Abstract
The conventional frequency domain method (CFDM) and dual-force-based time domain method (DTDM) are often used to solve the steady-state response of system with complex damping under an arbitrary force. However, the calculation efficiency of the DTDM is low due to the straightforward summation operation of series even if the solution of the DTDM is the exact real part of the solution. In addition, since the CFDM only can obtain the real part of solution not the complete solution, it gives misleading information that the solution does not have an imaginary part. In this paper, a fast frequency domain method (FFDM) is proposed to calculate the complete response of complex damping system including the imaginary part with a higher accuracy in a much faster manner. The new FFDM uses half of the Fourier series of the discrete Fourier transform of the actual arbitrary force to construct the Fourier series of the dual force, followed by calculating the time history response using the inverse fast Fourier transform. The new developed method is validated through three numerical examples with harmonic and seismic excitations. The numerical results show that the accuracy of the new FFDM is compatible to the DTDM but with much higher computational efficiency.
Highlights
In structural dynamics, the damping force of a complex damping system [1,2,3] which is known as hysteretic damping, rate-independent damping, structural damping, fd, can be calculated as: fd = −iηku, (1) √in which i = −1 is a pure imaginary number, and k is the stiffness of the structure, η is the complex damping factor, and u is the displacement
For the forced vibration of system with complex damping, two methods are commonly used to obtain the steady-state responses of such a system, including the conventional frequency domain method (CFDM) and the dual-force-based time domain method (DTDM)
A fast frequency domain method is developed for the steady-state solution of the forced vibration of system with complex damping
Summary
For the forced vibration of system with complex damping, two methods are commonly used to obtain the steady-state responses of such a system, including the conventional frequency domain method (CFDM) and the dual-force-based time domain method (DTDM). Methods using frequency domain which can only obtain the real part of the solution satisfy the engineering demand To obtain both the real and imaginary parts of the solution, the DTDM can be applied. A fast frequency domain method (FFDM) without constructing dual force is developed, which can simultaneously compute the imaginary part of the solution to comprehensively realize the dual relation in the complex system.
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