scholarly journals Discussion: “On the Nonlinear Differential Equation for Beam Deflection” (Scott, E. J., and Carver, D. R., 1955, ASME J. Appl. Mech., 22, pp. 245–248)

1956 ◽  
Vol 23 (1) ◽  
pp. 144-145
Author(s):  
M. E. Raville
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Beam Deflection

On the Nonlinear Differential Equation for Beam Deflection: EI d 2 y / dx 2 = M ( x ) [ 1 + ( dy / dx ) 2 ] 3 ⁄ 2

1955 ◽  
Vol 22 (2) ◽  
pp. 245-248
Author(s):  
E. J. Scott ◽  
D. R. Carver
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Nonlinear Differential Equation ◽  
Beam Deflection ◽  
Beam Equation ◽  
Nonlinear Beam ◽  
Independent Variable ◽  
The Moment

Abstract A general solution of the nonlinear beam equation is given for all problems in which the moment can be expressed as a function of the independent variable alone.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

Magnetohydrodynamic Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime

1999 ◽  
Vol 66 (4) ◽  
pp. 1021-1023 ◽  
Author(s):  
R. Usha ◽  
P. Vimala
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Bubble Radius ◽  
Fluid Film ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Circular Plates ◽  
Air Bubble ◽  
Approximate Analytical Solutions

In this paper, the magnetic effects on the Newtonian squeeze film between two circular parallel plates, containing a single central air bubble of cylindrical shape are theoretically investigated. A uniform magnetic field is applied perpendicular to the circular plates, which are in sinusoidal relative motion, and fluid film inertia effects are included in the analysis. Assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained by approximating the momentum equation governing the magnetohydrodynamic squeeze film by the mean value averaged across the film thickness. Approximate analytical solutions for the air bubble radius, pressure distribution, and squeeze film force are determined by a perturbation method for small amplitude of sinusoidal motion and are compared with the numerical solution obtained by solving the nonlinear differential equation. The combined effects of air bubble, fluid film inertia, and magnetic field on the squeeze film force are analyzed.

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