Beam Theory Research Articles

Analysis of the transverse vibration of a multistepped FGM beam resting on a Winkler foundation in a thermal environment and carrying concentrated masses

This paper examines a novel case study involving the free vibration of a stepped FGM beam-mass system resting on elastic foundations and subjected to a nonlinear or uniform thermal load. The present study examines the complex interaction of thermal effects on dynamic behavior by varying the cross-section and length ratios, material parameters and mass magnitudes. After adopting Euler-Bernoulli's theory, the dynamic behavior of non-uniform FGM beams was investigated using the generalized finite element method (GFEM) and the Rayleigh quotient finite element method (RQFEM). In line with the objective set, relevant results derived from parametric studies, showcasing accentuated variation in dimensional frequency curves and bending moments, have been highlighted and discussed.

The novel Vogel's approximation method integrated with a random forest algorithm in the vibration analysis of a two-directional functionally graded taper porous beam: Assessment

A functionally graded material is a class of composite materials characterized by gradual variations in composition and microstructure, which further induces the respective changes in the material properties. This study focuses on evaluating the vibration behavior of two directional functionally graded taper porous beams (FGTPB). This approach adopts a rectangular cross-section in order to deal with the challenges related to fluctuating material characteristics and geometric tapering in both thickness and width dimensions. The research employs a novel approach that merges Vogel's approximation technique with the Random Forest algorithm, an approach that has not been used in analyzing structural vibrations, establish boundary conditions and solve equations of motion. Comparative results of the suggested beam theory with the existing literature on FGTPB materials such as alumina and SUS304 at various taper, porosity, gradient and width ratios verified it. The material gradation and porosity developed a uniform pattern in the first three modes of fundamental frequencies. Higher gradient indices increased the rigidity and natural frequencies of the beams whereas the porosity index decreased the rigidity, resulting in lower natural frequencies. By combining Vogel's approximation method with machine learning techniques, the study improved vibration behavior analysis in FGTPB. The disciplines of materials and structural engineering are significantly impacted by this.

A New Model for Thermal Buckling of FG-MEE Microbeams Based on a Non-Classical Third-Order Shear Deformation Beam Theory

A New Model for Thermal Buckling of FG-MEE Microbeams Based on a Non-Classical Third-Order Shear Deformation Beam Theory

Influence of Elastic Properties and Nodes on the Flexural Behaviour of Bamboo Culms

This study investigates the influence of elastic properties and nodes on the flexural behaviour of bamboo culms by comparing different characterization techniques and theoretical approaches. The most representative parts of the bamboo culm were selected using microscopic images of bamboo cross-sections. These were sliced from the bottom, middle, and top parts of a single culm and were analyzed with Digital Image Processing. Four-point bending tests were conducted on twelve culms of Phyllostachys aurea, subdivided into groups of untreated (UN) and heat-treated (HT) samples. The axial modulus of elasticity (Eb) and the shear modulus (G) were determined experimentally using four different mathematical models: (i) a global deflection model using the Euler-Bernoulli beam theory according to the ISO Standard; (ii) a global deflection model using the Timoshenko beam theory; (iii) a global deflection model based on the Timoshenko beam theory but accounting for the presence of nodes; and finally, (iv) a local model using extensometry. The dominant failure modes for UN and HT samples are described and discussed, and were influenced by the moisture content (MC). Approaches (i) and (ii) showed good agreement, giving reliable parameters to assess Eb. The third approach (iii) indicated that the nodes significantly influence the flexural behaviour of the culms. Approach (iv) was appropriate for determining G, but resulted in higher values of Eb, typically not representative of the material.

Mechanical Properties of Re-Entrant Hybrid Honeycomb Structures for Morphing Wings.

The exceptional energy absorption, deformability, and tuneable Poisson's ratio properties of negative Poisson's ratio (NPR) honeycomb biomimetic structures make them highly suitable for applications in aerospace, medical, and acoustic stealth industries. The present study proposes a re-entrant hybrid honeycomb (REHH) structure comprising a re-entrant octagonal unit cell and a re-entrant hexagonal unit cell. Theoretical models of the in-plane elastic modulus and Poisson's ratio are established based on beam theory, and these models are validated through finite element (FE) simulations and tensile experiments conducted on the REHH samples. The influence of the cell geometry parameters on the in-plane elastic behaviours is investigated. The results indicate that the NPR performance of the REHH structure exhibits superior deformation capability compared with the four-point star hybrid honeycomb (FSHH) structure. The experimental REHH structure samples exhibit significant tensile displacement capabilities in the x-direction.

Controllability with one scalar control of a system of interaction between the Navier–Stokes system and a damped beam equation

Controllability with one scalar control of a system of interaction between the Navier–Stokes system and a damped beam equation

A general framework for designing compliant deployable mechanisms via geometrically exact beam theory

Compliant deployable mechanisms (CDMs), as a novel and promising type of mechanisms, have been gradually used in medical industry, aerospace and other engineering fields that require high space utilization and compactness. Therefore, it is necessary to develop a general and efficient methodology to design and analyze CDMs. This paper proposes a general framework for designing and analyzing CDMs. The proposed framework has been verified by finite element method (FEM) first. Then, for practical validation, we design two types of compliant deployable mechanisms for different application scenarios within this framework, and experimental testing has been conducted to prove the feasibility of the proposed framework. Compared to the existing methods for designing CDMs, this framework demonstrates a more general scheme where different engineering scenarios can be taken into account to meet the design requirements, presenting several desired advantages over the existing methods, such as higher accuracy and less computational expense.

A magnetic plucking frequency up-conversion piezoelectric energy harvester with nonlinear energy sink structure

In low and wide frequency vibration environments, the efficiency of vibration energy harvesters is relatively low. This paper presents a magnetic plucking frequency-up-conversion bistable Piezoelectric Energy Harvester (PEH) that features a Nonlinear Energy Sink (NES) structure for low and wide frequency vibration absorption. Based on the Euler-Bernoulli stepped beam theory, a theoretical model was derived from the Lagrange equation. The system's bandwidth and power generation capability were analyzed through frequency sweeping. This study thoroughly investigated the up-conversion working mechanism of the NES magnetically plucked PEH super-harmonic vibration. The results reveal that the system encompasses two power generation frequency bands: interwell periodic vibration and chaotic vibration. Under an excitation acceleration of 0.25 g, the interwell periodic vibration range during forward frequency sweep is from 3.30 to 4.31 Hz with an average power of 4.71 mW, and during reverse sweep, it is from 2.02 to 4.05 Hz with 2.43 mW. The coordination between NES and PEH is one of the crucial factors affecting power generation. Frequency mismatch can lead to asymmetrical displacement and alternating strong-weak voltage outputs.

Transient Shallow Water Wave Interactions with a Partially Fragmented Ice Shelf

This work investigates the interaction between water waves and multiple ice shelf fragments in front of a semi-infinite ice sheet. The hydrodynamics are modelled using shallow water wave theory and the ice shelf vibration is modelled using Euler–Bernoulli beam theory. The ensuing multiple scattering problem is solved in the frequency domain using the transfer matrix method. The appropriate conservation of energy identity is derived in order to validate our numerical calculations. The transient scattering problem for incident wave packets is constructed from the frequency domain solutions. By incorporating multiple scattering, this paper extends previous models that have only considered a continuous semi-infinite ice shelf. This paper serves as a fundamental step towards developing a comprehensive model to simulate the breakup of ice shelves.

Machine learning and numerical approaches for vibration behavior prediction of rotating nanobeams in complex environments

This work scrutinized the vibration behavior of nanoscale beam structures with rotating motion according to the nonlocal stress-strain gradient theory (NSSGT). The surface layer energy, rotary inertia factor, and thickness-dependent scale impacts are considered in the mathematical simulation. Additionally, parametric examinations are exploited to comprehend the impressions of varying environmental fields and follower and axial forces. Adopting Hamilton’s principle, the dynamic equation of nanoscale beams with rotation is achieved. The eigenvalue analysis is accomplished with the aid of the Galerkin decomposition scheme, and dynamic characteristics are recognized. Besides, machine learning (ML)-based approaches, viz., artificial neural network (ANN) and Gaussian support vector machine (GSVM) techniques, are exploited to predict the vibration frequencies. Comparison analyses with existing scientific reports in the open technical literature are conducted to guarantee the correctness of the deduced outcomes. The performance and correctness of ANN and GSVM techniques are verified by assessing the performance parameters of ML approaches. The numerical technique outcomes are consistent with those of ML-assisted models. Furthermore, the proposed ML prediction models are perceived to have excellent performance (viz., low mean square error and high determination coefficient) and superior computational time and cost-effectiveness. It is deduced that the scale-dependency in the thickness direction improves the vibration frequency. Moreover, the vibration frequencies are decreased/increased with increasing nanobeam thickness/length by considering the surface layer energy. The current research outcomes can be valuable in designing next-generation high-speed rotating nanodevices, inspiring further innovation and development in the field.

Vibration Characteristics of Magnetostrictive Composite Cantilever Resonator with Nonlocal Effect.

Taking the nonlocal effect into account, the vibration governing differential equation and boundary conditions of a magnetostrictive composite cantilever resonator were established based on the Euler magnetoelastic beam theory. The frequency equation and vibration mode function of the composite cantilever were obtained by means of the separation of variables method and the analytic solution of ordinary differential equations. The lateral deflection, vibration governing equations, and boundary conditions were nondimensionalized. Furthermore, the natural frequency and modal function of the composite beam were quantitatively analyzed with different nonlocal parameters and transverse geometry dimensions using numerical examples. Compared with the results without considering the nonlocal effect, the influence of the nonlocal effect on the vibration characteristics was analyzed. The numerical results show that the frequency shift and frequency band narrowing of the magnetostrictive cantilever resonator are induced by nonlocal effects. In particular, the high-frequency vibration characteristics, such as vibration amplitude and modal node of the composite beam, are significantly affected. These analysis results can provide a reference for the functional design and optimization of magnetostrictive resonators.

Hermite element for vibration analysis of thin-walled beams with higher-order beam theory

Hermite element for vibration analysis of thin-walled beams with higher-order beam theory

Vibration characteristics of rotor system with coupling misalignment and disc-shaft nonlinear contact

Typically, the interference fit is used to perform the tight junction between disc and shaft. Nevertheless, the nonlinear contact between disc-shaft is neglected in tradition research. Hence, aimed at the shortcoming, considering the nonlinear contact between disc-shaft, the finite element model of rotor system featured with coupling parallel misalignment is established based on Timoshenko beam theory. Firstly, due to the nonlinear of disc-shaft contact, Newmark-β method is employed to combine Newton-Raphson method to solve the dynamic response. Then, according to the comparative analysis between dynamic characteristics of rotor systems operated with three conditions, the concretely discussion on the effect of initial interference and parallel misalignment degree are performed. The results show that disc-shaft nonlinear contact can cause the slight collision between disc-shaft, and the existence of parallel misalignment can intensify the slight collision. Besides, as rotation speed up, the contact states between disc-shaft become the process of repeated cycles: separation, contact, and then separation. Finally, the experiment study is conducted, and the concluded that the experiment result is corresponding to the simulation result can be obtained. It is established that the research results can provide possibilities for the identification and diagnosis of the rotor system with disc-shaft nonlinear contact.

Nonlocal dynamic response of FGP sandwich microbeam with 2D PSH network incorporating adatoms-surface interactions energy under magnetic field

The present work models and studies the resonance frequency change due to adsorption phenomena in a simply-supported adatom-microbeam system under an axial magnetic environment. The microbeam structure is a functionally graded (FG) sandwich that includes a rectangular configuration and a ceramic perforated core with periodic square holes network and FG porous material faces. To evaluate the adsorption-induced energies produced by van der Waals interaction (vdW), the Morse and Lennard-Jones (6–12) potentials are included in conjunction with nonlocal material elasticity to adopt the small-scale impact. Moreover, the explicit formulas for the inertia moments and shear force are developed by the Timoshenko beam equations, considering the residual stress influence as an additional axial load. The Navier-type solution and the differential quadratic method (DQM) are implemented to compute the solution of the governing equations. It is established that the resonance frequency change for the O/Si (100) and H/Si (100) is dependent on the geometrical, perforation, and porosity parameters, adsorption density, mode number, and the magnetic field intensity as well. Therefore, these numerical results have been discussed in detail to properly examine dynamic vibration behavior and a suitable mass detection design of M/NEMS structures.

A Fast Numerical Approach for Investigating Adhesion Strength in Fibrillar Structures: Impact of Buckling and Roughness

This study presents a numerical investigation into the adhesion strength of micro fibrillar structures, incorporating statistical analysis and the effects of excessive pre–load leading to fibril buckling. Fibrils are modeled as soft cylinders using the Euler–Bernoulli beam theory, with buckling conditions described across three distinct states, each affecting the adhesive properties of the fibrils. Iterative simulations analyze how adhesion strength varies with pre–load, roughness, number of fibrils, and the work of adhesion. Roughness is modeled both in fibril heights and in the texture of a rigid counter surface, following a normal distribution with a single variance parameter. Results indicate that roughness and pre–load significantly influence adhesion strength, with excessive pre–load causing substantial buckling and a dramatic reduction in adhesion. This study also finds that adhesion strength decreases exponentially with increasing roughness, in line with theoretical expectations. The findings highlight the importance of buckling and roughness parameters in determining adhesion strength. This study offers valuable insights into the complex adhesive interactions of fibrillar structures, offering a scalable solution for rapid assessment of adhesion in various rough surface and loading scenarios.

On Hybrid and Non-Hybrid Discrete Fractional Difference Inclusion Problems for the Elastic Beam Equation

On Hybrid and Non-Hybrid Discrete Fractional Difference Inclusion Problems for the Elastic Beam Equation

A generalized Timoshenko beam with embedded rotation discontinuity coupled with a 3D macroelement to assess the vulnerability of reinforced concrete frame structures

A generalized finite element beam with an embedded rotation discontinuity coupled with a 3D macroelement is proposed to assess, till complete failure (no stress transfer), the vulnerability of symmetrically reinforced concrete frame structures subjected to static (monotonic, cyclic) or dynamic loading. The beam follows the Timoshenko beam theory and its sectional behavior is described in terms of generalized forces and generalized strains. The beam response up to the peak is described by a macroelement, based on plasticity theory, that adopts a 3D failure criterion expressed in terms of axial force, shear force and bending moment. The Embedded Finite Element Method is then adopted to reproduce bending dominated failure, with a global cohesive model that links the cohesive moment to a rotational jump. The formulation allows for remedy of localization phenomena and significant reduction of the necessary computational time. The performance of the proposed simplified strategy is illustrated by comparison with experimental results.

Nonlinear Analysis of Plane Frames Using a Co-Rotating Timoshenko Beam Element

The present work describes a co-rotating shear flexible beam element without shear locking and integrating Euler-Bernoulli's and Timoshenko's beam theories. The co-rotational kinematics is based on the separation of the motion in deformational and rigid body components. The deformation of the beam element is composed by three natural modes of deformation: the extension mode, the symmetric bending mode, and the anti-symmetric bending mode. The respective generalized stresses from these natural modes are self-balanced, allowing the achievement of a consistent tangent stiffness matrix. In this paper, it is detailed and deduced all the algebraic steps for the deduction of the elastic stiffness matrix, the geometric stiffness matrix, and the co-rotation stiffness matrix. Some examples are presented and the numerical results demonstrate that the beam element here presented is able to handle large rotations.

Damage detection of beam-like structures using a combination of wavelet transform and subtraction of intact and damaged mode shapes

Detection of damages with low levels has been one of the most critical challenges. As a result, many damage detection methods cannot detect damages or cracks with a level lower than 10%. On-surface damages as low-level damages are challenging to localize. A new technique is proposed to eliminate this challenge based on wavelet transformation of the difference in damaged and intact mode shapes. In this way, a finite element model is developed for obtaining governing equations of thin beams. The developed finite element model provides the mode shape signals. Then, the signals are decomposed by wavelet transform. The findings of this study show that in both numerical and experimental investigations, the proposed method is very efficient since the proposed method can detect on-surface damages having a level below 10%.

Slip modulus of inclined screw connectors in glued laminated bamboo and wood-concrete composite beams

ABSTRACT The existing research has predominantly focused on the shear behavior of inclined screws in wood-concrete composite beams. However, there is a significant research gap regarding the slip modulus of inclined screw connectors in glued laminated bamboo and wood (GLBW)-concrete composite beam. To address this gap, nine groups of shear tests were performed to study the load-slip behavior of inclined screw connectors in GLBW-concrete composite beams. This study analyzed the impacts of screw embedding length, screw diameter, screw embedding angle, and bamboo board thickness on the slip modulus of inclined screw connectors. The results showed that in comparison to inclined screw connectors with a 90 mm embedding length, the slip modulus of screw connectors with 110 and 130 mm embedding lengths increased by 11% and 19%, respectively. As the screw embedding angle decreased, the slip modulus of inclined screw connectors increased. For bamboo thicknesses of 30, 60, and 300 mm, the slip modulus of inclined screws was improved by 40%, 78%, and 89%, respectively, compared to the screws in pure wood beam. This study presented an analytical model for predicting the slip modulus of inclined screws in GLBW-concrete composite beam based on the layering method and elastic foundation beam theory.