Static Analysis for Vibration Problems
Prof. Eisenberger Moshe
Israel Inst. of Technology, Haifa, Israel
21/09/2015
ore 11:00-13:00
LAMC
Abstract: The vibration analysis of structures is a widely researched area. Hundreds of papers were published on the topic. The problem can be divided into two groups: the first group includes cases for which an analytical solution is known, and the second group includes cases with no known analytic solutions. Benchmark solutions for the cases in the second group are highly desired for validation and comparison of existing and future numerical solutions. In this seminar a new method for solutions to the natural frequencies is found using static analysis. Starting from the equations of motion for a structure supported by elastic foundation, it is pointed out that the foundation stiffness and the inertia effect of the mass have opposite effect on the solution for the vibrating structure: The difference of these two factors is treated as a generalized elastic foundation parameter, and it can have a positive or negative value. In either case, one can solve the displacements under a given concentrated load. This deflection will be infinite if the structure losses its stiffness, or in other words, the generalized foundation is causing the structure to be unstable. Then, the solution for the vibration frequencies is equivalent to finding the values of the negative elastic foundation that will yield infinite deflection under a point load. Several examples, for rods, beams and plates are presented. Exact values are obtained with smaller computational effort.