Analytical solutions for Euler-Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads

2017 ◽  
Vol 41 (8) ◽  
pp. 1125-1137 ◽  
Author(s):  
H. Yu ◽  
C. Cai ◽  
Y. Yuan ◽  
M. Jia
Keyword(s):  
Analytical Solutions ◽  
Dynamic Loads ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

Nonlinear Vibration of Nanobeam With Quadratic Rational Bezier Arc Curvature

2014 ◽  
Author(s):  
Hassan Askari ◽  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Governing Equation ◽  
Oscillation Amplitude ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Linear Frequency ◽  
Euler Bernoulli Beam

Nonlinear vibration of nanobeam with the quadratic rational Bezier arc curvature is investigated. The governing equation of motion of the nanobeam based on the Euler-Bernoulli beam theory is developed. Accordingly, the non-uniform rational B-spline (NURBS) is implemented in order to write the implicit form of the governing equation of the structure. The simply-supported boundary conditions are assumed and the Galerkin procedure is utilized to find the nonlinear ordinary differential equation of the system. The nonlinear natural frequency of the system is found and the effects of different parameters, namely, the waviness amplitude, oscillation amplitude, aspect ratio, curvature shape and the Pasternak foundation coefficient are fully investigated. The hardening and softening responses of the natural frequency of structure are detected for variations of the shape and amplitude of the curvature waviness. It is revealed that the ratio of nonlinear to linear frequency increases with an increase in the oscillation amplitudes. It is found that by increasing the Pasternak foundation coefficient, the ratio of nonlinear to linear frequency decreases.

On the Dynamics of Fractional Visco-Elastic Beams

2012 ◽  
Author(s):  
Salvatore Di Lorenzo ◽  
Francesco P. Pinnola ◽  
Antonina Pirrotta
Keyword(s):  
Elastic Beam ◽  
Constitutive Law ◽  
Dynamic Loads ◽  
Elastic Behavior ◽  
Advanced Manufacturing ◽  
Suitable Model ◽  
Bernoulli Beam ◽  
Static Behavior ◽  
Creep Tests ◽  
Euler Bernoulli Beam

With increasing advanced manufacturing process, visco-elastic materials are very attractive for mitigation of vibrations, provided that you may have advanced studies for capturing the realistic behavior of such materials. Experimental verification of the visco-elastic behavior is limited to some well-known low order models as the Maxwell or Kelvin models. However, both models are not sufficient to model the visco-elastic behavior of real materials, since only the Maxwell type can capture the relaxation tests and the Kelvin the creep tests, respectively. Very recently, it has been stressed that the most suitable model for capturing the visco-elastic behavior is the spring-pot, characterized by a fractional constitutive law. Based on this assumption, the quasi-static behavior has been investigated very recently, however for noise control there is a need of exploiting the dynamic behavior of such a fractional visco-elastic beam. The present paper introduces the dynamic response of fractional visco-elastic Euler-Bernoulli beam under dynamic loads.

scholarly journals The nonlinear thermomechanical vibration of a functionally graded beam on Winkler-Pasternak foundation

2018 ◽  
Vol 148 ◽  
pp. 13004 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Geometric Nonlinearity ◽  
Beam Theory ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Functionally Graded Beam ◽  
Pasternak Elastic Foundation ◽  
Euler Bernoulli Beam

By using the Optimal Auxiliary Functions Method (OAFM), nonlinear free thermomechanical vibration of functionally graded beam (FGB) on Winkler-Pasternak elastic foundation is studied. Based on von Karman geometric nonlinearity, on Euler-Bernoulli beam theory and also on Galerkin procedure we obtain a second-order nonlinear differential equation with quadratic and cubic nonlinear terms. The results obtained by means of OAFM are compared and shown to be in an excellent agreement with available solutions known in the literature.

scholarly journals Dynamic response of the tower of a NREL5MW wind turbine generator

2018 ◽  
Vol 234 ◽  
pp. 04008
Author(s):  
Ivo Angelov
Keyword(s):  
Wind Turbine ◽  
Forced Vibrations ◽  
Dynamic Loads ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Turbine Generator ◽  
Wind Turbine Generator ◽  
Forced Motion ◽  
Aerodynamic Interaction ◽  
Euler Bernoulli Beam

Considering the complexity of the aerodynamic interaction between a non-homogeneous, nonstationary wind field and a wind turbine, one can easily establish that the constructive elements of the turbine will be exposed to dynamic loads, which will eventually lead to forced motion and particularly to forced vibrations. One of the most significant elements of every wind turbine is the tower of the generator. The tower is subjected to forced vibrations and transmits all dynamic loads that appear in the wind turbine. That is why a dynamic analysis of the tower is worth executing. In this research such an analysis is made considering the tower of the generator as Euler-Bernoulli beam structure and considering it as a Love-Kirchhoff shell structure.

Sign in / Sign up

Export Citation Format

Share Document