Gültekin Sinir B.2024-07-222024-07-2220150307904Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/16497This study proposes a general solution procedure for infinite mode analysis. The equation of motion is written in a general form using spatial differential operators, which are suitable for perturbation techniques. The multiple time scales method is applied directly to solve the proposed equation of motion. General investigations of some resonance cases are provided, such as parametric, sum type, difference type, and a combination of sum and difference type resonances. The proposed general solution procedure is applied to one- and two-dimensional problems. The results demonstrate that this general solution procedure obtains good solutions in the dynamic analysis of beams, plates, and other structures. © 2014 Elsevier Inc.EnglishAll Open Access; Bronze Open AccessDifference equationsMathematical operatorsPerturbation techniquesPlates (structural components)PlatingResonanceBeamEquation of motionGeneral modelHarmonic excitationMode analysisMultiple time scaleSpatial differential operatorsTwo-dimensional problemEquations of motionArticle10.1016/j.apm.2014.10.001