scholarly journals Nonlocal beam theory for nonlinear vibrations of a nanobeam resting on elastic foundation

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Necla Togun
Keyword(s):  
Elastic Foundation ◽  
Nonlinear Vibrations ◽  
Beam Theory ◽  
Nonlocal Beam

scholarly journals Analytical corrections for double-cantilever beam tests

2021 ◽  
Author(s):  
T. Chen ◽  
C. M. Harvey ◽  
S. Wang ◽  
V. V. Silberschmidt
Keyword(s):  
Elastic Foundation ◽  
Analytical Solutions ◽  
Data Reduction ◽  
Crack Tip ◽  
Beam Theory ◽  
Dynamic Loads ◽  
Structural Vibration ◽  
Mode I ◽  
Mode I Fracture ◽  
Reduction Methods

AbstractDouble-cantilever beams (DCBs) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness under quasi-static loads. Recently, the authors have developed analytical solutions for DCBs under dynamic loads with consideration of structural vibration and wave propagation. There are two methods of beam-theory-based data reduction to determine the energy release rate: (i) using an effective built-in boundary condition at the crack tip, and (ii) employing an elastic foundation to model the uncracked interface of the DCB. In this letter, analytical corrections for a crack-tip rotation of DCBs under quasi-static and dynamic loads are presented, afforded by combining both these data-reduction methods and the authors’ recent analytical solutions for each. Convenient and easy-to-use analytical corrections for DCB tests are obtained, which avoid the complexity and difficulty of the elastic foundation approach, and the need for multiple experimental measurements of DCB compliance and crack length. The corrections are, to the best of the authors’ knowledge, completely new. Verification cases based on numerical simulation are presented to demonstrate the utility of the corrections.

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.

Effect of a breathing crack on the damping changes in nonlinear vibrations of a cracked beam: Experimental and theoretical investigations

2020 ◽  
pp. 107754632096031
Author(s):  
Masoud Kharazan ◽  
Saied Irani ◽  
Mohammad Ali Noorian ◽  
Mohammad Reza Salimi
Keyword(s):  
Nonlinear Vibrations ◽  
Crack Depth ◽  
Beam Theory ◽  
Experimental Tests ◽  
Damping Coefficient ◽  
Crack Identification ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Identification Method ◽  
Nonlinear Crack

The attempts to identify damping changes in a cracked beam can improve the accuracy of the nonlinear crack identification method. For the purpose of this aim, a parametric nonlinear equation of motion is obtained using the Euler–Bernoulli beam theory and parametric nonlinear breathing crack assumptions. Several experiments were conducted to identify the effect of breathing cracks on changing the damping value in nonlinear vibrations of a cracked beam. Experimental tests have revealed that increasing the crack depth and the level of excitation enlarges the damping coefficient in a vibrating beam. For this reason, the effects of the excitation force and crack depth on the structural damping coefficient are investigated. The obtained results indicated that considering the nonlinear response of a cracked beam and measuring the value of the damping changes can significantly improve the accuracy of the nonlinear crack identification method.

Solution of contact problems for Gao beam and elastic foundation

2017 ◽  
Vol 23 (3) ◽  
pp. 473-488 ◽  
Author(s):  
Jitka Machalová ◽  
Horymír Netuka
Keyword(s):  
Contact Problem ◽  
Elastic Foundation ◽  
Variational Equation ◽  
Main Idea ◽  
Axial Loading ◽  
Elastic Beam ◽  
Beam Theory ◽  
Contact Problems ◽  
Problem Formulations ◽  
Nonlinear Elastic

This paper presents mathematical formulations and a solution for contact problems that concern the nonlinear beam published by Gao (Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech Res Commun 1996; 23: 11–17) and an elastic foundation. The beam is subjected to a vertical and also axial loading. The elastic deformable foundation is considered at a distance under the beam. The contact is modeled as static, frictionless and using the normal compliance contact condition. In comparison with the usual contact problem formulations, which are based on variational inequalities, we are able to derive for our problem a nonlinear variational equation. Solution of this problem is realized by means of the so-called control variational method. The main idea of this method is to transform the given contact problem to an optimal control problem, which can provide the requested solution. Finally, some results including numerical examples are offered to illustrate the usefulness of the presented solution method.

Free Vibration of a Rotating Ring on an Elastic Foundation

2017 ◽  
Vol 09 (04) ◽  
pp. 1750051 ◽  
Author(s):  
Hu Ding ◽  
Minghui Zhu ◽  
Zhen Zhang ◽  
Ye-Wei Zhang ◽  
Li-Qun Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Theory ◽  
Element Analysis ◽  
Flexural Mode ◽  
Simulation And Experiment ◽  
The Difference

In the present paper, free vibration of a rotating ring supported by an elastic foundation is studied by analytical method, finite element (FE) simulation and experiment. By adopting the ring analogy of Timoshenko beam theory, the nonlinear vibration of the rotating ring on an elastic foundation is modeled based on Hamilton’s principle. Radial and tangential deformation are considered. By solving the generalized eigenvalue problem, natural frequencies and flexural modes are obtained. Furthermore, the Euler–Bernoulli (E–B) theory is also employed to investigate the free vibration. For determining the necessity of the Timoshenko theory, the flexural vibration frequencies from two theories are compared. Specifically, the effects of the radius and the radial height (the thickness) of the ring on the difference between the two models are studied. In order to confirm the analytical results, finite element analysis and experiments on three test specimens are used to verify the natural frequency and flexural mode predictions. Overall, this work shows the necessity of the Timoshenko theory for studying free vibration of an elastic ring.

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