Undamped Beam Research Articles

Vibration damping of large structures induced by attached small substructures each with multiple degrees of freedom

At the previous meeting [J. Acoust. Soc. Am. 94, 1814 (A) (1993)] a relatively simple method was described for estimating the vibration damping introduced into a large structure by a multitude of small substructures compliantly connected to the large structure. The analysis in that talk assumed that the substructures behaved as sprung masses with different but closely spaced frequencies of resonance, each mass having a single frequency of resonance corresponding to one degree of freedom. The analysis is now extended to attached substructures each with multiple degrees of freedom. As an example, calculations are presented of the damping of flexural vibrations induced in a large undamped beam by a large number of small cantilevered strips of gradually varying length attached to the beam. The calculated results are compared with experimental data for this arrangement described some years ago by M. Heckl. [Work supported by ONR.]

The influence of an intermediate support on the stability behaviour of cantilever beams subjected to follower forces

A non-uniform undamped beam, which is simply supported at one end, resting on an elastically flexible support at an intermediate abscissa q, is examined. The beam is subjected to a generic set of follower forces along the axis, so that Beck, Leipholz and Hauger problems can be easily recovered as particular cases. In all these systems a location for the intermediate support exists, which corresponds to passage from flutter to divergence.

Dynamic stiffness and response analysis

The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method has been extended to frame structures with uniform or non-uniform, straight or curved, damped or undamped beam members. An orthonormal condition is suggested here for the natural modes resulting from the dynamic stiffness method; modal analysis in the classical sense is then made possible. Modes corresponding to repeated natural frequencies are discussed in detail. An expansion theorem for expanding from a finite number of degrees of freedom by means of an infinite number of modes is validated by means of the frequency-dependent shape functions. Distributed modal participation factors are introduced for distributed excitations.

A new approximate method of finding the loss factors of a sandwich cantilever

Extensively used methods for finding the loss factors of sandwich designs are predominantly based on the assumption, for the sake of simplicity, that only symmetrical boundary conditions occur. In this paper a new approximate method for the calculation of loss factors and other dynamical characteristics of the damped normal modes for sandwich beams with arbitrary boundary conditions is developed. Based on the linearization of a hysteretically damped sandwich beam in the neighborhood of the corresponding undamped beam, the theory has a number of advantages from the analytical and computational points of view. The method is applied to a damped sandwich cantilever. Numerical results for the fundamental damped normal mode as well as a comparison with the exact method are presented graphically.