Vibration Of Linear Structures Research Articles

Vibrations of linear structures with spatial local nonlinearities

AbstractClassical Modal Analysis can be applied to linear systems if the corresponding damping matrix is proportional to the mass or/and stiffness matrices. Otherwise, e.g., in case of structures with single external damping devices, an alternative or approximate solution procedure for determining the dynamic response has to be chosen, compare [1]–[3]. Vibration problems of linear structures with spatially localized nonlinearities are related to those non‐classically damped systems. Such systems are characterized by the fact that their nonlinear behavior is largely restricted to a limited number of single points in the structure. The objective of this paper is to present an approximate semi‐analytical procedure for analyzing the steady‐state harmonic response of those locally nonlinear structures, where special emphasis is laid on beams with single nonlinear devices. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Active and Reactive Structural Energy Flow

Vibration of linear structures having internal material damping is considered. Energy supplied to such structures by external dynamic loads and mechanical energy flow inside these structures are investigated. The paper aims at presenting and discussing relations which are useful when studying energy transmission through mechanical systems. Special attention is paid to the case of stationary harmonic vibration, but general stationary vibration is also discussed. Continuity equations for the active and reactive mechanical intensities are derived for a solid continuum model. Limits for the active and reactive power supplied to a structure in terms of structural and loading properties are also established. Numerical examples with discrete, continuous and discretized structures demonstrate the results obtained.

Forced harmonic vibration of rotating beam systems in space analysed by use of exact finite elements

A general computational technique is developed for the accurate analysis of forced non-synchronous harmonic vibration of linear structures rotating with constant speed about a fixed axis in the inertial space. The structures studied are built up from piecewise uniform straight Rayleigh-Timoshenko beam members having coinciding cross-sectional centres of geometry, shear and mass, and vibrating in coupled tension, torsion, bending and shearing. Hysteretic and viscous dampings in the beam material and in a Winkler-type ambient medium are considered. Rigid bodies and modal bodies and also discrete masses, springs and dampers can be included in the structure. The six coupled scalar partial linear differential equations governing the motion of a loaded beam are established in a corotating local co-ordinate system. A transcendentally frequency-dependent non-symmetric complex-valued 12 × 12 stiffness matrix is derived, over a state-space analogy and an associated eigenproblem, for a harmonically vibrating beam member non-synchronously excited at its ends. This matrix is exact in the sense that no assumed shape functions and no lumped masses are used. The general computational technique is here applied to a simple beam rotating about (1) its longitudinal axis and (2) about a transverse axis. The study clarifies the influence of gyroscopic effects and of material and support dampings on the dynamical behaviour of the beam at different rotational speeds and forcing frequencies. Resonance frequencies are found. Frequency response functions and frequency maps are plotted.