Three images of molecular mechanics simulations of the vibration of nanoparticles of varying shape. As the size of solids decreases into the nanoscale, the basic behavior of the continuous solid changes from a representation of essentially infinite points to a finite number of atoms. These simulations represent the lowest vibrational mode (typical a shearing deformation, as is clear from the cube and pyramid geometries) for these three shapes. These tools are being used to determine estimates of elastic constants of solids at the nanoscale. (Images are courtesy of the doctoral dissertation of Dr. Feranndo Ramirez).

Resonant ultrasound is the study of the fundamental behavior of solids using characteristics associated with their vibration properties. This study has combined elements of free and forced vibration theory of elastic, piezoelectric, and magnetoelectroelastic media with an experimental measurement program to determine behaviors such as the presence of flaws and the basic material properties of these elements. Of primary interest are the regular shapes of spheres, cylinders, and parallelepipeds. Our main computational tool is the Ritz method applied to these shapes, although we sometimes resort to finite element models for some applications.

Layered systems and piezoelectric/magnetostrictive solids are of particular current interest, as are materials with unusual constitutive relations. Current examples of materials under study are the elastic constants of cultured quartz, the vibration characteristics of trigonal cylinders, and the effective elastic constants of finite laminated paralellepipeds.

Co-workers on this study include Mr. Sudook Kim (NIST), Dr. Hassel Ledbetter (CU), Dr. Ward Johnson (NIST), Dr. Ivar Reimanis (Colorado School of Mines), Dr. Fernando Ramirez (Universidad de los Andes), and Professor Paul Heyliger. Past and current funding of this work has been supplied by the National Science Foundatiuon, NIST, the United States Department of Agriculture, and Storage Tech.
These six images represent the mode shapes corresponding to the lowest frequencies of traction-free vibration of a trigonal elastic cylinder. These solids have three-fold symmetry, resulting in a reduction of the standard eigenvalue problem into six distinct modal groups that depend on the nature of the elastic stiffness tensor and the form of the approximation functions used in our Ritz model. The vibration is periodic, and shown here are the maximum displacement patterns.