The influence of various boundary conditions on dynamic stability of a beam-moving mass system

الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک

Ramin Motiei ¹ (Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran)
Mostafa Pirmoradian ² (Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran)
Hossein Karimpour ³ (Department of Mechanical Engineering, University of Isfahan, Isfahan, Iran)

تاريخ الإرسال : 03 الثلاثاء , صفر, 1444 تاريخ التأكيد : 07 السبت , جمادى الثانية, 1444 تاريخ الإصدار : 07 الخميس , جمادى الأولى, 1444

الکلمات المفتاحية: Dynamic stability, Boundary Condition, Moving mass, Viscoelastic medium,

ملخص المقالة :

In this paper, the effect of different boundary conditions on dynamic stability of a beam located on a viscoelastic medium stimulated by moving masses and periodic axial force is studied. Partial differential equations governing the system are derived using Hamilton's method and based on Euler-Bernoulli beam theory. Then, equations are converted into a set of ordinary differential equation with time-varying coefficients using Galerkin method along with trigonometric shape functions. The time-varying position of moving loads causes these time-varying coefficients in the governing equations. By applying Floquet's theory to the obtained equations, the conditions of parametric resonance are analyzed for different values of mass and velocity of passing loads. The results obtained from this research show that the stiffness and viscosity of the elastic medium have positive effects on the stability of the beam under moving and fluctuating axial loads. So, with a suitable choice for these values in practical applications, it is possible to prevent unexpected vibrations of the structure. In addition, the use of fixed supports for the two ends of the beam exposed to the mentioned loadings has high reliability in the discussion of dynamic stability.

المصادر:

 

• Esen, I., Eltaher, M. A., & Abdelrahman, A. A. (2021). Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass. Mechanics Based Design of Structures and Machines, 1-25.


• Foyouzat, M. A., Abdoos, H., Khaloo, A. R., & Mofid, M. (2022). In-plane vibration analysis of horizontally curved beams resting on visco-elastic foundation subjected to a moving mass. Mechanical Systems and Signal Processing, 172, 109013.


• Torkan, E., Pirmoradian, M., & Hashemian, M. (2019). Dynamic instability analysis of moderately thick rectangular plates influenced by an orbiting mass based on the first-order shear deformation theory. Modares Mechanical Engineering, 19(9), 2203-2213.


• Torkan, E., & Pirmoradian, M. (2019). Efficient higher-order shear deformation theories for instability analysis of plates carrying a mass moving on an elliptical path. Journal of Solid Mechanics, 11(4), 790-808.


• Hu, J., Hu, W., Xiao, C., & Deng, Z. (2022). Coupling Vibration of Simply-Supported Damping Beam Carrying a Moving Mass. Acta Mechanica Solida Sinica, 1-7.


• Khajekhabaz, M., Eftekhari, A., & Hashemian, M. (2018). Free vibration analysis of sandwich micro beam with piezoelectric based on modified couple stress theory and surface effects. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 10(4), 33-48.


• Alimoradzadeh, M., Salehi, M., & Mohammadi Esfarjani, S. (2017). Vibration Analysis of FG Micro-Beam Based on the Third Order Shear Deformation and Modified Couple Stress Theories. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 10(3), 51-66.


• Oveissi, S., Toghraie, D., & Eftekhari, S. A. (2016). Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid. Physica E: Low-dimensional Systems and Nanostructures, 83, 275-283.


• Mackertich, S. (2004). Dynamic stability of a beam excited by a sequence of moving mass particles (L). The Journal of the Acoustical Society of America, 115(4), 1416-1419.


• Senalp, A. D., Arikoglu, A., Ozkol, I., & Dogan, V. Z. (2010). Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force. Journal of Mechanical Science and Technology, 24(10), 1957-1961.


• Mirzabeigy, A., & Bakhtiari-Nejad, F. (2014). Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends. Frontiers of Mechanical Engineering, 9(2), 191-202.


• Pirmoradian, M., Keshmiri, M., & Karimpour, H. (2015). On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: instability and resonance analysis. Acta Mechanica, 226(4), 1241-1253.


• Pirmoradian, M., Torkan, E., & Karimpour, H. (2018). Parametric resonance analysis of rectangular plates subjected to moving inertial loads via IHB method. International Journal of Mechanical Sciences, 142, 191-215.


• Nayfeh, A. H., & Mook, D. T. (2008). Nonlinear oscillations. John Wiley & Sons.


• Murphy, B. R. I. G. I. D., & Glendinning, P. A. U. L. (2019). Piecewise smooth models of pumping a child’s swing. preprint, University of Manchester.