Meccanica最新文献

Shaft-gear systems are integral parts of industry. To analyze these systems using an existing classical method, one should first write the static equilibrium and compatibility equations and then solve these equations simultaneously, which is tedious for complex problems. This study proposes a novel method for analyzing shaft-gear systems. The systems are modeled as parallel or series arrangements using torsional springs. By introducing a concept of torque propagation, relationships of the stiffness/flexibility, torque, and twist angle are derived, resulting in closed-form equations with the unknown torques or the twist angles that can be directly found without concurrently solving the static equilibrium and compatibility equations. Illustrative examples are presented to validate and address the efficiency of the proposed method to quickly analyze the shaft-gear systems, even for a combination of parallel and series ones. The results are exact and portend that the technique requires cost-efficiency of computations compared to the existing method, especially when the systems are hybrid, or the number of unknowns is high. Also, a concise computer program can be provided by the proposed equations.

Under adiabatic conditions, and neglecting temperature variations due to entropy production, we present a set of Reynolds Averaged Navier–Stokes (RANS) equations for fluids of low compressibility, i.e., fluids in the liquid state. In the low Mach number limit, we specialize the RANS equations to the one-dimensional unsteady pipe flow, and we deduce the dimensionless number that plays a predominant role in the flow behavior. We reduce the system of equations to a linear damped wave equation, and use its analytical solution to investigate the propagation of large amplitude pressure waves in liquid-filled pipes (water hammer phenomenon). We test the model reliability by comparing the analytical solution of the proposed model against experimental data available in the literature.

In the thin airfoil theory, the camber line and the thickness distribution of general airfoils are mainly extracted by a linear combination of the upper and lower surfaces, giving rise to geometric distortions at the leading edge. Furthermore, despite the recent effort to obtain analytic expressions for the zero-lift angle of attack and quarter-chord moment coefficient, analytic generalizations are needed for the camber line component in the trigonometric series coefficients. In this sense, the present paper proposes a straightforward algorithm to extract the camber line and thickness distribution of general-shaped airfoils based on a finite difference method and the Bézier curve fitting. Integrals in the thin airfoil theory involving a Bernstein basis are performed, leading to series coefficients related to Gegenbauer polynomials. The algorithm is validated against analytical expressions of the NACA airfoils without introducing or adapting geometric parameters, and the results demonstrate good accuracy. In addition, the proposed algorithm indicated a significantly different geometric behavior for the SD7003 and E387 airfoils’ camber slope at the leading edge in contrast with the classical linear approximation. Moreover, the method can be coupled conveniently in recent unsteady aerodynamic models established on the thin airfoil theory to obtain closed-form expressions for general airfoils.

In this paper we develop a new model for the simulation of the mechanical behavior of rayon twisted yarns, at macroscopic level. A yarn with its continuous filaments is represented by an equivalent three-dimensional solid of cylindrical shape, discretized by finite elements, with properly defined local anisotropic material properties. The new constitutive model, inspired by experimental results on rayon untwisted yarns, is formulated in the framework of the thermodynamics of irreversible processes and includes visco-elastic and visco-plastic dissipation mechanisms. The effect of twist is taken into account by including the direction of the fibers in the free energy definition. The overall model is validated comparing numerical and experimental results on twisted rayon yarns.

Owing to the high fluid content, most incompressible soft structures typically exhibit viscosity, which has a significant influence on wave characteristics, especially attenuation. Meanwhile, they are inevitably prestressed owing to the volume-preserving deformations. Therefore, it is essential to investigate acoustoelastic and viscoelastic effects to better understand guided wave characteristics in a pre-stressed soft plate. To this end, a hyperviscoelastic model concerning viscoelasticity, acoustoelasticity, and nonlinearity is established to deduce the governed equations. An analytical integration orthogonal polynomial method is employed to solve complex solutions of wave equations. The dispersion, attenuation, and wave shapes are illustrated. The acoustoelastic and viscoelastic effects are analyzed. Some new wave phenomena are revealed: The pre-stretching inhibits wave attenuation, and the pre-compression promotes attenuation; As the pre-stress increases, high-frequency phase velocity and incremental displacement amplitudes increase. The results lay a theoretical foundation for guided wave elastography, quantitative characterization, and disease diagnosis of biological soft tissue.

Nonlinear energy sinks (NESs) have been extensively studied to develop passive suppression strategies, with the primary objective of minimizing hazardous oscillatory responses in structures. In this work, we investigate the dynamical regimes of a parametrically excited one-degree-of-freedom system with a rotary NES (RNES) acting as a passive suppressor. By performing numerical pseudo-arclength continuations we determine the comprehensive local bifurcation scenario and illustrate, through locus maps, the impact of various RNES parameters. We identify configurations of the parametric excitation amplitude, mass, and absorber radius that result in stable vibration ranges. The dynamic scenario necessitates a precise adjustment of the RNES characteristics, tailored for either passive suppression or energy harvesting applications. Finally, we assess the resilience of the suitable vibration regions by examining the global dynamics. Basins of attraction display a fractal form, indicating a high sensitivity of the response to initial conditions.

The article presents physics based time invariant generalized flutter reliability approach for a wing in detail. For carrying flutter reliability analysis, a generalized first order reliability method (FORM) and a generalized second order reliability method (SORM) algorithms are developed. The FORM algorithm requires first derivative and the SORM algorithm requires both the first and second derivatives of a limit state function; and for these derivatives, an adjoint and a direct approaches for computing eigen-pair derivatives are proposed by ensuring uniqueness in eigenvector and its derivative. The stability parameter, damping ratio (real part of an eigenvalue), is considered as implicit type limit state function. To show occurrence of the flutter phenomenon, the limit state function is defined in conditional sense by imposing a condition on flow velocity. The aerodynamic parameter: slope of the lift coefficient curve ((C_{L})) and structural parameters: bending rigidity (EI) and torsional rigidity (GJ) of an aeroelastic system are considered as independent Gaussian random variables, and also the structural parameters are modeled as second-order constant mean stationary Gaussian random fields having exponential type covariance structures. To represent the random fields in finite dimensions, the fields are discretized using Karhunen–Loeve expansion. The analysis shows that the derivatives of an eigenvalue obtained from both the adjoint and direct approaches are the same. So the cumulative distribution functions (CDFs) of flutter velocity will be the same, irrespective of the approach chosen, and it is also reflected in CDFs obtained using various reliability methods based on adjoint and direct approaches: first order second moment method, generalized FORM, and generalized SORM.

In this work, the numerical analysis of the modified Reynolds equation is compared. The difference between the two analyses is the porous media flow equation; the first considers the Darcy model, and the other the Darcy–Forchheimer model. The solution algorithms were developed using finite center differences for the geometric variable. This numerical scheme resulted in a non-linear set of equations solved with the Newton–Raphson method. Due to the nonlinearity of the problem, the relationship between the steps between axial and circumferential dimensions and the initial assumption is the main conditions for the solution to converge; the precision of the results obtained, in comparison with previous works, was acceptable; this contributes an additional effort in the development of the technology of the porous gas bearings. This work analyzed the differences in predicting the static behavior of a porous gas bearing using the Darcy model and the extended Darcy–Forchheimer model to determine the flow behavior through the porous medium. The solution algorithm of the modified Reynolds equation with the Darcy–Forchheimer model offers a broader range of solutions because it is capable of predicting both the linear and non-linear behavior of the flow through the porous medium and the influence in the lubricant film; this is essential for the design of porous gas bearings for industrial applications. The Finite Difference solutions are compared with a Finite Element and Finite Volume solution. The results show similar approximations with the advantage that the finite difference solution is more straightforward and can be coupled with a dynamic lump-mass model.