Sentence examples for modal truncation problem from inspiring English sources

The modal truncation problem is frequently encountered in nonviscously (viscoelastically) damped systems since only the modes of interest are usually considered in the dynamic analysis of engineering problems.

By considering the first-order terms of the Neumann expansion, a generalized mode acceleration method (GMAM) is presented to handle the modal truncation problem.

Increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping, the need to consider the modal truncation problem of viscoelastic systems is more than ever before.

The modal truncation augmentation method (MTAM) is also presented to handle the modal truncation problem by making the equilibrium equations into a subspace equation spanned in terms of the columns of a projection basis given in the GMAM.

For viscoelastic systems, the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small-scaled problem is considered for some eigensolution methods.

Concerning the finite-dimensional systems, using the proposed method in conjunction with pseudo-inversion theorems, proves that "inertia relief corrections" remedy modal truncation problems in singular floating systems, just as static corrections do for simply supported systems.

Since the large cable net structures have many closely spaced vibrational modes in the range of low frequencies, traditional modal based control may cause modal truncation and spillover problems.

Afterwards, modal truncation is applied, the dynamic equations of the passive electrical network are integrated into the piezoelectric model and eigenvalue problems are solved to extract the increase in modal damping ratios.

A reduced order model is obtained using modal truncation.

It is shown that the proposed method can reduce the modal truncation error significantly.

Two modal truncation schemes, middle-high-modal and low-high-modal truncation schemes, are presented according to the values of the exciting frequencies.