A study of internal and distributed damping for vibrating turbomachiner blades

Internal and distributed damping as possible methods for reducing the vibration response of turbomachine blades and theoretical methods for analyzing damped vibration were studied. It is demonstrated how the Ritz-Galerkin methods may be used to straightforwardly to analyze forced vibrations with damping. This is done directly without requiring the free vibration eigenfunctions. The Galerkin method is an effective technique for these types of problems. The Ritz method has the further advantage of not needing to satisfy the force type boundary conditions, which is particularly important for plates and shells. But proper functionals representing the forcing and damping terms must be developed, and this is done. Two types of damping--viscous and material (hysteretic) are considered. Both distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. Studies showing the rates of convergence of the solutions are made. In the case of the cantilever beam, approximate solutions from the present methods are compared with the exact solutions

Periodic solutions of forced Kirchhoff equations

We consider Kirchhoff equations for vibrating bodies in any dimension in presence of a time-periodic external forcing with period 2pi/omega and amplitude epsilon, both for Dirichlet and for space-periodic boundary conditions. We prove existence, regularity and local uniqueness of time-periodic solutions of period 2pi/omega and order epsilon, by means of a Nash-Moser iteration scheme. The results hold for parameters (omega, epsilon) in Cantor sets having measure asymptotically full as epsilon tends to 0. (What's new in version 2: the case of finite-order Sobolev regularity, the case of space-periodic boundary conditions, a different iteration scheme in the proof, some references).Comment: 23 page

Noise transmission through plates into an enclosure

An analytical model is presented to predict noise transmission through elastic plates into a hard-walled rectangular cavity at low frequencies, that is, frequencies up through the first few plate and cavity natural frequencies. One or several nonoverlapping and independently vibrating panels are considered. The effects on noise transmission of different external-pressure excitations, plate boundary conditions, fluid parameters, structural parameters, and geometrical parameters were investigated

The reasons for the collapse of the Tacoma Narrows Bridge and the lessons for the classroom

On 7 November 1940, a historical event occurred for suspension bridge construction and aerodynamic engineering around suspension bridges. Engineers investigating the event concluded the bridge collapsed due to high winds but did not explain how. Later lab tests by other engineers and scientists demonstrated that the collapse happened either due to forced oscillations with Resonance or aeroelastic flutter. Forced oscillations with Resonance treated the bridge as an object being periodically pushed by the winds in Resonance with its natural frequency. And aeroelastic flutter treats the bridge as a wingspan in a fluid stream where the winds would alternate the pushing of the bridge span as it enters above and under the plate. Due to historical similarities, some believed the collapse occurred due to Resonance. However, later articles would discuss the aeroelastic flutter and criticize the resonance argument. One of these articles would be written by Billah and Scanlan, criticizing the use of the bridge as an example of Resonance in physics books and showing an alternative interpretation of the collapse. After discussing the collapse with an expert in aerodynamics on bridges from the University of Stavanger, we were informed that the Billah and Scanlan article is considered the modern explanation by the professional community. However, there are still physics books today that still misrepresent the circumstances around the collapse. We, as teaching students, agree with the Billah and Scanlan article and the opinion of the professional community that the collapse was most likely due to aeroelastic flutter. And that the collapse being represented as Resonance simplifies and misrepresents a more complicated and comprehensive problem around the Tacoma Narrows Bridge.On 7 November 1940, a historical event occurred for suspension bridge construction and aerodynamic engineering around suspension bridges. Engineers investigating the event concluded the bridge collapsed due to high winds but did not explain how. Later lab tests by other engineers and scientists demonstrated that the collapse happened either due to forced oscillations with Resonance or aeroelastic flutter. Forced oscillations with Resonance treated the bridge as an object being periodically pushed by the winds in Resonance with its natural frequency. And aeroelastic flutter treats the bridge as a wingspan in a fluid stream where the winds would alternate the pushing of the bridge span as it enters above and under the plate. Due to historical similarities, some believed the collapse occurred due to Resonance. However, later articles would discuss the aeroelastic flutter and criticize the resonance argument. One of these articles would be written by Billah and Scanlan, criticizing the use of the bridge as an example of Resonance in physics books and showing an alternative interpretation of the collapse. After discussing the collapse with an expert in aerodynamics on bridges from the University of Stavanger, we were informed that the Billah and Scanlan article is considered the modern explanation by the professional community. However, there are still physics books today that still misrepresent the circumstances around the collapse. We, as teaching students, agree with the Billah and Scanlan article and the opinion of the professional community that the collapse was most likely due to aeroelastic flutter. And that the collapse being represented as Resonance simplifies and misrepresents a more complicated and comprehensive problem around the Tacoma Narrows Bridge

Preface for Millard Beatty

Professor Beatty has contributed a wide variety of research papers and book articles on topics in finite elasticity, continuum mechanics and classical mechanics, including some fundamental experimental work. His works are clear and informative and expose a didactic quality. In the following, we briefly touch upon some of the highlights of his research involvement throughout the years