Free transverse vibrations analysis of size-dependent cracked piezoelectric nano-beam based on the strain gradient theory under mechanic-electro forces

Eghbali, Mohammadreza; Hosseini, Seyyed Amirhosein; Pourseifi, Mehdi

doi:10.1016/j.enganabound.2022.07.006

Cited by 13 publications

(6 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where Δ ψ c does the crack cause the additional strain energy. This equation can be stated in terms of the axial force and the bending moment as 25,26 :…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In this paper, cross-sectional vibration is considered, and longitudinal movement is not considered ( Δ u = 0 ) . Δ θ it can be expressed in this way 25,26 :…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…After defining how the crack is modeled, the free cross-sectional vibration analysis of the beam can be continued by applying the motion equation in the vertical direction to each of the following two sections 26 :…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The above equations include several constants that must be solved by applying the boundary conditions and the conditions expressed in the crack section. The boundary conditions are expressed as follows 24,[26][27][28] :…”

Section: Nanobeam Crack Modelmentioning

confidence: 99%

See 3 more Smart Citations

An dynamical evaluation of size-dependent weakened nano-beam based on the nonlocal strain gradient theory

Eghbali

Hosseini

Pourseifi

2022

The Journal of Strain Analysis for Engineering Design

Self Cite

View full text Add to dashboard Cite

This paper examines the free lateral vibration of a cracked nano-beam based on Euler-Bernoulli beam theory and nonlocal strain gradient theory (NSGT). Due to the importance and application of nanostructures, their mechanical and mechanical properties are essential. The governing equations and boundary conditions related to using the Hamilton principle have been extracted. The beam separation with the nano-beams division into two parts attached to the Torsion spring is modeled. The model calls the excess strain energy due to crack and increases the discontinuity in the deflection slope. This study investigated the effects of crack propagation, crack intensity, material length scale parameter, and various nonlocal parameters. A comparison of previous studies has been published, where a good agreement is observed. The results show that the parameters mentioned above play an important role in dynamical behavior.

show abstract

“…where Δ ψ c does the crack cause the additional strain energy. This equation can be stated in terms of the axial force and the bending moment as 25,26 :…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In this paper, cross-sectional vibration is considered, and longitudinal movement is not considered ( Δ u = 0 ) . Δ θ it can be expressed in this way 25,26 :…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Nanobeam Crack Modelmentioning

confidence: 99%

See 2 more Smart Citations

An dynamical evaluation of size-dependent weakened nano-beam based on the nonlocal strain gradient theory

Eghbali

Hosseini

Pourseifi

2022

The Journal of Strain Analysis for Engineering Design

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, this study is important in exploring the dynamic response of a graphene‐reinforced aluminum‐based composite (GRAC) sandwich beam on an elastic foundation using an analytical solution. The investigation considers various parameters such as the percentage of graphene, the spring constant, the speed ratio, the moving load speed, and the distribution pattern 1–7 …”

Section: Introductionmentioning

confidence: 99%

A complex solution on the dynamic response of sandwich graphene‐reinforced aluminum‐based composite beams with copper face sheets under two moving constant loads on an elastic foundation

Eghbali,

Hosseini

2023

Int Journal of Mech Sys Dyn

Self Cite

View full text Add to dashboard Cite

An analytical solution was used to investigate the elastic response of a sandwich beam with a graphene‐reinforced aluminum‐based composite (GRAC) on an elastic foundation using copper as the face layer of the functionally graded composite beam and a simply supported boundary condition. Mantari's higher‐order shear deformation theory was utilized to derive the equations, which were solved in Laplace space and then converted into space–time using Laplace inversion. The exact response of the GRAC sandwich beam was obtained by considering the displacement at the mid‐span of the sandwich beam. Two moving loads with different speed ratios were applied at a single point, and the effect of various parameters, including the spring constant, the speed ratio, the percentage of graphene, the moving load speed, and the distribution pattern, was investigated. This study aimed to eliminate any overlap and improve the accuracy of the results. The exact solving method presented has not been reported in other articles so far. Additionally, due to the difficulty of solving mathematical equations, this method is only applicable to simple boundary conditions.

show abstract

Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method

Attia,

Matbuly,

Osman

et al. 2024

Acta Mech

View full text Add to dashboard Cite

This study investigates the free vibration behavior of a double cracked nanobeam composed of bi-directional functionally graded material. The analysis incorporates Eringen’s nonlocal elasticity theory and the Euler–Bernoulli theory. The material properties are considered to vary in both the thickness and length directions. The cracked nanobeam is modeled as a series of interconnected sub-beams, with rotational springs placed at the cracked sections. This modeling approach accounts for the discontinuities in rotational displacement resulting from bending, which is directly related to the bending moment transmitted by the cracked section. The problem is solved using the differential quadrature method, which approximates the derivatives of the field quantities by employing a weighted linear sum of the nodal values. By doing so, the problem is transformed into a linear algebraic system. Various supporting cases are examined, and a parametric study is conducted to analyze the impact of the axial and transverse gradient indices, nonlocal parameter, and crack severity on the obtained results.

show abstract

Free transverse vibrations analysis of size-dependent cracked piezoelectric nano-beam based on the strain gradient theory under mechanic-electro forces

Cited by 13 publications

References 19 publications

An dynamical evaluation of size-dependent weakened nano-beam based on the nonlocal strain gradient theory

An dynamical evaluation of size-dependent weakened nano-beam based on the nonlocal strain gradient theory

A complex solution on the dynamic response of sandwich graphene‐reinforced aluminum‐based composite beams with copper face sheets under two moving constant loads on an elastic foundation

Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method

Contact Info

Product

Resources

About