In order to investigate the effects of non-linear springs in vibrating behavior of vehicles, the independent suspension of conventional vehicles could be modeled as a non-linear single degree of freedom system. The equation of motion for the system would be a non-linear third order ordinary differential equation, when considering the elasticity of rubber bushings in joints of shock absorber. It...

piezoelectric microcantilevers (mcs) are a new generation of microbeams used in atomic force microscopes (afms). due to their miniaturization of afms as well as their increased imaging precision and speed, these mcs are more popular than their classical counterparts. given the widespread application of these beams in nanoparticle topography, analysis of their vibrating motion has attracted much...

Abstract: The present paper concludes via an analytical method to reduced formulae for determining the eigenfrequencies and eigenmodes of multi-span continuous beams with spans of different lengths and bending rigidities in a very easy and efficient way. The rigorous determination of eigenfrequencies and eigenmodes allows us to focus on the derivation of the time function for the forced vibrati...