Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach

Joshi, P.V.; Jain, Nitin; Ramtekkar, Gangadhar

doi:10.1016/j.tws.2015.02.004

Cited by 48 publications

(17 citation statements)

References 35 publications

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“…When = 0.07, the speed 0 ≤ < 8. 16, the imaginary parts of the first three modes are zero, and the real parts are decreased with the increase of the speed. When the speed c=8.…”

Section: Numerical Resultsmentioning

confidence: 94%

“…When the speed c=8. 16, the first-order mode is divergence instability. When the speed c=10.12, the membrane becomes stable again.…”

Section: Numerical Resultsmentioning

confidence: 98%

“…Substituting (17) into (16) and then performing inverse Lagrangian transformation, the differential equation of the moving hard membrane in the time domain that satisfies the Kelvin-Voigt model is obtained:…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Wang et al [15] employed the DQM (differential quadrature method) to analyze vibration and stability of a viscoelastic cracked plate containing changing thickness. Joshi and Jain [16] applied the classical plate theory to study the parameter vibration and thermal buckling behavior of a thin plate with internal crack. It was noted that the temperature affected natural frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Transverse Vibration of a Moving Viscoelastic Hard Membrane Containing Scratches

Shao

Wang

et al. 2019

Mathematical Problems in Engineering

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The transverse vibration and stability of a moving viscoelastic hard printing membrane containing scratches are investigated. Based on the viscoelastic differential constitutive relation, thin plate theory, and d' Alembert principle, the differential equation of a moving viscoelastic hard membrane with a straight scratch through the surface is derived by using the continuity condition of the scratches. The complex characteristic equation is obtained by using the differential quadrature method. The effects of the scratch depth and scratch position on the critical instability speed of the moving hard membrane were highlighted by solving the differential equation and numerical calculation, and the coupling effects of speed and scratch depth on vibration characteristics of the hard membrane are also analyzed. Numerical calculation results show that the hard membrane experiences divergence instability when the actual printing speed is v=23.2 m/s, and the membrane is stable when v<23.2 m/s. The theoretical guidance and method for scratches detection of the precision coated hard membrane are provided.

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“…When = 0.07, the speed 0 ≤ < 8. 16, the imaginary parts of the first three modes are zero, and the real parts are decreased with the increase of the speed. When the speed c=8.…”

Section: Numerical Resultsmentioning

confidence: 94%

“…When the speed c=8. 16, the first-order mode is divergence instability. When the speed c=10.12, the membrane becomes stable again.…”

Section: Numerical Resultsmentioning

confidence: 98%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transverse Vibration of a Moving Viscoelastic Hard Membrane Containing Scratches

Shao

Wang

et al. 2019

Mathematical Problems in Engineering

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show abstract

“…It was obvious that the deflection of the FGM plates increased as the temperature increased. According to Equation (19), the axial tensile or compressive forces could be generated because of the sudden temperature change, which led to the peak deflection increases [40].…”

Section: The Influence Of Temperature Changesmentioning

confidence: 99%

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

et al. 2019

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The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.

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Vibration and flutter analysis of piezoelectric plates in an electrothermal field using higher order theories

Khoshgoftar

2024

Engineering Reports

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In this study, we investigate the vibration and dynamic stability of a thick rectangular plate that is restrained on four edges by simple clamps. Nonlocal elasticity based on high‐order shear theories is used to model the structure, which takes into account not only shear flow along the thickness, but also different distributions of shear deformations. The inclusion of rotational inertia also significantly impacts the accuracy of the results. The aerodynamic flow on the plate surface is modeled using the linear piston theory, which relates the incoming load from the aerodynamic flow to the transversal deformation of the plate. By utilizing Hamilton's principle, the governing equations for the system are obtained and solved using the weighted residual method. The results are validated by comparing them to previous studies. The effects of various parameters, such as the plate's geometrical properties, the impact of different theories, heat, electric voltage, and nonlocal variables, on the vibration and flutter behavior of the plate are examined. Additionally, it is found that the application of negative voltage increases the critical aerodynamic pressure by creating a traction force, and that a suitable thermal load can avoid instability caused by aerodynamic load. By applying voltage and heat, it is possible to increase the flutter threshold and delay it.

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Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach

Cited by 48 publications

References 35 publications

Transverse Vibration of a Moving Viscoelastic Hard Membrane Containing Scratches

Transverse Vibration of a Moving Viscoelastic Hard Membrane Containing Scratches

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

Vibration and flutter analysis of piezoelectric plates in an electrothermal field using higher order theories

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