scholarly journals Nonlinear Vibrations in Homogeneous Non-Prismatic Timoshenko Cantilevers

2021 ◽  
Author(s):  
Navid Navadeh ◽  
Pooya Sareh ◽  
Vladimir G. Basovsky ◽  
Irina M. Gorban ◽  
Arash S. Fallah
Keyword(s):  
Dynamic Response ◽  
Analytical Model ◽  
Timoshenko Beam ◽  
Nonlinear Oscillations ◽  
Vibration Modes ◽  
Cantilever Beams ◽  
Nonlinear Dynamic Response ◽  
Beam Motion ◽  
The Mathematical Model ◽  
Special Case

Abstract Deep cantilever beams, modelled using Timoshenko beam kinematics, have numerous applications in engineering. This study deals with the nonlinear dynamic response in a non-prismatic Timoshenko beam characterized by considering the deformed configuration of the axis. The mathematical model is derived using the extended Hamilton's principle under the condition of finite deflections and angles of rotation. The discrete model of the beam motion is constructed based on the finite difference method (FDM), whose validity is examined by comparing the results for a special case with the corresponding data obtained by commercial finite element (FE) software ABAQUS 2019. The natural frequencies and vibration modes of the beam are computed. These results demonstrate decreasing eigenfrequency in the beam with increasing amplitudes of nonlinear oscillations. The numerical analyses of forced vibrations of the beam show that its points oscillate in different manners depending on their relative position along the beam. Points close to the free end of the beam are subject to almost harmonic oscillations, and the free end vibrates with a frequency equal to that of the external force. When a point approaches the clamped end of the beam, it oscillates in two-frequency mode and lags in phase from the oscillations of the free end. The analytical model allows for the study of the influence of each parameter on the eigenfrequency and the dynamic response. In all cases, a strong correlation exists between the results obtained by the analytical model and ABAQUS, nonetheless, the analytical model is computationally less expensive.

Temperature Influence on Nonlinear Responses of Timoshenko Beam

2013 ◽  
Author(s):  
Anna Warminska ◽  
Jerzy Warminski ◽  
Emil Manoach
Keyword(s):  
Elevated Temperature ◽  
Timoshenko Beam ◽  
Nonlinear Oscillations ◽  
Multiple Time ◽  
Vibration Modes ◽  
Nonlinear Responses ◽  
Large Amplitude Vibrations ◽  
The Galerkin Method ◽  
The Mathematical Model ◽  
Multiple Time Scale Method

The goal of this paper is to study large amplitude vibrations of a Timoshenko beam under an influence of the elevated temperature. It is assumed that the beam gets the elevated temperature instantly and the temperature is uniformly distributed along the beam’s length and cross-section. The mathematical model represented by a set of partial differential equations is derived taking into account boundary conditions for a simply supported beam in the both ends. Next, the problem is reduced by the Galerkin method by means of free vibration modes. The influence of the temperature on a resonance localisation and nonlinear oscillations is studied numerically and analytically by the multiple time scale method.

Nonlinear Dynamic Response of Nanocomposite Cantilever Beams

2020 ◽  
pp. 49-57
Author(s):  
Michela Talò ◽  
Biagio Carboni ◽  
Giovanni Formica ◽  
Giulia Lanzara ◽  
Matthew Snyder ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Cantilever Beams ◽  
Nonlinear Dynamic Response

Shaking Table Tests of a Four-Story Miniature Steel Building— Model Validation

2006 ◽  
Vol 22 (3) ◽  
pp. 755-780 ◽  
Author(s):  
Mario E. Rodríguez ◽  
José I. Restrepo ◽  
John J. Blandón
Keyword(s):  
Dynamic Response ◽  
Analytical Model ◽  
Shaking Table ◽  
Experimental Program ◽  
Shake Table ◽  
Base Shear ◽  
Shake Table Tests ◽  
Nonlinear Dynamic Response ◽  
Building Model ◽  
High Level

This paper discusses an analytical model developed to study the linear and nonlinear dynamic response of a four-story steel miniature building subjected to low-level and high-level shake table tests inducing nominally elastic and inelastic response, respectively. The analytical model was calibrated and validated against the results of the experimental program. A comparison of measured and calculated responses is made in the paper. Of particular interest, absolute floor accelerations were found more sensitive to high-frequency content than other response parameters such as base shear force and overturning base moment. The seismic performance of gravity-dominated beams is also examined in this paper. It was found that the cumulative nature of rotation demands in this type of beams should be considered in seismic design. The model is also used to observe differences in dynamic response of buildings when subjected to shake table tests with low fidelity in the reproduction of earthquake records.

DYNAMIC BEHAVIOR OF TELESCOPIC CRANES BOOM

2013 ◽  
Vol 13 (01) ◽  
pp. 1350010 ◽  
Author(s):  
IOANNIS G. RAFTOYIANNIS ◽  
GEORGE T. MICHALTSOS
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Constant Velocity ◽  
Steel Beam ◽  
Continuum Approach ◽  
Theoretical Formulation ◽  
Modal Superposition ◽  
Superposition Technique

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.

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