Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

Sharma, Pankaj; Parashar, S. K. S.

doi:10.1016/j.compstruct.2016.07.077

Cited by 50 publications

(14 citation statements)

References 23 publications

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“…Nevertheless, in its initially proposed form, DQM produced ill-conditioned matrices for large systems from which the weighting coefficients are obtained. This drawback was overcome with the introduction of the generalized differential quadrature method (GDQM) by Shu and Richards, where the weighting coefficients are obtained from an explicit algebraic formula [19] and since then GDQM has been efficiently applied to the vibration analysis of structures [16,[20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method

Demir

Balkan

Peker

et al. 2018

Jnl of Sandwich Structures & Materials

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This paper focuses on the vibration analysis of three-layered curved sandwich beams with elastic face layers and viscoelastic core. First, the equations of motion that govern the free vibrations of the curved beams together with the boundary conditions are derived by using the principle of virtual work, in the most general form. Then, these equations are solved by using the generalized differential quadrature method in the frequency domain, for the first time to the best of the authors’ knowledge. Verification of the proposed beam model and the generalized differential quadrature solution is carried out via comparison with the results that already exist in literature and the ANSYS finite element solution combined with the modal strain energy method. The effect of system parameters, i.e. layer thicknesses, the lamination angle of layers and the curvature on the vibration and damping characteristics of a curved sandwich beam with laminated composite face layers and a frequency dependent viscoelastic core is investigated in detail.

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Section: Introductionmentioning

confidence: 99%

Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method

Demir

Balkan

Peker

et al. 2018

Jnl of Sandwich Structures & Materials

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show abstract

“…Exact analytical solution was reported by Sharma and Parashar 49 to demonstrate the modal behavior of the FGM beam with piezoelectric properties under shear effect. A generalized DQ method was used by the same authors 50 to obtain the Eigen frequencies of the FGM annular plate with piezoelectric properties for different modes. Parashar and Sharma 51 obtained the Eigen frequencies of the FGM beam with piezoelectric properties under shear effect.…”

Section: Introductionmentioning

confidence: 99%

“…Parashar and Sharma 51 obtained the Eigen frequencies of the FGM beam with piezoelectric properties under shear effect. It may be seen from literature 47–51 that modal characteristics of functionally graded piezoelectric material (FGPM) beam was presented where mechanical properties were graded smoothly along the thickness direction with power law and sigmoid law distribution. In most of the above papers 20–32,47–51 modal analysis of FGM/FGPM beams has been performed without considering the thermal effect.…”

Section: Introductionmentioning

confidence: 99%

“…It has been revealed from the literature 20–32,47–68 that the mechanical properties are varying smoothly along the thickness of the beam. To the author's best knowledge, modal analysis of FGM beam under hygrothermal effect where material properties are graded continuously along the length of the beam has not been reported in the literature before.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On modal analysis of axially functionally graded material beam under hygrothermal effect

Sharma

Singh

Hussain

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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This investigation focuses on the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam are supposed to be graded smoothly along the axial direction under both power law and sigmoid law distribution. A finite element analysis with COMSOL Multiphysics® (version 5.2) package is used to find the Eigen frequencies of the beam. The accuracy of the technique is authenticated by relating the results with the prior investigation for reduced case. The effects of moisture changes, temperature, and volume fraction index, length-to-thickness ratio on the Eigen frequencies are investigated in detail. It is believed that the present investigation may be useful in the design of highly efficient environmental sensors for structural health monitoring perspective.

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“…Also, the free vibration analysis of FGPM annular plates resting on elastic foundations was conducted by Yas and Moloudi (2015). Adopting Mindlin plate theory, Sharma and Parashar (2016) studied the natural frequencies of FGPM annular plates using the generalized differential quadrature method. Phung-Van et al (2017) investigated the nonlinear transient responses of FGPM plates, where the von Ka´rma´n strains were considered and the Newmark time integration scheme was used to obtain the solutions.…”

Section: Introductionmentioning

confidence: 99%

Speed-dependent nonlinear broadband vibrations of smart functionally graded piezoelectric material plates

Wang

2018

Journal of Intelligent Material Systems and Structures

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In this work, speed-dependent nonlinear vibrations of functionally graded piezoelectric material plates are investigated both analytically and numerically. The functionally graded piezoelectric material plates move in the longitudinal direction at a constant speed. The material properties of functionally graded piezoelectric material plates have graded distribution in the thickness direction that obeys a power law. Adopting the Kármán nonlinear geometrical relations, the transverse equation of motion is derived from d’Alembert’s principle by considering the dynamic equilibrium relationships. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by utilizing the method of harmonic balance. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge–Kutta technique. The stability of approximate analytical solutions is also examined via the perturbation method. Nonlinear frequency-amplitude characteristics show some interesting nonlinear vibration phenomena in the smart structures. Specially, the nonlinear broadband vibration is detected in the translational functionally graded piezoelectric material plates due to the mode interaction. Finally, a parametric study is conducted to reveal the effects of system parameters on the nonlinear vibration characteristics of the translational functionally graded piezoelectric material plates.

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Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

Cited by 50 publications

References 23 publications

Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method

Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method

On modal analysis of axially functionally graded material beam under hygrothermal effect

Speed-dependent nonlinear broadband vibrations of smart functionally graded piezoelectric material plates

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