Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling

2013 ◽  
Vol 100 ◽  
pp. 186-194 ◽  
Author(s):  
Samir A. Emam
Keyword(s):  
Analytical Solutions ◽  
Composite Beams ◽  
Free Vibrations ◽  
Approximate Analytical Solutions

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Approximate analytical solutions of stability problems for skew plates under combined loading

2011 ◽  
Vol 54 (2) ◽  
pp. 115-124 ◽  
Author(s):  
N. I. Akishev ◽  
I. I. Zakirov ◽  
V. A. Ivanov ◽  
V. N. Paimushin ◽  
M. A. Shishov
Keyword(s):  
Analytical Solutions ◽  
Combined Loading ◽  
Stability Problems ◽  
Approximate Analytical Solutions

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

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