The determination of frequencies of laminated conical shells via the discrete singular convolution method

Abstract

The discrete singular convolution (DSC) algorithm for determining the frequencies of the free vibration of laminated conical shells is developed by using a numerical solution of the governing differential equations of motion based on Love's first approximation thin shell theory. By applying the discrete singular convolution method, the free vibration equations of motion of the composite laminated conical shell are transformed to a set of algebraic equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method.

Modal Analysis of Tapered Beam-Column Embedded in Winkler Elastic Foundation

“…The method of discrete singular convolution (DSC) was proposed to solve linear and nonlinear differential equations by Wei [15,16], and later it was introduced to solid and fluid [17][18][19]. It has been also successfully employed for different vibration problems of structural members such as plates and shells [20][21][22][23]. For more details of the mathematical background and application of the DSC method in solving problems in engineering, the readers may refer to some recently published reference [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Elasti̇k Bi̇r Malzeme İle Temas Hali̇nde Olan Grafen Tabakanin Ti̇treşi̇m Hesabi

“…47 tekil konvolüsyon çekirdeklerin (delta tip) ayrık yaklaşımlar sağlaması için kullanılabilir [40]. Örneğin bir fonksiyon için herhangi bir mertebeden türev δ Δ (x-x k )= Δδ α (x-x k ) olarak belirtilmiştir ve (n) türevin mertebesini göstermektedir [41].…”

Discrete Singular Convolution for Free Vibration Analysis Annular Membranes

“…In the present paper, details of the DSC method are not given; interested readers may refer to the works of [9][10][11][12][13][14][15][16]. Since it was first introduced by Wei [10], the discrete singular convolution method had been applied to many problems [17][18][19][20][21][22][23]. Consider a distribution, T and ) (t η as an element of the space of the test function.…”

“…Note that, the original test function η(x) has been replaced by f(x). Recently, the use of some new kernels and regularizer such as delta regularizer [14][15][16][17][18][19][20][21] was proposed to solve applied mechanics problem. The Shannon's kernel is regularized as [16] …”