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

Abstract

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.

Lời giải Navier phân tích ổn định và dao động riêng tấm chữ nhật bằng vật liệu FGM rỗng bão hòa chất lỏng đặt trên nền đàn hồi Pasternak

“…[14] tính toán tần số dao động riêng của tấm chữ nhật FGP đặt trên nền đàn hồi Pasternak. Bằng phương pháp vi phân cầu phương tổng quát (generalized differential quadrature method), Khouzestani và Khorshidvand [15] phân tích ứng suất và dao động riêng của tấm FGP hình vành khuyên bão hòa chất lỏng theo lý thuyết biến dạng cắt bậc nhất. Lixian [16] khảo sát đặc trưng động lực học của tấm chữ nhật FGP bão hòa chất lỏng, tựa khớp trên chu vi.…”

Dynamic responses of clearance-type non-linear systems subjected to base harmonic excitation and their experimental verification

“…There are several methods (Mendelson Kenneth 1970; Nayfeh 1973; Thomsen 2003; Khouzestani and Khorshidvand 2019; Civalek et al, 2020) such as the method of iteration, method of averaging, harmonic balance method, method of multiple scales, differential quadrature and non-local finite element method and their variants for theoretically estimating the response of a non-linear system. Miles (1993) estimated response of a bilinear oscillator by considering it as a linear system with randomly varying natural frequency.…”

A unified Jacobi–Ritz approach for the FGP annular plate with arbitrary boundary conditions based on a higher-order shear deformation theory

“…This method simplifies the partial differential equations into an eigenvalue problem through discretizing the spatial derivatives, which is considered as a highly efficient numerical technique. The generalized differential quadrature method (GDQM) (Bemani Khouzestani and Khorshidvand, 2019; Shahraki et al, 2020) is a solution methodology that is newly applied to the vibration problems. It uses a new discrete function, which in arbitrary point is estimated as a linear summation of the weighting function values at all adjacent points.…”