Nonlinear Solution
Adnan Maqsood; Muhammad Kamran Khan Tareen; Rizwan Riaz; Laurent Dala
Abstract
The paper discusses the effect of compressor characteristic on surge phenomena in axial flow compressors. Specifically, the effect of nonlinearities on the compressor dynamics is analyzed. For this purpose, generalized multiple time scales method is used to parameterize equations in amplitude and frequency ...
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The paper discusses the effect of compressor characteristic on surge phenomena in axial flow compressors. Specifically, the effect of nonlinearities on the compressor dynamics is analyzed. For this purpose, generalized multiple time scales method is used to parameterize equations in amplitude and frequency explicitly. The pure surge case of the famous Moore-Greitzer model is used as the basis of the study. The compressor characteristic used in the Moore-Greitzer model is generalized to evaluate the effect of the parameters involved. Subsequently, bifurcation theory is used to study the effect of nonlinear dynamics on surge behavior. It has been found that the system exhibits supercritical Hopf bifurcation under specific conditions in which surge manifests as limit cycle oscillations. Key parameters have been identified in the analytical solution which govern the nonlinear dynamic behavior and are responsible for the existence of limit cycle oscillations. Numerical simulations of the Moore-Greitzer model are carried out and are found in good agreement with the analytical solution
Nonlinear Solution
Harsh Kumar Dixit; T.C Gupta
Abstract
The simplified analytical method has developed to analyze the effect of bearing geometrical parameters, i.e. eccentricity ratio, journal rotation speed, slenderness ratio, bearing radial clearance, pad pivot offset and the number of pads on tilting pad journal bearing (TPJB) properties, i.e. fluid film ...
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The simplified analytical method has developed to analyze the effect of bearing geometrical parameters, i.e. eccentricity ratio, journal rotation speed, slenderness ratio, bearing radial clearance, pad pivot offset and the number of pads on tilting pad journal bearing (TPJB) properties, i.e. fluid film thickness, fluid film forces and fluid film stiffness and damping coefficients of TPJB. Reynolds equation was solved for each pad to determine fluid film pressure on pads. The infinite short bearing assumption used to determine pressure distribution on pads integrated over the pad surface to find fluid film forces. The pressure distribution and fluid film forces validated with previous researches. Error bars presented to indicate accuracy measurement. The maximum error found was not more than 6 percent corresponding to loaded pads. The percentage error found maximum when the eccentricity ratio is 0.25 while it found a minimum when the eccentricity ratio is 0.62. The Matlab code has been developed for the solution of non-linear equations. Results produced in the form of design curves which compares changes in fluid film properties corresponding to TPJB geometric parameters. The results obtained in this manuscript are applicable in other similar researches to find appropriate and limiting values of fluid film properties at different geometrical and parametric conditions. The generated plots and data are helpful in dynamic analysis to find the value of a specific parameter corresponding to a specific value of fluid film coefficient, which makes an easier selection of suitable numerical integration technique and boundary conditions to avoid non-significant results, which save time and effort in the nonlinear analysis.
Nonlinear Solution
saeed mahmoudkhani
Abstract
An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. ...
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An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordinary differential equation, which is then solved by the homotopy analysis method (HAM). An explicit expression is obtained for the nonlinear frequency amplitude relation. It is found that the proper value of the so-called auxiliary parameter for the HAM solution is dependent on the vibration amplitude, making it difficult to rapidly obtain accurate frequency-amplitude curves using a single value of the auxiliary parameter. The homotopy-Pade technique remedied this issue by leading to the approximation that is almost independent of the auxiliary parameter and is also more accurate than the conventional HAM. Highly accurate results are found with only third order approximation for a wide range of vibration amplitudes.
Nonlinear Solution
M. Matinfar; M. Ghasemi
Abstract
Variational Iteration method using He's polynomials can be used to construct solitary solution and compacton-like solution for nonlinear dispersive equatioons. The chosen initial solution can be determined in compacton-like form or in solitary form with some compacton-like or solitary forms with ...
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Variational Iteration method using He's polynomials can be used to construct solitary solution and compacton-like solution for nonlinear dispersive equatioons. The chosen initial solution can be determined in compacton-like form or in solitary form with some compacton-like or solitary forms with some unknown parameters, which can be determined in the solution procedure. The compacton-like solution and solitary solution can be converted into each other.
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