An approach for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies

2017 ◽  
Vol 26 (8) ◽  
pp. 1079-1093 ◽  
Author(s):  
A. Khalili ◽  
Ali R. Vosoughi
Keyword(s):  
Elastic Foundation ◽  
Parameters Estimation ◽  
Pasternak Elastic Foundation ◽  
Foundation Parameters

scholarly journals Analysis of beam-column elements on non-homogeneous soil using the differential transformation method

2021 ◽  
Author(s):  
Juan Sebastián Carvajal-Muñoz ◽  
Carlos Alberto Vega-Posada ◽  
Julio César Saldarriaga-Molina
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Mathematical Formulation ◽  
Transformation Method ◽  
Transverse Load ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Pasternak Elastic Foundation ◽  
Wide Range ◽  
Homogeneous Soil

This paper describes an analytical approach to conduct an analysis of beam-column elements with generalized end-boundary conditions on a homogeneous or non-homogeneous Pasternak elastic foundation. The mathematical formulation utilized herein is that presented by the senior author in a recent work. The differential equation (DE) governing the behavior of the beam-column element is solved using the differential transformation method (DTM). The DTM offers practical advantages over other conventional approaches when solving the proposed structural model. The proposed formulation provides the flexibility to account for i) combined lateral and axial load at the ends of the element, ii) homogeneous or non-homogeneous soil, iii) Pasternak elastic foundation, and iv) an external arbitrary transverse load acting on the element. The effects of various slenderness ratios, pile-soil stiffness ratios, and classical and semirigid boundary conditions can be easily studied with the proposed formulation. Examples are presented to validate the accuracy of the model and its applicability over a wide range of analyses.

scholarly journals Multi-moving Loads Induced Vibration of FG Sandwich Beams Resting on Pasternak Elastic Foundation

2021 ◽  
Vol 18 (9) ◽  
Author(s):  
Wachirawit SONGSUWAN ◽  
Monsak PIMSARN ◽  
Nuttawit WATTANASAKULPONG
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Moving Loads ◽  
Layer Thickness Ratio ◽  
Pasternak Elastic Foundation

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange’s equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams’ deflection results under a number of moving loads.

FLUTTER SUPPRESSION OF AN ELASTICALLY SUPPORTED PLATE WITH ELECTRO-RHEOLOGICAL FLUID CORE UNDER YAWED SUPERSONIC FLOWS

2013 ◽  
Vol 13 (01) ◽  
pp. 1250073 ◽  
Author(s):  
SEYYED M. HASHEMINEJAD ◽  
M. NEZAMI ◽  
M. E. ARYAEE PANAH
Keyword(s):  
Elastic Foundation ◽  
Sandwich Plate ◽  
Sliding Mode ◽  
Plate Theory ◽  
System Response ◽  
First Order ◽  
Fluid Core ◽  
Pasternak Elastic Foundation ◽  
Elastically Supported ◽  
Er Fluid

This paper investigates the active control of the supersonic flutter motion of an elastically supported rectangular sandwich plate, which has a tunable electrorheological (ER) fluid core and rests on a Winkler–Pasternak elastic foundation, subjected to an arbitrary flow of various yaw angles. The classical thin plate theory is adopted. The ER fluid core is modeled as a first order Kelvin–Voigt material, and the quasi-steady first order supersonic piston theory is employed for the aerodynamic loading. The generalized Fourier expansions in conjunction with Galerkin method are employed to formulate the governing equations in the state-space domain. The critical dynamic pressures at which unstable panel oscillations occur are obtained for a square sandwich plate, with or without an interacting soft/stiff elastic foundation, for selected applied electric field strengths and flow yaw angles. The Runge–Kutta method is then used to calculate the open-loop aeroelastic response of the system in various basic loading configurations. Subsequently, a sliding mode control (SMC) synthesis is set up to actively suppress the closed loop system response in yawed supersonic flight conditions with imposed excitations. The results demonstrate the performance, effectiveness, and insensitivity with respect to the spillover of the proposed SMC-based control system.

A Novel Refined Plate Theory for Free Vibration Analyses of Single-Layered Graphene Sheets Lying on Winkler-Pasternak Elastic Foundations

2019 ◽  
Vol 58 ◽  
pp. 151-164 ◽  
Author(s):  
Fatima Boukhatem ◽  
Aicha Bessaim ◽  
Abdelhakim Kaci ◽  
Abderrahmane Mouffoki ◽  
Mohammed Sid Ahmed Houari ◽  
...  
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Displacement Field ◽  
Scale Effects ◽  
Plate Theory ◽  
Small Scale ◽  
Graphene Sheets ◽  
Refined Plate Theory ◽  
Foundation Parameters

In this article, the analyses of free vibration of nanoplates, such as single-layered graphene sheets (SLGS), lying on an elastic medium is evaluated and analyzed via a novel refined plate theory mathematical model including small-scale effects. The noteworthy feature of theory is that the displacement field is modelled with only four unknowns, which is even less than the other shear deformation theories. The present one has a new displacement field which introduces undetermined integral variables, the shear stress free condition on the top and bottom surfaces of the plate is respected and consequently, it is unnecessary to use shear correction factors. The theory involves four unknown variables, as against five in case of other higher order theories and first-order shear deformation theory. By using Hamilton’s principle, the nonlocal governing equations are obtained and they are solved via Navier solution method. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all examined. From this work, it can be observed that the small-scale effects and elastic foundation parameters are significant for the natural frequency.

scholarly journals An Efficient Analytical Method for Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mustafa Özgür Yayli ◽  
Murat Aras ◽  
Süleyman Aksoy
Keyword(s):  
Elastic Foundation ◽  
Analytical Method ◽  
Vibration Analysis ◽  
Beam On Elastic Foundation ◽  
Fourier Sine Series ◽  
Governing Differential Equation ◽  
General Frequency ◽  
Elastically Restrained ◽  
Foundation Parameters ◽  
Euler Bernoulli Beam

An efficient analytical method for vibration analysis of a Euler-Bernoulli beam on elastic foundation with elastically restrained ends has been reported. A Fourier sine series with Stoke’s transformation is used to obtain the vibration response. The general frequency determinant is developed on the basis of the analytical solution of the governing differential equation for all potential solution cases with rigid or restrained boundary conditions. Numerical analyses are performed to investigate the effects of various parameters, such as the springs at the boundaries to examine how the elastic foundation parameters affect the vibration frequencies.

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