Dynamic response and stability of an inclined Euler beam under a moving vertical concentrated load

2019 ◽  
Vol 186 ◽  
pp. 243-254 ◽  
Author(s):  
Der-Shen Yang ◽  
C.M. Wang
Keyword(s):  
Dynamic Response ◽  
Euler Beam ◽  
Concentrated Load

Dynamic Response of an Infinite Beam

1975 ◽  
Vol 97 (2) ◽  
pp. 107-109 ◽  
Author(s):  
H. Durlofsky
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Dynamic Response ◽  
Elastic Foundation ◽  
Fourier Transforms ◽  
Euler Beam ◽  
Concentrated Load ◽  
Conservation Of Energy ◽  
Infinite Beam ◽  
Good Agreement

Both the exact and an approximate solution for the dynamic response of an infinite Bernoulli-Euler beam under an instantaneously applied, concentrated load are presented in this paper. The exact solution is obtained by means of complex Fourier transforms. The approximate solution is obtained by assuming the dynamic response has the form of a deflected infinite beam on an elastic foundation, with wavelength a function of time. This assumption is motivated by the similarity between the dynamic response problem and the problem of an infinite beam on an elastic foundation. A governing equation for the wavelength in the assumed response is derived by application of the principle of conservation of energy, and solved by straightforward methods. A comparison of the two solutions shows good agreement near the point of loading. Results applicable to pipe whip problems are presented.

Calculation of the Additional Constants for fcc Materials in Second Strain Gradient Elasticity: Behavior of a Nano-Size Bernoulli-Euler Beam With Surface Effects

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
H. M. Shodja ◽  
F. Ahmadpoor ◽  
A. Tehranchi
Keyword(s):  
Strain Gradient ◽  
Gradient Elasticity ◽  
Surface Effects ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Strain Gradient Elasticity ◽  
Euler Beam ◽  
Concentrated Load ◽  
Material Constants ◽  
Nano Size

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework, sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fee metals are given in terms of the parameters of Sutton-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a nano-size Bernoulli-Euler beam in second strain gradient elasticity is provided; the appearance of the additional constants in the corresponding formulations, through the governing equation and boundary conditions, can serve to delineate the true behavior of the material in ultra small elastic structures, having very large surface-to-volume ratio. Now that the values of the material constants are available, a nanoscopic study of the Kelvin problem in second strain gradient theory is performed, and the result is compared quantitatively with those of the first strain gradient and traditional theories.

Dynamic Response of a Beam With a Geometric Nonlinearity

1981 ◽  
Vol 48 (2) ◽  
pp. 404-410 ◽  
Author(s):  
S. F. Masri ◽  
Y. A. Mariamy ◽  
J. C. Anderson
Keyword(s):  
Dynamic Response ◽  
Mechanical Model ◽  
Geometric Nonlinearity ◽  
Experimental Studies ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
System Response ◽  
Experimental Measurements ◽  
Euler Beam ◽  
Practical Engineering

Analytical and experimental studies were made of the dynamic response of a system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped Bernoulli-Euler beam with an unsymmetric geometric nonlinearity, under the action of harmonic excitation. Experimental measurements of a mechanical model under harmonic as well as random excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.

Dynamic analysis of the flexible hub-beam system based on rigid-flexible coupling mechanism

2020 ◽  
Vol 234 (3) ◽  
pp. 536-545
Author(s):  
Xiaowei Guo ◽  
Xin Yang ◽  
Fuqiang Liu ◽  
Zhangfang Liu ◽  
Xiaolin Tang
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Flexible Beam ◽  
Coupling Mechanism ◽  
Mass System ◽  
Typical Structure ◽  
Concentrated Load ◽  
Flexible Coupling ◽  
Beam System ◽  
Tip Mass

The flexible hub-beam system is a typical structure of the rigid-flexible coupling dynamic system. In this paper, the dynamic property of the flexible hub-beam system is investigated. First, based on the dynamic analysis of the flexible beam in the flexible hub-beam system, the dynamic model of a flexible hub-beam-tip mass system is established and researched. Second, the dynamic response of the flexible beam under different external loads, including end concentrated load, end sinusoidal load, and uniform load, is analyzed and calculated. Finally, the influence of magnitude, direction, and type of load on the dynamic response of the flexible beam is also discussed. This research can provide a novel strategy for controlling the maximum stress of the structural components to be lower than the yield stress of the material, and flexible components remain in the linear elastic range even under the condition of high-speed rotation.

Steady-State Dynamic Response of a Bernoulli–Euler Beam on a Viscoelastic Foundation Subject to a Platoon of Moving Dynamic Loads

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Lu Sun ◽  
Feiquan Luo
Keyword(s):  
Dynamic Response ◽  
Critical Speed ◽  
Complex Function ◽  
Vertical Displacement ◽  
Dynamic Loads ◽  
Dimensionless Frequency ◽  
Vertical Acceleration ◽  
Viscoelastic Foundation ◽  
Efficient Computation ◽  
Euler Beam

A Bernoulli–Euler beam resting on a viscoelastic foundation subject to a platoon of moving dynamic loads can be used as a physical model to describe railways and highways under traffic loading. Vertical displacement, vertical velocity, and vertical acceleration responses of the beam are initially obtained in the frequency domain and then represented as integrations of complex function in the space-time domain. A bifurcation is found in critical speed against resonance frequency. When the dimensionless frequency is high, there is a single critical speed that increases as the dimensionless frequency increases. When the dimensionless frequency is low, there are two critical speeds. One speed increases as the dimensionless frequency increases, while the other speed decreases as the dimensionless frequency decreases. Based on the fast Fourier transform, numerical methods are developed for efficient computation of dynamic response of the beam.

DYNAMIC RESPONSE OF RIGID ROADWAY PAVEMENT UNDER MOVING TRAFFIC LOADS

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Sofia W. Alisjahbana ◽  
Wiratman Wangsadinata
Keyword(s):  
Dynamic Response ◽  
Static Load ◽  
Variable Speed ◽  
Rigid Pavement ◽  
Concentrated Load ◽  
Rigid Pavements ◽  
Vehicle Load ◽  
Traffic Loads ◽  
Vehicle Loads ◽  
Significant Attention

The study of the dynamic response of rigid roadway pavements subjected to dynamic loads such as vehicle loads has received significant attention in recent years, because of the relevance to the design of pavements. This paper presents an analytical solution based on the Modified Bolotin Method to analyze rigid pavements under moving traffic loads. The concrete pavement is modelled as an orthotropic damped plate resting on a continuous elastic foundation, whereby at its edges it is partially fixed. The natural frequencies of the system are computed from a system of two transcendental equations, obtained from the solution of two auxiliary Levy’s type problems. The dynamic vehicle load is expressed as a concentrated load of harmonically varying magnitude, travelling with a variable speed along the rigid pavement. A numerical example is given, demonstrating the applicability of the theory to rigid roadway pavements under actual loading conditions. Therefore, it may be expected that this dynamic load approach may lead to more economic solutions as compared to those obtained from the conventional static load approach.

A Laminated Beam Theory With Interlayer Slip

1984 ◽  
Vol 51 (3) ◽  
pp. 551-559 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Virtual Work ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Transverse Shear Strain ◽  
Beam Model ◽  
Euler Beam ◽  
Concentrated Load ◽  
Laminated Beam ◽  
Wide Range ◽  
Interlayer Slip

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.

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