Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler–Pasternak elastic foundation using a new refined beam theory: an analytical approach

2020 ◽  
Vol 135 (2) ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty ◽  
Mohammad Malikan
Keyword(s):  
Magnetic Field ◽  
Elastic Foundation ◽  
Analytical Approach ◽  
Beam Theory ◽  
Pasternak Elastic Foundation ◽  
Refined Beam Theory ◽  
Nonlocal Beam

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.

Research on Mechanical Behavior of Pipe-Roof Reinforcement Applied in Tunnel Based on MATLAB

2013 ◽  
Vol 353-356 ◽  
pp. 1394-1397
Author(s):  
Zhi Jie Sun ◽  
Jun Min Shen ◽  
Zhong Ming Su ◽  
Xiao Hui Xue
Keyword(s):  
Mechanical Behavior ◽  
Elastic Foundation ◽  
Beam Theory ◽  
Surrounding Rock ◽  
Tunnel Face ◽  
Pasternak Elastic Foundation ◽  
Mechanical Models ◽  
Support Conditions ◽  
Elastic Foundation Beam ◽  
Roof Support

Based on the Pasternak elastic foundation beam theory, mechanical models solving process of pipe-roof based on the MATLAB is elaborate, and the mechanical behavior of pipe-roof reinforcement is analyzed. Results show that the pipe-roof can play an leveraged part in surrounding rock, which can make the deformation and the load around tunnel face effectively passing to no excavation section near the excavation. In pipe-roof support conditions, the longitudinal influence scope of tunnel due to excavation is about 1.3~1.5 times the excavation height.

scholarly journals The nonlinear thermomechanical vibration of a functionally graded beam on Winkler-Pasternak foundation

2018 ◽  
Vol 148 ◽  
pp. 13004 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Geometric Nonlinearity ◽  
Beam Theory ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Functionally Graded Beam ◽  
Pasternak Elastic Foundation ◽  
Euler Bernoulli Beam

By using the Optimal Auxiliary Functions Method (OAFM), nonlinear free thermomechanical vibration of functionally graded beam (FGB) on Winkler-Pasternak elastic foundation is studied. Based on von Karman geometric nonlinearity, on Euler-Bernoulli beam theory and also on Galerkin procedure we obtain a second-order nonlinear differential equation with quadratic and cubic nonlinear terms. The results obtained by means of OAFM are compared and shown to be in an excellent agreement with available solutions known in the literature.

scholarly journals Analytical corrections for double-cantilever beam tests

2021 ◽  
Author(s):  
T. Chen ◽  
C. M. Harvey ◽  
S. Wang ◽  
V. V. Silberschmidt
Keyword(s):  
Elastic Foundation ◽  
Analytical Solutions ◽  
Data Reduction ◽  
Crack Tip ◽  
Beam Theory ◽  
Dynamic Loads ◽  
Structural Vibration ◽  
Mode I ◽  
Mode I Fracture ◽  
Reduction Methods

AbstractDouble-cantilever beams (DCBs) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness under quasi-static loads. Recently, the authors have developed analytical solutions for DCBs under dynamic loads with consideration of structural vibration and wave propagation. There are two methods of beam-theory-based data reduction to determine the energy release rate: (i) using an effective built-in boundary condition at the crack tip, and (ii) employing an elastic foundation to model the uncracked interface of the DCB. In this letter, analytical corrections for a crack-tip rotation of DCBs under quasi-static and dynamic loads are presented, afforded by combining both these data-reduction methods and the authors’ recent analytical solutions for each. Convenient and easy-to-use analytical corrections for DCB tests are obtained, which avoid the complexity and difficulty of the elastic foundation approach, and the need for multiple experimental measurements of DCB compliance and crack length. The corrections are, to the best of the authors’ knowledge, completely new. Verification cases based on numerical simulation are presented to demonstrate the utility of the corrections.

scholarly journals What Density of Magnetosheath Sodium Ions Can Provide the Observed Decrease in the Magnetic Field of the “Double Magnetopause” during the First MESSENGER Flyby?

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1168
Author(s):  
Elena Belenkaya ◽  
Ivan Pensionerov
Keyword(s):  
Magnetic Field ◽  
Analytical Approach ◽  
Field Structure ◽  
Sodium Ions ◽  
Plasma Parameters ◽  
Calculation Results ◽  
Magnetizing Current ◽  
The Magnetic Field ◽  
Density Excess

On 14 January 2008, the MESSENGER spacecraft, during its first flyby around Mercury, recorded the magnetic field structure, which was later called the “double magnetopause”. The role of sodium ions penetrating into the Hermean magnetosphere from the magnetosheath in generation of this structure has been discussed since then. The violation of the symmetry of the plasma parameters at the magnetopause is the cause of the magnetizing current generation. Here, we consider whether the change in the density of sodium ions on both sides of the Hermean magnetopause could be the cause of a wide diamagnetic current in the magnetosphere at its dawn-side boundary observed during the first MESSENGER flyby. In the present paper, we propose an analytical approach that made it possible to determine the magnetosheath Na+ density excess providing the best agreement between the calculation results and the observed magnetic field in the double magnetopause.

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