### Journals Information

**
Mathematics and Statistics Vol. 12(4), pp. 324 - 330 DOI: 10.13189/ms.2024.120403 Reprint (PDF) (634Kb) **

## Some New Oscillation Criteria for Euler-Bernoulli Beam Equations with Damping Term

**S. Priyadharshini ^{1}, V. Sadhasivam ^{1}^{,*}, K. K. Viswanathan ^{2}**

^{1}Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, India

^{2}Department of Mathematical Modeling, Faculty of Mathematics, Samarkand State University, Uzbekistan

**ABSTRACT**

The main objective of this study is to investigate some new oscillation criteria for Euler-Bernoulli beam equations with damping term by using the integral average method and Riccati technique. Philo introduces the following new integral operator, which is the main tool in this paper. Our plan of action is to reduce the multidimensional problems to ordinary differential problem by using Jenson's inequality, assuming the assumptions and integration by parts with boundary conditions. With hinged, sliding and hinged-sliding end boundary conditions, several new sufficient conditions are established. The results improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper. The majority of engineering constructions, ships, support buildings, airplanes, and rotor blades all use beams as structural elements. It is presumed that these elements are only subjected to static loads; yet, dynamic loads induce vibrations, which affect the stress and strain values. These mechanical phenomena also result in noise, instability, and the potential for resonance, which enhances deflections and failure. We analyze the spatial force load the equations of a damped Euler-Bernoulli beam derived from the equation for the velocity or final time displacement that we measured. Usually, internal damping determines the nature of this term.

**KEYWORDS**

Euler-Bernoulli Beam, Oscillation, Damping Term, Hinged-sliding Ends

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] S. Priyadharshini , V. Sadhasivam , K. K. Viswanathan , "Some New Oscillation Criteria for Euler-Bernoulli Beam Equations with Damping Term," Mathematics and Statistics, Vol. 12, No. 4, pp. 324 - 330, 2024. DOI: 10.13189/ms.2024.120403.

(b). APA Format:

S. Priyadharshini , V. Sadhasivam , K. K. Viswanathan (2024). Some New Oscillation Criteria for Euler-Bernoulli Beam Equations with Damping Term. Mathematics and Statistics, 12(4), 324 - 330. DOI: 10.13189/ms.2024.120403.