Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method

Effect of the Simultaneous Variation in Blade Root Chord Length and Blade Taper on Helicopter Flight Control Effort

“…For example, in [5], flapwise bending vibration analysis of a rotating, tapered cantilever Bernoulli-Euler beam (e.g., helicopter blade) was conducted using the differential transform method (i.e., DTM). The effect of blade taper on natural frequencies was also studied.…”

Thermal Buckling Analysis of Functionally Graded Circular Plate Resting on the Pasternak Elastic Foundation via the Differential Transform Method

“…(13)(14)(15)(16) into Eq. (19), setting the resultant expression into the expression of the total potential energy function, Eq. (17), and employing Euler equations [5], the governing equilibrium equations in the buckling of the plate resting on the Pasternak foundation based on the von-Karman nonlinearity are obtained as follows [10]:…”

“…The literature review indicates that the present work is the first attempt to exploit DTM to evaluate the critical buckling temperature. A number of studies have been carried out by this method [18][19][20][21][22][23][24]. The results are presented in four categories based on linear and uniform thermal load and simply supported and clamped edge conditions in the proceeding sections.…”

Approximate Solution for Longitudinal Vibration of Non-Uniform Beams by Differential Transform Method (DTM)

“…In another paper, they used this method to solve the initial-value problems [13]. The DTM was used to find the dimensionless natural frequencies of the tapered cantilever Bernoulli-Euler beam by Ozdemir and Kaya [14]. Free vibration differential equations of motion of one end-fixed, the other simply supported and axial loaded beams on elastic soil was solved using DTM by Catal [15].…”