A vital subject of engineering structures is mechanical oscillations. If the mechanical oscillation is uncontrolled, it can lead to structural failure due to large dynamic stresses developed, as the collapse occurred on the Broughton Suspension bridge due to soldiers walking in step. This paper addresses mechanical oscillation problems employing a proposed modified variant of coyote optimizer. Coyote optimization algorithm (COA) is a new meta-heuristic which mimics the social behavior of coyotes. COA suffers with stagnation problems and immature convergence while solving optimization problems. In this paper, the COA is hybridized with Laplace Crossover operator and new culture tendency strategies are adapted, modified variants of coyote optimization algorithm (MvCOA). The proposed MvCOA is presented to approximately solve mechanical oscillation problems independently of their order, form, and stated conditions. With the fundamental concepts of ordinary differential equations and Fourier series expansion, mechanical oscillation problems can be modeled as a problem of optimization whereby the optimization task is achieved using the proposed MvCOA. Five different ordinary differential equations and four mechanical oscillation problems are solved approximately and then compared with their corresponding exact solutions. The statistical analysis validates that the presented MvCOA is an effective algorithm for different optimization problems. However, from the empirical results, it is visible that the suggested MvCOA approximate approach was able to reach a successful performance solving different mechanical oscillation problems.
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