Shear Deformable Elastic Beam Models in Vibration and Sensitivity of Natural Frequencies to Warping Effects

2021 ◽  
pp. 217-236
Author(s):  
Castrenze Polizzotto ◽  
Isaac Elishakoff ◽  
Paolo Fuschi
Keyword(s):  
Natural Frequencies ◽  
Elastic Beam ◽  
Shear Deformable

scholarly journals A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System

2017 ◽  
Vol 2017 ◽  
pp. 1-20
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku ◽  
Patrick S. Olayiwola
Keyword(s):  
Incompressible Fluid ◽  
Coriolis Force ◽  
Analytic Solution ◽  
Natural Frequencies ◽  
Integral Transform ◽  
Elastic Beam ◽  
Pipeline System ◽  
Complex Frequency ◽  
Validity Of Results ◽  
Pipeline Segment

This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work) as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system’s natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre- and postdivergence behaviours are exhibited.

scholarly journals Enhanced Energy Harvesting of Flexural Waves in Elastic Beams by Bending Mode of Graded Resonators

2021 ◽  
Vol 8 ◽  
Author(s):  
Jacopo Maria De Ponti ◽  
Luca Iorio ◽  
Emanuele Riva ◽  
Francesco Braghin ◽  
Alberto Corigliano ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Natural Frequencies ◽  
Elastic Beam ◽  
Flexural Waves ◽  
Vibration Energy Harvesting ◽  
Micro Fabrication ◽  
Wave Propagation Direction ◽  
Practical Applications ◽  
Bending Mode ◽  
Definition Of

We show efficient elastic energy transfer and wave confinement through a graded array of resonators attached to an elastic beam. Experiments demonstrate that flexural resonators of increasing lengths allow to reduce wave scattering and to achieve the rainbow effect with local wavefield amplifications. We show that the definition of a monotonically decreasing distribution of the natural frequencies of the resonators along the wave propagation direction, is the preferable choice to increase the energy efficiency of the system. The proposed configuration is suitable for micro-fabrication, envisaging practical applications for micro-scale vibration energy harvesting.

On Flexural Vibrations of Shear Deformable Laminated Beams

2012 ◽  
Author(s):  
Stefano Lenci ◽  
Francesco Clementi
Keyword(s):  
Mechanical Characteristics ◽  
Natural Frequencies ◽  
Normal Direction ◽  
Rotational Inertia ◽  
Shear Deformations ◽  
Various Boundary Conditions ◽  
Elastic Interface ◽  
Shear Deformable ◽  
Perfect Adherence ◽  
Tangential Directions

The natural frequencies of a two-layer beam with an elastic interface are investigated. Each beam is modeled by the Timoshenko kinematics, and the interface coupling is linear in both normal and tangential directions. Attention is focused on the shear deformation, axial and rotational inertia, and interface normal stiffness. The dependence of the natural frequencies on these mechanical characteristics is investigated by solving the associated eigenvalue problem. The convergence of the solution toward that of a simplified problem obtained by neglecting axial and rotational inertia, shear deformations and by considering interface perfect adherence in the normal direction, is studied. Various boundary conditions are investigated to extend the generality of the proposed results.

scholarly journals On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
M. Tahmaseb Towliat Kashani ◽  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Axial Load ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Elastic Beam ◽  
Axial Compressive Force ◽  
Various Boundary Conditions ◽  
Linear Eigenvalue Problem ◽  
The Moment

The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MATLAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

An Analytical Investigation for Vibration Characteristics of a Beam-Type Liquid Micro-Pump

2020 ◽  
Vol 12 (02) ◽  
pp. 2050016
Author(s):  
Hamed Hatami ◽  
Ahmad Bagheri ◽  
Reza Ansari
Keyword(s):  
Fluid Flow ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Elastic Beam ◽  
Coupled System ◽  
Analytical Investigation ◽  
Mode Shapes ◽  
Micro Pump ◽  
Cartesian Coordinate ◽  
Forced Vibration Analysis

This paper studies the characteristics of a micro-beam interacting with an incompressible fluid in a fluid chamber with an opening in its bottom face for fluid flow. The Euler–Bernoulli equation for transverse deformation of an elastic beam is coupled with the fundamental hydrodynamic equation, which is solved by Galerkin and separation of variables method. The 2D fluid flow assumption in Cartesian coordinate has been used. Natural frequencies and mode shapes of wet beam are calculated and compared with the dry beam. The effects of geometrical parameter changes are also computed as a benchmark for the design of the micro-pump. It is observed that fluid coupling causes a decrease for beam’s natural frequencies, especially in higher modes. Furthermore, since the results of the dry and wet beam show a small discrepancy in lower modes, the mode related to the dry beam was employed as the trial function in the forced vibration analysis of the coupled system.

Natural frequencies and buckling of pressurized nanotubes using shear deformable nonlocal shell model

2012 ◽  
Vol 26 (2) ◽  
pp. 563-573 ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. M. Fotouhi ◽  
M. R. Permoon ◽  
H. Haddadpour
Keyword(s):  
Shell Model ◽  
Natural Frequencies ◽  
Shear Deformable

FREE VIBRATIONS OF SHEAR DEFORMABLE CIRCULAR CURVED BEAMS RESTING ON ELASTIC FOUNDATIONS

2002 ◽  
Vol 02 (01) ◽  
pp. 77-97 ◽  
Author(s):  
BYOUNG KOO LEE ◽  
SANG JIN OH ◽  
KWANG KYOU PARK
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotary Inertia ◽  
Transverse Shear Deformation ◽  
Curved Beams ◽  
System Parameters ◽  
Elastic Foundations ◽  
Out Of Plane ◽  
Shear Deformable

The governing differential equations for the out-of-plane, free vibration of circular curved beams resting on elastic foundations are derived and solved numerically. The formulation takes into consideration the effects of rotary inertia and transverse shear deformation. The lowest three natural frequencies are calculated for beams with hinged–hinged, hinged-clamped, and clamped–clamped end constraints. The effects of various system parameters as well as rotary inertia and shear deformation on the natural frequencies are investigated.

scholarly journals On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

2021 ◽  
Author(s):  
M. Tahmaseb Towliat Kashani ◽  
Supun Jayasinghe Jayashinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Axial Load ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Elastic Beam ◽  
Axial Compressive Force ◽  
Various Boundary Conditions ◽  
Linear Eigenvalue Problem ◽  
The Moment

The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MAT LAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

scholarly journals Identification of dynamical characteristics for distributed parameters systems from measured vibration data

1995 ◽  
Vol 17 (1) ◽  
pp. 35-44
Author(s):  
Nguyen Tien Khiem ◽  
Dao Nhu Mai ◽  
Nguyen Van Dac ◽  
Nguyen Viet Khoa
Keyword(s):  
Natural Frequencies ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Mode Shapes ◽  
Vibration Data ◽  
Dynamical Characteristics ◽  
Distributed Parameters

This article is devoted to determinate the dynamical characteristics (Natural Frequencies, Mode Shapes, Damping Ratio) of elastic beam from measured responce auto-spectrum. Developed here method is based on the assumptions of smallness of the damping and sparse distribution of natural frequencies. Accuracy and practical meaning of the method are confirmed by the agreement of the theory with experiments.

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