To investigate the oscillatory and asymptotic behavior for a certain class of second order nonlinear neutral perturbed dynamic equations on time scales. By employing the time scales theory and some necessary analytic techniques, and introducing the class of parameter functions and generalized Riccati transformation, some new sufficient conditions for oscillation of such dynamic equations on tim...

In this paper, natural frequencies and dynamic response of thick beams made of saturated porous materials resting on viscoelastic foundation are investigated for the first time. The beam is modeled using higher-order beam theory. Kelvin-voight model is used to model the viscoelastic foundation. Distribution of porosity along the thickness is considered in two different patterns, which are symme...

This paper analyzes the effects of structures and loads on the static bending and free vibration problems of bilayer beams. Based on static mechanical equilibrium and energy equilibrium, the static and dynamic governing equations of bilayer beam are established. It is found that the value of the thickness ratio has a significant effect on the static and dynamic responses of the beam, and the st...

In this paper we shall reduce the problem of the oscillation of all solutions of certain nonlinear fourth-order dynamic equations to the problem of oscillation of two second-order dynamic equations, which are discussed intensively in the literature. Further oscillation criteria of fourth-order equations are given and proved using integration and Taylor’s formula on time scales. Some conditions ...

In this paper we establish the method of successive approximations within the field of “dynamic equations on time scales”. Our introduction and application of the method leads to new results concerning the qualitative and quantitative properties of solutions to nonlinear dynamic equations on time scales. The new discoveries include sufficient conditions under which we conclude: existence; uniqu...