Spectral analysis of systems with non‐classical damping using classical mode superposition technique

Abstract

SUMMARYA spectral method for random vibration analysis of a structural system with non-proportional damping is presented using classical (undamped) mode superposition technique. The method obtains the frequency response function of the system by solving the dynamic equilibrium equations in generalized co-ordinates through an iterative process. The iterative solution is written in closed form and the proof for convergence of the iterative process is given. Numerical examples show the convergence characteristics of the process and an excellent accuracy of the obtained results. The method turns out to be computationally more efficient than the conventional methods of spectral analysis using damped mode shapes and frequencies.

A method for the transfer function matrix of combined primary-secondary systems using classical modal decomposition

“…The variance ÿ 0 increases with 1 − 2 ; hence, greater mean maximum relative displacements are to be expected as damping of the appendix tends to be small compared to that of the primary system. Figure 4 also shows the exact solution as given by Jangid and Datta [6] and Igusa et al [9] As seen, the results with the proposed method coincide with those using the exact solution. Figure 5 shows the shape factor of the response power spectral density function, = {1 − (ÿ 1 ) 2 =(ÿ 0 ÿ 2 )} 1=2 , as a function of 1 − 2 .…”

“…The pseudo-force method is an iterative procedure to obtain the transfer function matrix of non-classically damped systems [5,6]. This method is extended here to evaluate the transfer function matrix of coupled primary-secondary systems.…”

“…An appendix with mass, sti ness and damping, m 2 , k 2 and c 2 , respectively, is connected to the primary system as shown in Figure 2. This system response has been analysed by Igusa [9] using complex eigenvalues and eigenvectors and by Jangid and Datta [6] using the pseudo-force approach but for the modal shapes and frequencies of the combined primary-secondary system. The system will have proportional damping if the sti ness ratio k 1 =k 2 is equal to the damping ratio c 1 =c 2 .…”

Time-Segmented Frequency-Domain Analysis for Non-Linear Multi-Degree-of-Freedom Structural Systems

“…The convergence of the iterative process was quite good. Jangid and Datta [7] employed the same procedure as Claret and Venancio-Filho; however the iterative process was performed in the frequency domain.…”

Simplified analysis of asymmetric structures with supplemental damping

“…Although appealing, this procedure requires solutions of the response in the time-domain, which can be numerically ine cient, and cannot be implemented on most commercially available structural analysis programs. Spectral method for random vibration analysis has also been proposed [10].…”