M.Sc Thesis

M.Sc StudentMeir Mergi
SubjectThe Influence of Residual Stresses and Geometry Changes on
Natural Frequencies in Thermally Stressed Bimetal
Rectangular Beam
DepartmentDepartment of Mechanical Engineering
Supervisors Full Professors Bucher Izhak
Full Professors Rittel Daniel
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


The thesis investigates the vibrations of a bi-layered, initially straight beam that curves due to thermal stresses. The identification and influence of curvature and residual stresses caused by film deposition on natural frequencies and mode shapes are introduced.

Film depositions and coating have many applications in the mechanical and electronics industries where they are usually referred to as bimetal materials, bi-layers or multilayer. The temperature of the deposition processes is usually different from room temperature, so that the process introduces residual stresses and curvature in the assembly, impairing its functionality.

A non-linear 3D FEM analysis of a rectangular beam with coating was carried out for three cases: a beam with residual stresses and curvature effects; initially curved beam without residual stresses; straight beam with coating. The natural frequencies and mode shapes of these three cases were calculated using a modal analysis solver. Comparing the cases revealed that the effect of curvature can be seen for two mode shapes (lateral bending and torsion). Calculating Stoney’s curvature yields with constant radius whereas the FEM analysis resulted with parabolic curvature with varying radius. A very large difference was calculated between Stoney’s formula to the FEM analysis and a large difference was calculated to Freund formula.

An investigation of the effect of process temperature on the curvature, residual stresses and natural frequencies were conducted with FEM analyses. A linear correlation was found between the residual stresses and the process temperature. Several more FEM analyses, of other bimetal material, were carried out in purpose to validate the effect, which complied with the former results. A sensitivity analysis assessed the effect of each parameter from the FEM model on the residual stresses and the natural frequencies.

A base excitation experiment was set to compare the model to an experiment result measuring with laser the velocity changes of the beam. The experiment results agree well with the model.

A microcantilever model was analyzed with FEM to verify the change in natural frequencies due to curvature and residual stresses. The results showed a change in natural frequencies therefore, a new routine procedure for microcantilever curvature and residual stress detection is essential, especially when employing such techniques.