Dynamics of Euler-Bernoulli beams with unknown viscoelastic boundary conditions under a moving load

2021 ◽  
Vol 491 ◽  
pp. 115771
Author(s):  
Guandong Qiao ◽  
Salam Rahmatalla
Keyword(s):  
Boundary Conditions ◽  
Moving Load

Nonlinear vibrations of a thin isotropic circular plate subjected to moving point loads

2020 ◽  
pp. 095440622097615
Author(s):  
Amit K Rai ◽  
Shakti S Gupta
Keyword(s):  
Boundary Conditions ◽  
Frequency Response ◽  
Circular Plate ◽  
Nonlinear Vibrations ◽  
Moving Load ◽  
Harmonic Balance Method ◽  
Angular Speed ◽  
Transverse Displacement ◽  
Governing Equations ◽  
Rotating Load

Here, we have studied the linear and nonlinear vibrations of a thin circular plate subjected to circularly, radially, and spirally moving transverse point loads. We follow Kirchoff’s theory and then incorporate von Kármán nonlinearity and employ Hamilton’s principle to obtain the governing equations and the associated boundary conditions. We solve the governing equations for the simply-supported and clamped boundary conditions using the mode summation method. Using the harmonic balance method for frequency response and Runge-Kutta method for time response, we solve the resulting coupled and cubic nonlinear ordinary differential equations. We show that the resonance instability due to a circularly moving load can be avoided by splitting it into multiple loads rotating at the same radius and angular speed. With the increasing magnitude of the rotating load, the frequency response of the transverse displacement shows jumps and modal interaction. The transverse response collected at the centre of the plate shows subharmonics of the axisymmetric frequencies only. The spectrum of the linear response due to spirally moving load contains axisymmetric frequencies, the angular speed of the load, their combination, and superharmonics of axisymmetric frequencies.

Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen’s theory

2019 ◽  
Vol 26 (11-12) ◽  
pp. 913-928 ◽  
Author(s):  
Seyed Amirhosein Hosseini ◽  
Farshad Khosravi ◽  
Majid Ghadiri
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Classical Theory ◽  
Moving Load ◽  
Nonlocal Parameter ◽  
Excitation Frequency ◽  
Single Walled Carbon Nanotubes ◽  
Axial Displacement ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

The main objective of the present work is devoted to the study of both free and time-dependent forced axial vibration simultaneously in single-walled carbon nanotubes subjected to a moving load. The governing equation is derived via Hamilton’s principle. Classical theory, along with the Rayleigh and Bishop theories, is used to analyze the nonlocal vibrational behaviors of single-walled carbon nanotubes. A Galerkin method is established to solve the derived equations. The boundary conditions are assumed to be clamped-clamped and clamped-free. Firstly, the variation of nondimensional natural frequencies is calculated based on the classical theory, and the effect of the nonlocal parameter, the mode number and the length is illustrated and schematically compared for clamped-clamped and clamped-free boundary conditions. Besides, the obtained nondimensional responses are compared with the results of another study to validate the accuracy of the used method. Ultimately, the dynamic axial displacement due to the moving load in the time domain has been studied for the first time. Furthermore, the effects of the thickness, length, velocity of the moving load, excitation frequency, and the nonlocal parameter based on the classical, Rayleigh, and Bishop theories are investigated in this paper. Also, the influence of the nonlocal parameter on the variations of maximum axial displacement with respect to the velocity parameter for the aforementioned boundary conditions and theories is evaluated relative to each other.

scholarly journals Wavelet Approach for Vibration Analysis of Fast Moving Load on a Viscoelastic Medium

2010 ◽  
Vol 17 (4-5) ◽  
pp. 461-472 ◽  
Author(s):  
Piotr Koziol ◽  
Cristinel Mares
Keyword(s):  
Boundary Conditions ◽  
Fast Moving ◽  
Moving Load ◽  
Finite Thickness ◽  
Constant Load ◽  
Order Of Accuracy ◽  
Wavelet Approximation ◽  
Complex Models ◽  
The Mathematical Model ◽  
Different Order

This paper analyses theoretically the response of a solid for fast moving trains using models related to real situations: a load moving in a tunnel and a load moving on a surface. The mathematical model is described by Navier's elastodynamic equation of motion for the soil and Euler-Bernoulli equation for the beam with appropriate boundary conditions. Two modelling approaches are investigated: the model with half space under the beam and the model with finite thickness of supporting medium. The problem of singularities for displacements calculation is discussed in relation with boundary conditions and types of considered loads: harmonic and constant, point and distributed moving loads. The analysis in frequency-time and frequency-velocity domains is presented and discussed with regard to critical velocities.A wavelet approximation method based on application of coiflet filters is used for the derivation of displacements in physical domain. A new, modified filter is used in numerical calculations allowing to alleviate numerical difficulties related to the form of approximating sequences based on classical filters, formulated in previous publications. The effectiveness of the coiflet approach is discussed for filter coefficients with different order of accuracy. This methodology is very efficient for the analysis in the range of relatively high and low load frequencies (treated as an approximation of a constant load) which are especially important for the analysis of vibrations generated by trains moving with velocities near critical values.Results of numerical simulations are presented, demonstrating their utility for modelling and preliminary analysis of complex models.

scholarly journals Simulation of vibrations of a continuously elastic supported rod with varying boundary conditions under the action of a movable

2018 ◽  
Vol 196 ◽  
pp. 01053
Author(s):  
Sergey Gridnev ◽  
Yuriy Skalko ◽  
Ilya Ravodin ◽  
Victoria Yanaeva
Keyword(s):  
Boundary Conditions ◽  
Piecewise Linear ◽  
Moving Load ◽  
Continuous System ◽  
Basis Functions ◽  
Non Linear ◽  
Linear Vibrations ◽  
Floating Bridge ◽  
Model Equations ◽  
Elastically Supported

To simulate the non-linear vibrations of a floating bridge of a continuous system on separate floating supports with additional limiting supports at the ends with a moving load solves the most complicated problem which is the problem of describing the behavior of a span structure. A technique for simulating the vibration of an elastically supported deformable rod with limiting supports at the ends, which is a design scheme of a span structure, under the action of a moving force is developed. A computational algorithm for solving partial differential equations with varying boundary conditions is proposed, which includes boundary conditions in the model equations and does not require the subordination of basis functions to the boundary conditions. During the calculation, the basis remains constant. Piecewise linear basis functions are used to solve the differential equation. The technique is tested using a computational program Matlab, which is implemented when performing numerical studies of the behavior of the dynamic system as a function of the parameter changes. The developed technique is universal for studying the dynamics of a number of constructively non-linear systems.

Random Base Excitation of Timoshenko Beam Traversed by Moving Load

2011 ◽  
Author(s):  
Fahim Javid ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Base Excitation ◽  
Lateral Direction ◽  
Beam Dynamic

The study of dynamic response of Timoshenko beam traversed by moving load subjected to random base excitation is carried out. By applying the theory of dynamic response of Timoshenko beam as well as finite element theory, beam finite element governing equations of motion are developed and they are solved using Galerkin method. To validate the model, some results of the model are compared with those available in literatures and very close agreement is achieved. The beam is subjected to travelling load and random base excitation in lateral direction simultaneously. Three types of boundary conditions, namely, hinged-hinged, hinged-clamped, and the clamped-clamped ends, are considered and beam dynamic behavior; such as deflection, velocity, and bending moment of beam midpoint, with all so-called boundary conditions are studied. To get better understanding of base excitation effects on the beam dynamic performance, all the results are presented with and without base excitation, in which considerably difference is observed. Moreover, the effect of base excitation on beam with different span-length is monitored.

Mechanics-based algorithms to determine the current state of a bridge using quasi-static loading and strain measurement

2018 ◽  
Vol 18 (5-6) ◽  
pp. 1874-1888 ◽  
Author(s):  
Pandi Pitchai ◽  
U Saravanan ◽  
Rupen Goswami
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Material Properties ◽  
High Performance ◽  
High Performance Concrete ◽  
Young's Modulus ◽  
Moving Load ◽  
Material Parameters ◽  
Current State ◽  
Slow Moving

Knowing the current state of a bridge is of interest for a variety of reasons. Some parameters that determine the current state of a bridge are the material properties and boundary conditions. Using strain measurements obtained from a slow-moving vehicle on a bridge, the boundary condition and material properties are determined through a mechanistic-based approach. Observing that the sign of the curvature would change at locations near the support when a load passes over a bridge with end rotational restraints, a methodology for determining the boundary conditions is proposed and validated. The linear elastic properties of the material that the bridge is made up of is determined from the strain measured at locations where the stress is independent of the material property. In this procedure, the structure is analyzed assuming some material properties and the stress at the measured point is determined. Then, the material parameters in the isotropic Hooke’s law are determined so that the stress estimated from the experimentally determined strains agrees with that obtained from the analysis with arbitrarily assumed material parameters. A prestressed high-performance concrete pi-shaped girder tested under a three-axle slow-moving load with strains measured at different locations is used to bring out the efficacy and appropriateness of the proposed methodologies. The mean value of Young’s modulus of the prestressed concrete bridge agrees well with the experimentally determined Young’s modulus.

Dynamic Response of a Spinning Timoshenko Beam With General Boundary Conditions and Subjected to a Moving Load

1994 ◽  
Vol 61 (1) ◽  
pp. 152-160 ◽  
Author(s):  
J. W.-Z. Zu ◽  
R. P. S. Han
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Original System ◽  
Adjoint System ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Adjoint Systems ◽  
Analysis Technique

The dynamic response of a spinning Timoshenko beam with general boundary conditions and subjected to a moving load is solved analytically for the first time. Solution of the problem is achieved by formulating the spinning Timoshenko beams as a non-self-adjoint system. To compute the system dynamic response using the modal analysis technique, it is necessary to determine the eigenquantities of both the original and adjoint systems. In order to fix the adjoint eigenvectors relative to the eigenvectors of the original system, the biorthonormality conditions are invoked. Responses for the four classical boundary conditions which do not involve rigidbody motions are illustrated. To ensure the validity of the method, these results are compared with those from Euler-Bernoulli and Rayieigh beam theories. Numerical simulations are performed to study the influence of the four boundary conditions on selected system parameters.

Dynamic Responses of Functionally Graded Sandwich Beams Resting on Elastic Foundation Under Harmonic Moving Loads

2018 ◽  
Vol 18 (09) ◽  
pp. 1850112 ◽  
Author(s):  
Wachirawit Songsuwan ◽  
Monsak Pimsarn ◽  
Nuttawit Wattanasakulpong
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Moving Load ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Harmonic Load ◽  
Sandwich Beams

This paper investigates the free vibration and dynamic response of functionally graded sandwich beams resting on an elastic foundation under the action of a moving harmonic load. The governing equation of motion of the beam, which includes the effects of shear deformation and rotary inertia based on the Timoshenko beam theory, is derived from Lagrange’s equations. The Ritz and Newmark methods are employed to solve the equation of motion for the free and forced vibration responses of the beam with different boundary conditions. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, spring constants, etc. on natural frequencies and dynamic deflections of the beam. It was found that increasing the spring constant of the elastic foundation leads to considerable increase in natural frequencies of the beam; while the same is not true for the dynamic deflection. Additionally, very large dynamic deflection occurs for the beam in resonance under the harmonic moving load.

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