Application of Elzaki Transform to Vibrations in Mechanical System

Elzaki Transform Method for Natural Frequency Analysis of Euler-Bernoulli Beams

“…The characteristic frequency equation is obtained for nontrivial solutions as shown: (31) Expansion gives the eigenequation:…”

“…Rama [31], applied the Elzaki transform method to the analysis of undamped, damped and forced vibrations of mechanical systems. Rama [31] transformed the governing single degree of freedom (SDOF) equation of motion using the ETM to an algebraic equation in the Elzaki-transformed space.…”

“…Rama [31], applied the Elzaki transform method to the analysis of undamped, damped and forced vibrations of mechanical systems. Rama [31] transformed the governing single degree of freedom (SDOF) equation of motion using the ETM to an algebraic equation in the Elzaki-transformed space. The researcher in [31], was able to derive analytical solutions to the resulting problem for undamped, damped, and forced vibrations of mechanical systems considered.…”

“…Rama [31] transformed the governing single degree of freedom (SDOF) equation of motion using the ETM to an algebraic equation in the Elzaki-transformed space. The researcher in [31], was able to derive analytical solutions to the resulting problem for undamped, damped, and forced vibrations of mechanical systems considered. Ramachandruni and Namala [32], have applied Elzaki transform method to obtain analytical solutions to some problems in engineering mechanics.…”

On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations

“…e Taylor collocation, Adomian decomposition, Chebyshev, Haar wavelet, successive approximation, Bernstein, homotopy perturbation, and other technologies are widely used to work with the IDEs of higher-order [3][4][5][6][7][8][9][10][11][12][13]. In recent years, Elzaki transform (ET) was introduced by Tarig Elzaki where it was used to solve different types of equations with integral, differential, partial integral, integro-differential, and fractional-order equations [14][15][16][17][18][19][20].…”