Nonlinear Dynamic Response of an Axially Functionally Graded (AFG) Beam Resting on Nonlinear Elastic Foundation Subjected to Moving Load

Alimoradzadeh, Mehdi; Salehi, Mehdi; Esfarjani, Sattar Mohammadi

doi:10.1515/nleng-2018-0051

Cited by 21 publications

(6 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where u and w are the axial and transverse displacements of any point on the neutral axis, respectively. The Von-Karman's nonlinear strain-displacement relationship based on assumptions of large transverse displacements, moderate rotation, and small strain for straight beams are given by [47][48][49]:…”

Section: Modified Couple Stress Theorymentioning

confidence: 99%

“…Variation of first and second fundamental frequencies due to system parameters is studied. In [47] nonlinear vibration analysis of a simply supported AFG beam subjected to a moving harmonic load as an Euler-Bernoulli beam utilizing Green's strain tensor. The results indicate that these parameters have a considerable effect on both nonlinear natural frequency and response amplitude [47].…”

Section: Introductionmentioning

confidence: 99%

“…In [47] nonlinear vibration analysis of a simply supported AFG beam subjected to a moving harmonic load as an Euler-Bernoulli beam utilizing Green's strain tensor. The results indicate that these parameters have a considerable effect on both nonlinear natural frequency and response amplitude [47]. In another study, free and forced vibration analysis of FG doubly clamped micro-beams was investigated based on the third order shear deformation and modified couple stress theories [48].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Alimoradzadeh

Salehi

Esfarjani

2020

Period. Polytech. Mech. Eng.

Self Cite

View full text Add to dashboard Cite

In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

show abstract

Section: Modified Couple Stress Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Alimoradzadeh

Salehi

Esfarjani

2020

Period. Polytech. Mech. Eng.

Self Cite

View full text Add to dashboard Cite

show abstract

“…FG materials have attracted considerable interest from many researchers in structural dynamics and statics, and they have been extensively studied, especially in the last few years. Alimoradzadeh et al [2] proposed the nonlinear vibration analysis of a simply supported axial FG beam subjected to a moving harmonic load and resting on a Winkler-Pasternak nonlinear elastic foundation using Green's strain tensor. An approximate analytical solution for forced nonlinear vibration was obtained using the variational iteration method.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Herişanu

Marinca

2023

Symmetry

View full text Add to dashboard Cite

This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered the longitudinal–transverse vibration of a simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including the first-order strain–displacement relationship. The FG nanobeam was made of a mixture of metals and ceramics, while the volume fraction varied in terms of thickness when a power law function was used. The nonlocal Eringen theory of elasticity was used to study the simple supported Euler–Bernoulli nanobeam. The nonlinear governing equations of the FG nanobeam and the associated boundary conditions were gained using Hamilton’s principle. To truncate the system with an infinite degree of freedom, the coupled longitudinal–transverse governing equations were discretized using the Galerkin–Bubnov approach. The resulting nonlinear, ordinary differential equations, which took into account the curvature of the nanobeam, were studied via the Optimal Auxiliary Functions Method (OAFM). For this complex nonlinear problem, an explicit, analytical, approximate solution was proposed near the primary resonance. The simultaneous effects of the following elements were considered in this paper: the presence of a curved nanobeam; the transversal inertia, which is not neglected in this paper; the mechanical impact; and electromagnetic actuation. The present study proposes a highly accurate analytical solution to the abovementioned conditions. Moreover, in these conditions, the study of local stability was developed using two variable expansion methods, the Jacobian matrix and Routh–Hurwitz criteria, and global stability was studied using the Lyapunov function.

show abstract

“…The nonlinear free vibration of the non‐local bi‐directional graded FG Euler–Bernoulli nanobeams was analysed by Nejad and Hadi [10] using the generalised differential quadrature method (GDQM). Alimoradzadeh et al [11] studied nonlinear vibration analysis of axially functionally graded (AFG) beam Euler–Bernoulli beam subjected to a moving harmonic utilising Green's strain tensor. They investigated the effect of some parameters such as the power index and stiffness coefficients, among others, on the nonlinear natural frequency along with the velocity of the moving harmonic load on the nonlinear dynamic response of (AFG) Euler–Bernoulli, where it is found that these parameters have a considerable effect on both nonlinear natural frequency and response amplitude.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of FG nanobeam using a finite‐element method

Uzun

Yaylı

Deliktaş

2020

Micro & Nano Letters

View full text Add to dashboard Cite

In this work, a non-local finite-element formulation is developed to analyse free vibration of functionally graded (FG) nanobeams considering power-law variation of material through thickness of the nanobeam. The Euler-Bernoulli beam theory based on Eringen's non-local elasticity theory with one length scale parameter is used to model the FG nanobeam. To this end, two types of FG nanobeams composed of two different materials are analysed by using the developed non-local finite-element formulation. First FG nanobeam is made of alumina (Al 2 O 3) and steel, whereas second one is composed of silicon carbide (SiC) and stainless steel (SUS304). Numerical results are presented to show the effect of power-law exponent (k) and nanostructural length scale (e 0 a/L) on the free vibration of FG nanobeams.

show abstract

Nonlinear Dynamic Response of an Axially Functionally Graded (AFG) Beam Resting on Nonlinear Elastic Foundation Subjected to Moving Load

Cited by 21 publications

References 28 publications

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Free vibration of FG nanobeam using a finite‐element method

Contact Info

Product

Resources

About