On the Dynamic Response of a Beam on a Tensionless Elastic Foundation

2009 ◽  
Author(s):  
M. Mofid ◽  
M.R. Shadnam
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation

scholarly journals Multi-moving Loads Induced Vibration of FG Sandwich Beams Resting on Pasternak Elastic Foundation

2021 ◽  
Vol 18 (9) ◽  
Author(s):  
Wachirawit SONGSUWAN ◽  
Monsak PIMSARN ◽  
Nuttawit WATTANASAKULPONG
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Moving Loads ◽  
Layer Thickness Ratio ◽  
Pasternak Elastic Foundation

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange’s equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams’ deflection results under a number of moving loads.

The Effect of Structure Bury Depth on Dynamic Response of Underground Tunnel under Longitudinal Shearing Seismic Action

2014 ◽  
Vol 1020 ◽  
pp. 415-422
Author(s):  
Ying Qian Xu ◽  
Cheng Zhi Qi ◽  
Guo Xing Chen
Keyword(s):  
Dynamic Response ◽  
Rayleigh Wave ◽  
Elastic Foundation ◽  
Hyperbolic Type ◽  
Seismic Action ◽  
Linear Type ◽  
Underground Tunnel ◽  
Practical Engineering ◽  
S Curve ◽  
Effect Of Structure

In the present paper the model of beam on Winkler-type elastic foundation is used to model the underground tunnel. The soil displacement (mm)-stress (kpa) curve (p-s curve) is approximated in the form of hyperbolic type function by fitting the existing experimental data and then equivalent linear type of nonlinear bedding coefficient of foundation is derived from the fitting curve. Substitute the equivalent coefficient into the vibration equation of beam on Winkler-type elastic foundation, and we may assess the nonlinear effect of soil. Based on the hypothesis of large distance to earthquake source, Rayleigh wave is used to simulate the longitudinal shearing seismic wave. According to the amplitude attenuation law of Rayleigh wave in elastic half place, the effect of structure bury depth on dynamic response of underground tunnel is considered and the conception of critical bury depth is put forward. Finally the vibration differential equation of beam on Winkler-type elastic foundation is solved by using Matlab software, and the dynamic response of underground tunnel at different structure bury depth are compared. The results may provide a reference for practical engineering.

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