relationship is derived through the solution of governing equations incorporating cubic nonlinearity. This is achieved by employing Galerkin's method alongside a non-iterative high-order continuation technique based on the asymptotic numerical method coupled with the Tchebychev-radial point interpolation method (TRPIM), using a path-following where the solutions are obtained branch-by-branch by eliminating the need for iterative processes. In essence, this research underscores the pivotal role of porosity and GPL/CNT reinforcement in shaping the post-buckling configuration of both perfect and imperfect nanocomposite beams, thereby advancing our understanding of structural behavior in porous nanocomposite materials. The findings of this study illuminate the significant influence of parameters such as porosity coefficient, porosity distribution, GPL/CNT distribution, and GPL-weight/CNT-volume fraction on the nonlinear buckling behavior of porous beams.

Analysis of Elastic Buckling and Static Bending Properties of Smart Functionally Graded Porous Beam

Background: A Smart Functionally Graded (SFG) porous beam is a Functionally Graded (FG) Porous beam consisting of a piezo-electric layer integrated on the top layer. Aim: This research work addresses the lack of information by examining the bending as well as elastic buckling performance of SFG beams having two distinct Porosity Distributions (PDs). The main purpose of this research work is to study and analyze the bending deflections as well as CBLs of SFG beams with two different PDs, considering various boundary conditions, voltage levels (20V and 100V), and changes in slenderness ratio. Objective: The objectives of this work are as follows: to analyze the impact of variations in voltage levels and slenderness ratios on the critical buckling and bending properties of the SFG beam and to showcase the effect of variation in the slenderness ratio on the dimensionless normal stress through the thickness of the Hinge-Hinge beam. Method: The research work analyzes the elastic buckling as well as static bending of Smart Functionally Graded (SFG) porous beams, considering the equations derived from the Timoshenko beam theory. To simulate the results and analyze the various effects, the ANSYS software has been utilized in this paper. Results: This research work examines how the slenderness ratio impacts the maximum deflection, CBL, along with stress distribution. Experimental data demonstrates that as the slenderness ratio increases, CBL reduces, and maximum deflections in SFG porous beams increase. Also, it has been observed that normal stress distribution shifts from linear to non-linear and changes significantly. Further, the PDs significantly affect the static bending as well as the buckling performance of the beam. The symmetric distribution pattern provides superior buckling capability and enhanced bending resistance compared to the unsymmetric distribution pattern. Additionally, it has been found that as the voltage across the SFG increases, the buckling load increases and the deflection of the beam decreases. Conclusion: This research work has analyzed the effects of slenderness ratio and voltage level on the Critical Buckling Load (CBL) and bending properties of SFG porous beams, considering four different boundary conditions and a fixed set of parameters. The key findings of this paper are that as the slenderness ratio increases, the CBL decreases, and distribution shifts from linear to nonlinear region. Changes are significant, whereas maximum deflection increases. A significant effect is observed in the performance of static bending and buckling of SFG beams. It has been investigated that with an increase in voltage across the SFG beam, the buckling load increases, whereas the maximum deflection of the beam decreases.

Tunability in the polarization of light using nematic liquid crystal

Birefringent materials have the effect of diminishing the degree of polarization (DOP) of light passing through them, a phenomenon often colloquially referred to as depolarization. Nematic liquid crystal (NLC) materials are known for their substantial birefringence, leading to significant retardation lengths. This unique property allows for a unique means of reducing DOP of partially coherent light. In this study, a NLC is used for its electro-optical capability to modify its birefringence, allowing it to tune the retardation length. This enables us to develop a variable DOP source with wide range of coherence properties of light. Furthermore, we examine the changes in the state of polarization (SOP) using this method, which serves as a valuable tool in various optical applications. In the current investigation, electrooptically controlled NLC is also utilized by varying the NLC thickness and coherence length of light beam.

Vibration Analysis of Porous Cu-Si Microcantilever Beams in Fluids Based on Modified Couple Stress Theory.

The vibrations in functionally graded porous Cu-Si microcantilever beams are investigated based on physical neutral plane theory, modified coupled stress theory, and scale distribution theory (MCST&SDT). Porous microcantilever beams define four pore distributions. Considering the physical neutral plane theory, the material properties of the beams are computed through four different power-law distributions. The material properties of microcantilever beams are corrected by scale effects based on modified coupled stress theory. Considering the fluid driving force, the amplitude-frequency response spectra and resonant frequencies of the porous microcantilever beam in three different fluids are obtained based on the Euler-Bernoulli beam theory. The quality factors of porous microcantilever beams in three different fluids are derived by estimating the equation. The computational analysis shows that the presence of pores in microcantilever beams leads to a decrease in Young's modulus. Different pore distributions affect the material properties to different degrees. The gain effect of the scale effect is weakened, but the one-dimensional temperature field and amplitude-frequency response spectra show an increasing trend. The quality factor is decreased by porosity, and the degree of influence of porosity increases as the beam thickness increases. The gradient factor n has a greater effect on the resonant frequency. The effect of porosity on the resonant frequency is negatively correlated when the gradient factor is small (n<1) but positively correlated when the gradient factor is large (n>1).