Abstract
This paper presents two simple and robust technique for response estimating of single-degree-of-freedom (SDOF) structural systems. The impulse method, because it is formulated based on the fundamentals of dynamics; especially, the linear impulse concept, and also the energy method, because the main idea of this method is inspired by energy conservation principles. These methods can strongly cope with linear damped systems for which damping ratio ζ is greater than 0.01. Assessment of SDOF dynamic systems under any arbitrary excitations is easily possible through the proposed methods. There is no error propagation through the solving process. The numerical example reveals the simplicity and robustness of the new technique compared to Duhamel’s integral and similar techniques. Finally, a numerical example is investigated to demonstrate the efficiency of the algorithms. The most famous record of El Centro ground motion is applied to the systems. The obtained results show that the new algorithm works exactly enough to compete with a conventional method such as the Duhamel integration method and the Newmark-β method. A comparison between the results of this method with the solution methods used by other researchers is shown to be a good match.
Highlights
The response of various dynamic systems, undergoing time-dependent changes, can be described by a second-order ordinary differential equation (ODE)
The impulse method, because it is formulated based on the fundamentals of dynamics; especially, the linear impulse concept, and the energy method, because the main idea of this method is inspired by energy conservation principles
These methods can strongly cope with linear damped systems for which damping ratio ζ is greater than 0.01.Assessment of SDOF dynamic systems under any arbitrary excitations is possible through the proposed methods
Summary
The response of various dynamic systems, undergoing time-dependent changes, can be described by a second-order ordinary differential equation (ODE). Accuracy of some numerical stepwise procedures used to compute the dynamic structural response of the SDOF system to a time-dependent excitation is evaluated in technical report ITL-97-7 published by the U.S Army Corps of Engineers They mainly investigated the Wilson-θ method, linear acceleration method, Newmark-β algorithm, central difference method, the fourth-order Runge-Kutta method, and Duhamel’s integral and Piecewise Exact Method [4]. Most of the aforementioned conventional methods of solving SDOF’s equation of motion, such as interpolation of excitation, Duhamel integral, central difference method, Wilson-θ, and Newmark-β, have an insufficiently complex algorithm, offer a restricted level of precision, and almost difficult to understand techniques Sometimes, they need advanced mathematical background and technical expertise. Current approaches to the solution of linear differential equations are classified into two categories of numerical methods in mechanical systems Those which use the superposition principle in their formulation such as Duhamel ′s integral and Fourier integral methods.
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