On the use of differential quadrature method in the study of free axisymmetric vibrations of circular sandwich plates of linearly varying thickness

Magnetorheological fluids are materials that react to the applied magnetic field and are converted to the quasi-solid phase from the liquid one. Their applications in control and suppression of vibration have interested scientists nowadays. The present study is focused on the vibrational behavior of magnetorheological fluid circular plates that are embedded with magnetostrictive face layers. Magnetostrictive materials are also playing an important role in vibration control and are used widely in smart devices such as sensors and actuators. The structure is exposed to the transverse monotonic magnetic field and is located on the visco-Pasternak elastic substrate. Using Hamilton’s principle and based on classical plate theory, the motion equations and boundary conditions are extracted, and the generalized differential quadrature method is selected to solve them. Three different types of magnetorheological fluids are considered, and their effect on the results is discussed. The outcomes of this study can be used to design more capable and precise dampers, smart structures, and devices.

Section: Solution Methodsmentioning

confidence: 99%

Vibration analysis of magnetorheological fluid circular sandwich plates with magnetostrictive facesheets exposed to monotonic magnetic field located on visco-Pasternak substrate

Amir

Arshid

Maraghi

et al. 2020

“…Hamilton’s principle is employed in the present study to obtain the motions equations. This principle in absence of external works can be written as (Eslami and Khorshidvand, 2014; Lal and Rani, 2016; Ansari et al., 2018) …”

Section: Equations and Boundary Conditionsmentioning

confidence: 99%

Axisymmetric free vibration and stress analyses of saturated porous annular plates using generalized differential quadrature method

Khouzestani

Khorshidvand

2019

The current study presents free vibration and stress analyses of an annular plate which is made of saturated porous materials based on the first order shear deformation plate theory which accounts for the shear deformation effects. The pores are distributed in the thickness direction according to three different types, namely, porosity nonlinear nonsymmetric distribution, porosity nonlinear symmetric distribution, and porosity monotonous distribution. Employing Hamilton’s principle and variational formulation, the motion equations are derived and solved via the generalized differential quadrature method as a highly accurate and rapid convergence numerical method for various boundary conditions. The results are validated with simpler cases in the literature and different parameters of the structures such as pores distribution, porosity, pressure of fluids within the pores, and also the aspect ratio of the plate is considered and discussed regarding their effects on the results. It is seen that enhancing the porosity coefficient which means increasing the void volume, reduces the structure’s stiffness more than its density and so the frequency and stresses decrease. The findings of this work may be useful to design structures with desired mechanical properties.

“…Their paper presented the effects of some geometric and material properties on the frequencies, damping ratios, and also root mean square responses. Free axisymmetric vibrations of circular sandwich plates with linearly varying thickness were studied by Lal and Rani (2016). For moderate thickness, they assumed that the core is solid and the face sheets are treated as membranes of equal thickness.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a rectangular porous plate resting on an elastic foundation using high-order shear deformation theory

Arani

Khani

Maraghi

2017

This research deals with the dynamic analysis of a rectangular plate made of porous materials. The porous plate is subjected to a dynamic transverse load and is resting on a Pasternak foundation. Linear poroelasticity theory is used to obtain the Biot formulation of the constitutive equations for the porous material. Also, the Young modulus and density of the porous plate vary in the transverse direction versus the porosity of the plate. Tennessee marble is the porous material that used in this paper. Reddy’s third-order shear deformation theory with five unknowns, the energy method, and Hamilton’s principle are applied to derive the equations of motion of the porous plate. These equations are solved by a differential quadrature method as a numerical method due to five coupled large equations. A detailed numerical study indicates the significant effects of aspect ratio, thickness ratio, boundary conditions, elastic medium, load intensity, and porosity on deflection of the porous plate. Results of this study can be useful to design of pneumatic conveying, handling, and control systems.