کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
292005 509792 2006 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Particularities of Newton's method in space frame force determination, utilising eigenpair functions
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی عمران و سازه
پیش نمایش صفحه اول مقاله
Particularities of Newton's method in space frame force determination, utilising eigenpair functions
چکیده انگلیسی

Redundant space frame dynamics are modelled through the structural eigenproblem, which is formulated to account for the geometric stiffness due to self-equilibrating membrane forces. The resulting mathematical eigenvalues and eigenvectors, respectively indicative of natural frequencies and modes of oscillation, are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium. Newton's method—or sensitivity analysis—provides a means for minimising the difference between mathematical and physically observed eigenvalues, whereupon the axial forces are inferred from the model. Issues of convergence and root uniqueness are anticipated. Eigenvalue coalescence, in which eigenvalues transitorily coalesce to permute their arbitrarily numerical ordering, is seen to define non-smooth eigenvalue functions and hence encumber Newton's method; mode tracing strategies to overcome this are discussed. The existence of various degrees of eigenvalue degeneracy, owing to frame cyclic symmetry or otherwise, is anticipated in terms of the influence upon Newton's method. If the degree of frame static redundancy is greater than one and there exist a number of linearly independent force distributions, then the required force determination is a multidimensional Newton method. Problems encountered in these manifold dimensions, including those arising from frame spatial periodicity and the adversity of Newton's method, are overcome. Emphasis is placed upon minimising the dimensionality of Newton's method through enforcement of equilibrium constraints. Illustrative numerical simulations are given and some applications of the method are proposed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Sound and Vibration - Volume 291, Issues 1–2, 21 March 2006, Pages 462–490
نویسندگان
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