In Plane Radial Vibration of Uncracked and Cracked Circular Curved Beams Subjected to Moving Loads

2021 ◽  
pp. 2150146
Author(s):  
Jatin Poojary ◽  
Sankar Kumar Roy
Keyword(s):  
Dynamic Response ◽  
Moving Load ◽  
Real Life ◽  
Beam Theory ◽  
Point Of View ◽  
Curved Beam ◽  
Moving Loads ◽  
Curved Beams ◽  
Beam Elements ◽  
Curved Beam Element

The dynamic response of structures subjected to moving load is a subject of great importance from a practical point of view. In this work, the in-plane dynamic response of a cracked isotropic circular curved beam subjected to moving loads is investigated using the finite element method. The curved beam is modeled using curved beam elements, which is developed based on the Timoshenko beam theory. Furthermore, a cracked curved beam element is developed to incorporate the presence of cracks in the structure. The effect of moving load speed, depth, and the location of the crack on the dynamic response of the beam is investigated. The outcome of the work can be useful in the study of real-life moving load problems like bridges and railways and also in the field of condition monitoring using moving loads.

scholarly journals Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions

2012 ◽  
Vol 19 (2) ◽  
pp. 187-204 ◽  
Author(s):  
Ahmad Shahba ◽  
Reza Attarnejad ◽  
Mehran Eslaminia
Keyword(s):  
Special Functions ◽  
Free Vibration Analysis ◽  
Beam Element ◽  
Point Of View ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Curved Beam Element ◽  
Exact Shape ◽  
Basic Displacement Functions

The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.

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.

Inelastic Response of Nuclear Piping Subjected to Rupture Forces

1976 ◽  
Vol 98 (2) ◽  
pp. 98-104 ◽  
Author(s):  
J. C. Anderson ◽  
A. K. Singh
Keyword(s):  
Dynamic Response ◽  
Numerical Procedure ◽  
Beam Element ◽  
Piping System ◽  
Curved Beam ◽  
Blow Down ◽  
Curved Beam Element ◽  
Piping Systems ◽  
Support Element ◽  
System 1

A numerical procedure which can be used to evaluate the inelastic dynamic response of piping systems subjected to blow-down forces is described. The following finite elements are used to represent the piping system: (1) bilinear beam element, (2) bilinear curved beam element, and (3) bilinear support element with an initial gap. The method is then used to evaluate the dynamic response of two typical segments of a main steamline.

A Finite Element Modeling Framework for Planar Curved Beam Dynamics Considering Nonlinearities and Contacts

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Tianheng Feng ◽  
Soovadeep Bakshi ◽  
Qifan Gu ◽  
Dongmei Chen
Keyword(s):  
Finite Element ◽  
Beam Dynamics ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Modeling Framework ◽  
External Wall ◽  
Beam Elements ◽  
High Compression ◽  
Assumed Strain

Motivated by modeling directional drilling dynamics where planar curved beams undergo small displacements, withstand high compression forces, and are in contact with an external wall, this paper presents an finite element method (FEM) modeling framework to describe planar curved beam dynamics under loading. The shape functions of the planar curved beam are obtained using the assumed strain field method. Based on the shape functions, the stiffness and mass matrices of a planar curved beam element are derived using the Euler–Lagrange equations, and the nonlinearities of the beam strain are modeled through a geometric stiffness matrix. The contact effects between curved beams and the external wall are also modeled, and corresponding numerical methods are discussed. Simulations are carried out using the developed element to analyze the dynamics and statics of planar curved structures under small displacements. The numerical simulation converges to the analytical solution as the number of elements increases. Modeling using curved beam elements achieves higher accuracy in both static and dynamic analyses compared to the approximation made by using straight beam elements. To show the utility of the developed FEM framework, the post-buckling condition of a directional drill string is analyzed. The drill pipe undergoes spiral buckling under high compression forces, which agrees with experiments and field observations.

Dynamic Response of a Cantilevered Beam Under Combined Moving Moment, Torque and Force

2020 ◽  
Vol 20 (05) ◽  
pp. 2050065
Author(s):  
Denil Chawda ◽  
Senthil Murugan
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Moving Load ◽  
Numerical Results ◽  
Moving Loads ◽  
Element Analysis ◽  
Dirac Delta ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Cantilevered Beam

This paper studies the dynamic response of a cantilevered beam subjected to a moving moment and torque, and combination of them with a moving force. The moving loads are considered to traverse along the length of the beam either from fixed-to-free end or free-to-fixed end. The beam is considered to have constant material and geometric properties. The beam is modeled using the Rayleigh beam theory considering the rotary inertia effects. The Dirac-delta function used to model the moving loads in the governing partial differential equations (PDEs) has complicated the solution of the problem. The Eigenfunction expansions coupled with the Laplace transformation method is used to find the semi-analytical solution for the resulting governing PDEs. The effects of moving loads on the dynamic response are studied. The dynamic effects are quantified based on the number of oscillations per unit travel time of the moving load and the Dynamic Amplification Factor (DAF) of the beam’s tip response. Numerical results are also analyzed for the two-speed regimes, namely high-speed and low-speed regimes, defined with respect to the critical speed of the moving loads. The accuracy of the analytical solutions are verified by the finite element analysis. The numerical results show that the loads moving with low speeds have significant impact on the dynamic response compared to high speeds. Also, the moving moment has significant impact on the amplitude of dynamic response compared with the moving force case.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

Dynamic Response of an Elastic-Supported Bridge Beam Subjected to Velocity-Varied Moving Loads

2012 ◽  
Vol 594-597 ◽  
pp. 2802-2807
Author(s):  
Fu Liang Mei ◽  
Gui Ling Li
Keyword(s):  
Dynamic Response ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Force Model ◽  
Superposition Method ◽  
Moving Loads ◽  
Coupled Vibration ◽  
Vehicle Model ◽  
Vibration Model ◽  
Mass Spring

Dynamic response of an elastic-supported bridge under speed-varied moving loads was investigated. A mathematical model of vehicle-bridge coupled oscillation for an elastic-supported bridge was built up by means of 1/4 vehicle model (Mass-Spring-Mass) and Euler-Bernoulli beam theory. And then dynamic equations of vehicle-bridge coupled oscillation in matrix form were established using two former orders general coordinates of an elastic-supported beam and model superposition method. The influences of vehicle-bridge coupled vibration model, elastic-supported stiffness, entrance speeds and acceleration /deceleration of moving loads on the dynamic responses of bridges were studied. Vehicle-bridge coupled vibration model based on 1/4 vehicle model can more accurately describe the dynamic characters of bridges than that based on constant moving force model. Elastic-supported stiffness only has an impact on the fluctuation amplitudes of dynamic responses. The vehicle-induced impact factor is dependent on the entrance speeds, acceleration/deceleration of moving loads and elastic-supported stiffness.

Dynamic Response of Multi-bay Frames Subjected to Successive Moving Forces

2019 ◽  
Vol 19 (04) ◽  
pp. 1950042
Author(s):  
Salih Demirtas ◽  
Hasan Ozturk ◽  
Mustafa Sabuncu
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Moving Load ◽  
Single Point ◽  
Vertical Direction ◽  
Point Load ◽  
Dynamic Responses ◽  
Moving Loads ◽  
Element Analysis ◽  
Constant Interval

This paper investigates the dynamic responses of multi-bay frames with identical bay lengths subjected to a transverse single moving load and successive moving loads with a constant interval at a constant speed. The effects of the bay length and the speed of the moving load on the response of the multi-bay frame subjected to a single point load are investigated numerically by the finite element method. A computer code is developed by using MATLAB to perform the finite element analysis. The Newmark method is employed to solve for the dynamic responses of the multi-bay frame. With this, the dynamic response of the frame subjected to successive moving loads with a constant interval is investigated. Also, the resonance and cancellation speeds are determined by using the 3D relationship of speed parameter-force span length to beam length ratio-dynamic magnification factor and the associated contour lines. The maximum impact factor of a 1-bay frame and multi-bay frames under single moving load are determined at the specific speed parameters. Those values are independent of elastic modulus, area moment of inertia, beam/column lengths of the frame and also the number of bays forming the frame. It is also found that the first resonance response in the vertical direction of the frame is related to the second mode of vibration.

Vibration Analysis of a Circular Tunnel With Jointed Liners Embedded in an Elastic Medium Subjected to Seismic Waves

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Dong-Sheng Jeng ◽  
Jian-Fei Lu
Keyword(s):  
Elastic Medium ◽  
Seismic Waves ◽  
Differential Quadrature Method ◽  
Surrounding Medium ◽  
Beam Theory ◽  
Scattered Wave ◽  
Collocation Methods ◽  
Curved Beam ◽  
Curved Beams ◽  
Circular Tunnel

This paper presents a frequency domain analysis of a circular tunnel with piecewise liners subjected to seismic waves. In our model, the surrounding medium of the tunnel is considered as a linear elastic medium and described by the dynamic elasticity theory, while piecewise liners and connecting joints are treated as curved beams and described by a curved beam theory. Scattered wave field in the surrounding elastic medium are obtained by the wave function expansion approach. The governing equations for vibrations of a curved beam are discretized by the general differential quadrature method. We use domain decomposition methods to establish the global discrete dynamic equations for piecewise liners. Boundary least squares collocation methods, based on the continuity conditions of stresses and displacements between surrounding soil and the piecewise liners, are used to determine the response of the liners and the surrounding medium. Numerical results conclude that the presence of the joints significantly changes the distributions of the tunnel internal force, and dramatically increase shear forces and moment of the tunnel liners around joints.

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