• Advances in nano research
• /
• 제14권2호
• /
• pp.127-139
• /
• 2023

This paper studies the free vibration behavior of bi-dimensional functionally graded (BFG) nanobeams subjected to arbitrary boundary conditions. According to Eringen's nonlocal theory and Hamilton's principle, the underlying equations of motion have been obtained for BFG nanobeams. Moreover, the variable substitution method is utilized to establish the structure's state-space differential equations, followed by forming the dynamic stiffness matrix based on state-space differential equations. In order to compute the natural frequencies, the current study utilizes the Wittrick-Williams algorithm as a solution technique. Moreover, the nonlinear vibration frequencies calculated by employing the proposed method are compared to the frequencies obtained in previous studies to evaluate the proposed method's performance. Some illustrative numerical examples are also given in order to study the impacts of the nonlocal parameters, material property gradient indices, nanobeam length, and boundary conditions on the BFG nanobeam's frequency. It is found that reducing the nonlocal parameter will usually result in increased vibration frequencies.

• Kyungpook Mathematical Journal
• /
• 제31권2호
• /
• pp.161-169
• /
• 1991

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제2권2호
• /
• pp.31-40
• /
• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.487-494
• /
• 2016

In this paper, we study differential equations arising from the generating functions of tangent numbers. We give explicit identities for the tangent numbers.

• 대한수학회보
• /
• 제41권4호
• /
• pp.619-632
• /
• 2004

Some new oscillation criteria for parabolic neutral delay difference equations corresponding to two sets of boundary conditions are obtained. Our results improve the well known results in the literature.

• 전자공학회논문지B
• /
• 제32B권6호
• /
• pp.862-867
• /
• 1995

In this paper a method to perform Exclusive-OR operation between two tabular type Boolean expressions is presented. The proposed method allows to solve the switching equations and the simultaneous equations in a rather direct manner, compared with Unger's method.

• 충청수학회지
• /
• 제25권2호
• /
• pp.149-157
• /
• 2012

By means of fractional calculus techniques, we find explicit solutions of confluent hypergeometric equations. We use the N-fractional calculus operator $N^{\mu}$ method to derive the solutions of these equations.

• 대한수학회논문집
• /
• 제37권2호
• /
• pp.497-502
• /
• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

• Journal of applied mathematics & informatics
• /
• 제40권3_4호
• /
• pp.461-473
• /
• 2022

In this paper, we study differential equations arising from the generating functions of the geometric polynomials. We give explicit identities for the geometric polynomials. Finally, we investigate the zeros of the geometric polynomials by using computer.

• Journal of Mechanical Science and Technology
• /
• 제17권9호
• /
• pp.1287-1296
• /
• 2003

In this paper the dynamic analysis of the Macpherson strut motor-vehicle suspension system is presented. The equations of motion are formulated using a two-step transformation. Initially, the equations of motion are derived for a dynamically equivalent constrained system of particles that replaces the rigid bodies by applying Newton's second law The equations of motion are then transformed to a reduced set in terms of the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality For open chains, this process automatically eliminates all of the non-working constraint forces and leads to an efficient solution and integration of the equations of motion. For closed loops, suitable joints should be cut and few cut-joints constraint equations should be included for each closed chain. The chosen suspension includes open and closed loops with quarter-car model. The results of the simulation indicate the simplicity and generality of the dynamic formulation.