Oscillation Criteria for a Certain Class of Cantilever Beam Equations with Nonlinear Damping Term

Abstract

The main aim of this paper is to establish some new oscillation criteria for a certain class of cantilever beam equations with the clamped-free end boundary conditions. We will establish the sufficient conditions for the oscillation by using the generalized Riccati technique. Our main tool of this paper is to generalize the Philo’s criteria with three variables in the oscillation results. Our approach is using Jenson's inequality to reduce the problem to ordinary differential inequality and satisfy the clamped-free end boundary condition.  A solution of u is oscillatory if it has arbitrary large number of zeros, otherwise it is nonoscillatory. Some illustrative examples are given to explain our effectiveness of new results. Analytical methods are now used together with the cantilever beam methods and constitute a significant component in modern vibration analysis.These solutions provide accurate answers if the experiments include real-world problems, are too expensive, or cannot be solved analytically. Beams with a permanent support at one end and no support at the other are called cantilever (or clamped-free) beams. Engineers and architects usually have to build structures that wear the structure and limit radiated noise and substantial displacement amplitudes by designing structures that react minimally to applied loading.