A new approach for solving the fractal Euler-Bernoulli beam equation is proposed. The mapping of fractal problems in non-differentiable fractals into the corresponding problems for the fractal continuum applying the fractal continuum calculus (
This article considers an unsteady elastic diffusion model of Euler–Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum...
In this study, the bending behavior of beams is investigated using the fractional Euler–Bernoulli beam model. This model is developed based on fractional calculus, particularly employing the Riesz–Caputo derivatives, and is capable of acc...
The current article introduces a Petrov–Galerkin method (PGM) to address the fourth-order uniform Euler–Bernoulli pinned–pinned beam equation. Utilizing a suitable combination of second-kind Chebyshev polynomials as a basis in spati...
This article settles a new multi-fault-tolerant control problem of an Euler–Bernoulli beam system (EBBS) in the existence of multiplicative faults, additive faults, and control-matched disturbances simultaneously, using the direct adaptive lear...
First, we develop a direct operator method for solving boundary value problems for a class of nth order linear Volterra–Fredholm integro-differential equations of convolution type. The proposed technique is based on the assumption that the Volt...
Soft material-based pneumatic microtube actuators are attracting intense interest, since their bending motion is potentially useful for the safe manipulation of delicate biological objects. To increase their utility in biomedicine, researchers have b...
The bending of self-similar beams applying the Euler–Bernoulli principle is studied in this paper. A generalization of the standard Euler–Bernoulli beam equation in the
This study employs spatial optimization principles to investigate the nonlinear vibration of a flexibly supported Euler–Bernoulli beam, a (1 + 1)-dimensional system subjected to axial loads. The modified Khater method, a crucial tool in mechani...
Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally...
In this study, two closed-form solutions for determining the first two natural frequencies of the flapwise bending vibration of a cracked Euler–Bernoulli beam at low rotational speed have been developed. To solve the governing differential equa...
This paper presents a theoretical framework to enhance the prediction of dynamic responses in complex mechanical systems, such as vehicle structures, by incorporating both translational and rotational degrees of freedom. Traditional receptance coupli...
The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The el...
In practical engineering, uncertainties inevitably exist in the models and measurement data used for structures. Therefore, a statistical strategy related to damage detection methods become crucial. In this paper, a probabilistic statistical damage d...
In this part of the paper, the theory of nonlinear dynamics of flexible Euler–Bernoulli beams (the kinematic model of the first-order approximation) under transverse harmonic load and colored noise has been proposed. It has been shown that the introd...
Although small-scale effect or thermal stress significantly impact the mechanical properties of nanobeams, their combined effects and the temperature dependence of the elastic parameters have yet to attract the attention of researchers. In the presen...
The paper is concerned with the boundary conditions of explicit gradient elasticity of Mindlin’s type in dynamics. It has been argued in an earlier paper that acceleration terms should not be present in the boundary tractions because of objecti...
The subject of this study is the vibration of the Bernoulli–Euler beam on a three-parameter inertial foundation caused by a group of moving forces. The solution to the problem is obtained analytically. The influence of deformable foundation pro...
Permeable porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopaedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance approximately ma...
A ballistic parameter that influences the ballistic performances of a high-performance yarn is the critical velocity. The critical velocity is defined as the projectile striking velocity that causes instantaneous rupture of the yarn upon impact. In t...
In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating...
This study demonstrates the effectiveness of the differential transform method (DTM) in solving complex solid mechanics problems, focusing on static analysis of beams under various loads and boundary conditions. For cantilever beams (BSM1), DTM provi...
This article presents a modal analysis of an elastically constrained Rayleigh beam that is placed on an elastic Winkler foundation. The study of beams plays a crucial role in building construction, providing essential support and stability to the str...
This work presents a comprehensive model for nanobeams, incorporating beam curvature and surface energy. Gurtin–Murdoch surface stress theory is used, in conjunction with Euler–Bernoulli beam theory, to model the beams and take surface en...
This contribution considers a virtual experiment on the vibrational response of rail and road bridges equipped with smart devices in the form of damping elements to mitigate vibrations. The internal damping of the bridge is considered a discontinuity...
In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The go...
The bending resonance of micro-sized resonators has been utilized to study adsorption of analyte molecules in complex fluids of picogram quantity. Traditionally, the analysis to characterize the resonance frequency has focused solely on the mass chan...
In this study, the non-local Euler-Bernoulli beam theory was employed in the nonlinear free and forced vibration analysis of a nanobeam resting on an elastic foundation of the Pasternak type. The analysis considered the effects of the small-scale of...
In this paper, the dynamic response of a Euler–Bernoulli beam subjected to transverse harmonic forces is calculated. The method of separation of variables combined with the mode shape superposition method, which includes the determination of ei...
This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)-reinforced composite beams lying on an elastic medium. Despite the large amount of experimental and theoretical studies in the literature on the mechani...
Due to increasing costs and growing environmental concerns pertaining to the construction of structures, an alternative form of reinforcement has been proposed through our studies; through a new beam design methodology, referred to as triple composit...
In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The novelty of the research is in consideration of the models with an arbitrary variable coefficient of foundation. Qualitative results that influence...
Since pipelines experience the largest deformation during lowering-in, structural analysis for this construction sequence should be performed to ensure structural safety. In this study, a new analytical model named the “segmental pipeline model...
In this work, an analytical solution for the natural frequencies of elastically supported stepped beams with rigid segments is presented. The elastic end boundary conditions are modeled with a translational stiffness element, a rotational stiffness e...
Beam-type structures used in aerospace applications may experience simultaneous broadband dynamic excitation and thermal loads. Design sensitivity, as a powerful tool for structural optimization and reliability analysis, is investigated in this work....
This study employs a fully coupled fluid–structure interaction (FSI) to investigate the vibrations of an elastic micro-cantilever induced by a rarefied gas flow. Two distinct models are employed to characterize the beam vibrations: the small de...
In this manuscript, static and free vibration responses on Euler–Bernoulli beams with a Koch snowflake cross-section are studied. By applying the finite element method, the transversal displacement in static load condition, natural frequencies,...
The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using c...
Ride comfort is an important requirement that passenger rail vehicles must meet. Carbody–anti-bending system is a relatively new passive method to enhance the ride comfort in passenger rail vehicles with long and light carbody. The resonance fr...
Due to the large application of tapered beams in smart devices, such as scanning tunneling microscopes (STM), nano/micro electromechanical systems (NEMS/MEMS), atomic force microscopes (AFM), as well as in military aircraft applications, this study d...
The finite element method (FEM) is used to investigate the free and forced vibration characteristics of functionally graded graphene-nanoplatelet-reinforced composite (FG-GPLRC) beams. The weight fraction of graphene nanoplatelets (GPLs) is assumed t...
The present study deals with the transient interval analysis of a shallow beam having uncertainty in structural parameters viz. mass density and applied load. It is quite difficult to obtain information regarding the exact values of these parameters...
Because robotic soft arms have a high power-to-weight ratio, low cost, and ease of manufacturability, increasing numbers of researchers have begun to focus on their characteristics in recent years. However, many urgent problems remain to be resolved....
An analytical formulation involving residual force is proposed to predict the displacement of an existing structure by simplifying the tunnel as an infinite Euler–Bernoulli beam resting on a two-parameter Pasternak foundation. The feasibility is conf...
Multilayered microresonators commonly use sensitive coating or piezoelectric layers for detection of mass and gas. Most of these microresonators have a variable cross-section that complicates the prediction of their fundamental resonant frequency (ge...
Robot manipulators have played an enormous role in the industry during the twenty-first century. Due to the advances in materials science, lightweight manipulators have emerged with low energy consumption and positive economic aspect regardless of th...
This paper presents an analytical study of the dynamic responses in the vehicle–pavement–foundation system, where the vehicle is simplified to a two-degree-of-freedom system, the pavement is modeled using both Euler–Bernoulli (E-B)...
This study examines the geometrically nonlinear free vibration behaviour of a clamped–clamped Euler–Bernoulli beam weakened by an open transverse crack. The crack is modelled through an equivalent rotational flexibility formulation ground...
Piezoelectric nanogenerators can convert energy from ambient vibrations into electrical energy. In the future, these nanogenerators could substitute conventional electrochemical batteries to supply electrical energy to consumer electronics. The optim...
Aeronautical stiffened panels composed of thin shells and beams are prone to deformation or buckling due to the combined loading, functional boundary conditions and interface forces between joined parts in the assembly processes. In this paper, a mec...
of 8