The vibrational characteristics of a cantilever beam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical analysis of the frequency response of a cantilever beam, that is immersed in a viscous fluid and excited by an arbitrary driving force. Due to its practical importance in application to the atomic force microscope (AFM), we consider in detail the special case of a cantilever beam that is excited by a thermal driving force. This will incorporate the presentation of explicit analytical formulae and numerical results, which will be of value to the users and designers of AFM cantilever beams.

Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope

This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

/pdf/liquid-sloshing-dynamics-4apevf1yp2.pdf

Liquid Sloshing Dynamics

We have designed and tested a family of silicon nitride cantilevers ranging in length from 23 to 203 μm. For each, we measured the frequency spectrum of thermal motion in air and water. Spring constants derived from thermal motion data agreed fairly well with the added mass method; these and the resonant frequencies showed the expected increase with decreasing cantilever length. The effective cantilever density (calculated from the resonant frequencies) was 5.0 g/cm3, substantially affected by the mass of the reflective gold coating. In water, resonant frequencies were 2 to 5 times lower and damping was 9 to 24 times higher than in air. Thermal motion at the resonant frequency, a measure of noise in tapping mode atomic force microscopy, decreased about two orders of magnitude from the longest to the shortest cantilever. The advantages of the high resonant frequency and low noise of a short (30 μm) cantilever were demonstrated in tapping mode imaging of a protein sample in buffer. Low‐noise images were tak...

Short cantilevers for atomic force microscopy

This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.

/pdf/dynamics-of-rotating-machines-499re2kizd.pdf

N. Ganesan

Papers

Static analysis of functionally graded beams using higher order shear deformation theory

Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition

Vibration and acoustic response of a composite plate with inherent material damping in a thermal environment

Free vibration behaviour of multiphase and layered magneto-electro-elastic beam

Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells