Search results for "analytical solution"

Analytical solution for the transient response of symmetric magnetoelectric laminated beams

2010

In this paper an analytical solution is presented for the forced vibration problem of magnetoelectric symmetric laminated beams. In deriving the mathematical model the Timoshenko’s beam theory is used and the electric and magnetic fields are assumed to be quasi-static. The model is written for a magnetoelectric sensing device by applying proper magnetoelectric boundary conditions on the beam top and bottom surfaces. The model highlights that the magneto-electro-mechanical couplings affect the bending stiffness and that the magnetoelectric inputs can be treated as equivalent bending moments. Forced vibration analyses are presented to assess the reliability of the solution.

Experimental Tests to Validate a Simple Procedure to Design Dual-Diameter Drip Laterals on Flat Fields

2023

Multiple-diameter laterals reduce the total cost in microirrigation systems, however, the length of each sublateral should be determined carefully to assure appro-priate performance of emitter flow rates. The most accurate method is the numerical trial and error, which is time-consuming. A series of research efforts have been made to propose simple analytical design procedures. By using the power-law form of the Darcy-Weisbach formula, and equal emitters spacing for the sublaterals, Sadeghi et al. (Sadeghi et al. in J Irrig Drain E-ASCE 142:04,016,020, 2016) extended a previously introduced design solution for one-diameter laterals to tapered laterals. Recently, a simplified procedure to de…

Determining Probability Distribution of Hillslope Peak Discharge by Using an Analytical Solution of Kinematic Wave Time of Concentration.

2016

Hillslope hydrology is fundamental for understanding the flood phenomenon and for evaluating the time of concentration. The latter is a key variable for predicting peak discharge at the basin outlet and for designing urban infrastructure facilities. There have been a multitude of studies on the hydrologic response at the hillslope scale, and the time of concentration has been derived for different approaches. One approach for deriving hillslope response utilizes, in a distributed form, the differential equations of unsteady overland flow, specifically developed at the hydrodynamic scale, in order to account for the spatial heterogeneity of soil characteristics, topography, roughness and veg…

An analytical solution for multilayered beams subjected to ends loads

2014

An alternative model for multilayered beams undergoing axial, shear and bending loads applied at the beam's ends is developed. It is based on a layer-wise kinematics, which inherently fulfills the equilibrium equations at layer level and the interface continuity conditions. This kinematics is suitably expressed by introducing a set of generalized variables representative of the beam midline displacement field, which become the primary variables of the problem governing equations. As a consequence, the proposed beam model exhibits the computational characteristics of an equivalent single layer model and possesses the accuracy of layer-wise beam theories, as well. Closed form solutions for di…

Analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

2009

Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the def…

An equivalent single-layer model for magnetoelectroelastic multilayered plate dynamics

2012

Abstract An equivalent single-layer model for the dynamic analysis of magnetoelectroelastic laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static and the first-order shear deformation theory is used. The formulation of the model provides for a preliminary fulfillment of the electro-magnetic governing equations, which allows to determine the electric and magnetic potential as functions of the mechanical variables. Then, by using this result, the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-elect…

Analytical Solution of the Richards Equation under Gravity-Driven Infiltration and Constant Rainfall Intensity

2020

In the field of soil hydrology, the Richards equation is commonly used to model water flow in unsaturated soils. The high nonlinearity of the Richards equation makes it very challenging to solve analytically for situations that are meaningful in practical applications. In this paper, an exact and simple analytical solution of the Richards equation under gravity-driven infiltration and constant rainfall intensity is derived. First, the solution is presented under Torricelli's law, which mimics the soil hydraulic conductivity function and describes the emptying or filling process of a nonlinear water reservoir. Then, following a similar approach, the solution is extended to the Brooks and Cor…

AN EFFICIENT SOLUTION OF HETEROGENEOUS ANISOTROPIC CONVECTION/DIFFUSION TRANSPORT PROBLEMS

2012

Overland flow generation on hillslopes of complex topography: analytical Solutions

2007

The analytical solution of the overland flow equations developed by Agnese et al. (2001; Hydrological Processes15: 3225–3238) for rectangular straight hillslopes was extended to convergent and divergent surfaces and to concave and convex profiles. Towards this aim, the conical convergent and divergent surfaces are approximated by a trapezoidal shape, and the overland flow is assumed to be always one-dimensional. A simple ‘shape factor’ accounting for both planform geometry and profile shape was introduced: for each planform geometry, a brachistochrone profile was obtained by minimizing a functional containing a slope function of the profile. Minima shape factors are associated with brachist…

Dual-Diameter Laterals in Center-Pivot Irrigation System

2022

Design strategies to enhance modern irrigation practices, reduce energy consumption, and improve water use efficiency and crop yields are fundamental for sustainability. Concerning Center-Pivot Irrigation Systems, different design procedures aimed at optimizing water use efficiency have been proposed. Recently, following a gradually decreasing sprinkler spacing along the pivot lateral with constant diameter and sprinkler flow rate, a new design method providing a uniform water application rate has been introduced. However, no suggestions were given to design multiple-diameter laterals characterized by different values of the inside pipe diameter. In this paper, first the previous design pro…