University of Tehran Press Journal of Computational Applied Mechanics 2423-6713 46 2 2015 07 01 Numerical free vibration analysis of higher-order shear deformable beams resting on two-parameter elastic foundation 117 131 55094 10.22059/jcamech.2015.55094 EN Mohammad Zakeri School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran Reza Attarnejad School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran Journal Article 2014 11 26 Free vibration analysis of higher-order shear deformation beam resting on one- and two-parameter elastic<br />foundation is studied using differential transform method (DTM) as a part of a calculation procedure. First,<br />the governing differential equations of beam are derived in a general form considering the shear-free<br />boundary conditions (zero shear stress conditions at the top and bottom of a beam). Using DTM the derived<br />equations governing beams, followed by higher-order shear deformation model, Timoshenko model and<br />Bernoulli-Euler model are transformed to algebraic forms and a set of recurrence formulae is then derived.<br />Upon imposing the boundary conditions of the beam at hand, a set of algebraic equations are obtained and<br />expressed in matrix form. Finally, the transverse natural frequencies of the beam are calculated through an<br />iterative procedure. Several numerical examples have been carried out to demonstrate the competency of<br />the present method and the results obtained by DTM are in good agreement with those in the literature.<br />Afterward, the free vibration of beams followed up by different models (i.e. Bernoulli-Euler, Timoshenko<br />and different higher-order models) are taken into consideration. https://jcamech.ut.ac.ir/article_55094_6e407e5a5926101c0ceea80e9aa6a51a.pdf