Unsolved structural dynamic mathematical models via Novel technique approach

Abstract

Dynamic problems are solved using the Novel technique, considering the forcing term is free forced vibration, constantly forced vibration and harmonic function with mass and stiffness terms zeros. Two different interpolation functions have been considered for solving such problems, the first one × = a + bt and the second one × = acosωt + bsinωt. The results achieved from the novel technique using these interpolation functions are compared with the precise solutions. Not only this method other methods such as the Newmark-beta method, Runge-Kutta fourth-order and Laplace transforms have been applied to the same structural dynamic problems. The paper employs the novel technique method to various initial value problems such as emotional problems. This method has been adapted in various fields of Engineering. Limited research has been done in the past in the dynamics field using this method. So, an attempt has been made to examine the validity of such a method. The method gave exact solutions for most of the problems. It is observed that the complementary function of the solution obtained using the interpolation function × = acosωt + bsinωt is to be divided by the number of iterations to obtain the precise solution. The Novel technique gave an exact solution for cases where there is no force acting and in cases where a constant force is acting. In the cases in which a harmonic force is acting, when the mass term is zero, the novel technique method is overestimated. In the case of stiffness term zero, it is underestimated. The paper aims to obtain approximate dependent variable quantities for distinct displacement interpolation functions for various structural dynamic natural problems.