Free and Forced Vibration of Double Beam with Arbitrary End Conditions Connected With A Viscoelastic Layer and Discrete Points

2021 ◽  
pp. 106707
Author(s):  
Xingzhuang Zhao ◽  
Peter Chang
Keyword(s):  
Forced Vibration ◽  
Viscoelastic Layer ◽  
Double Beam ◽  
End Conditions

scholarly journals Nonlinear free and forced vibration of Euler-Bernoulli beams resting on intermediate flexible supports

2018 ◽  
Vol 211 ◽  
pp. 02003
Author(s):  
Hatim Fakhreddine ◽  
Ahmed Adri ◽  
Saïd Rifai ◽  
Rhali Benamar
Keyword(s):  
Forced Vibration ◽  
Algebraic System ◽  
Displacement Function ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Bending Vibration ◽  
End Conditions ◽  
Flexible Supports ◽  
Elastic Restraints ◽  
Forced Vibration Analysis

This paper deals with the geometrically nonlinear free and forced vibration analysis of a multi-span Euler Bernoulli beam resting on arbitrary number N of flexible supports, denoted as BNIFS, with general end conditions. The generality of the approach is based on use of translational and rotational springs at both ends, allowing examination of all possible combinations of classical beam end conditions, as well as elastic restraints. First, the linear case is examined to obtain the mode shapes used as trial functions in the nonlinear analysis. The beam bending vibration equation is first written in each span. Then, the continuity requirements at each elastic support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. Numerical results are given to illustrate the effects of the support stiffness and locations on the natural frequencies and mode shapes of the BNIFS. The nonlinear theory is then developed, based on the Hamilton’s principle and spectral analysis. The nonlinear beam transverse displacement function is defined as a linear combination of the linear modes calculated before. The problem is reduced to solution of a non-linear algebraic system using numerical or analytical methods. The nonlinear algebraic system is solved using an explicit method developed previously (second formulation) leading to the amplitude dependent nonlinear fundamental mode of the BNIFS.

scholarly journals Effect of Insertion Viscoelastic Damping Layer with Different Thicknesses on the Dynamic Response of Multi-layered Beam in Forced Vibration

2020 ◽  
Vol 65 (1) ◽  
pp. 1-9
Author(s):  
Messaoud Baali ◽  
Mohamed Nadir Amrane
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Sandwich Structure ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Viscoelastic Layer ◽  
Thickness Variation ◽  
Vertical Displacements ◽  
Nonlinear Equations Of Motion

In this work, we study the effect of the thickness variation of viscoelastic layer inserted in a laminated multi-layer beam in forced vibration on the vertical displacements and on the natural frequencies. The new structure is a sandwich structure composed by two external layers (top and bottom facesheets) of aluminum and viscoelastic core of 3M ISD112 polymers. The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. The finite element method including the viscoelastic model of fractional derivatives for modeling the sandwich structure is used. The system resolution of the nonlinear equations of motion of the sandwich structure is required to use a numerical integration method as the explicit method of Newmark to obtain the transient response. Also, ANSYS finite element modeling is applied to the sandwich structure to calculate the frequency response in harmonic vibration. The increase in the thickness of the viscoelastic layer leads to a decrease in the amplitudes of vibration. The natural frequencies found by the two methods are very close to the frequencies found experimentally in the literature.

Analytical and Experimental Natural Frequencies of Transverse Vibration of Sandwich Beams Interconnected by Winkler Elastic Foundation

Aerospace ◽  
2006 ◽  
Author(s):  
Mohamed Gaith ◽  
James Masters ◽  
Sinan Muftu
Keyword(s):  
Elastic Foundation ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Theoretical Models ◽  
Asynchronous Mode ◽  
Single Beam ◽  
Beam System ◽  
Winkler Elastic Foundation ◽  
Double Beam ◽  
End Conditions

The free transverse vibration of an elastically connected axially loaded double beam system for different materials and geometry were measured experimentally and analyzed theoretically. The theory predicts that natural frequencies of the system are composed of two infinite sets, describing in-phase and out-of-phase vibrations. It is observed, for the case of identical beams, that the in-phase frequencies are independent of the elastic foundation stiffness and its frequencies are identical to a single beam with the same boundary conditions. To compare and verify the accuracy and reliability of theoretical models, experimental measurements of natural frequencies of free vibration of axially tensioned, double beams interconnected by a silicone rubber foundation with fixed-fixed supported conditions are conducted. The first four synchronous natural frequencies were measured, and they were found to increase with increasing tension. The experiments showed that the synchronous natural frequencies of axially tensioned double beam system with fixed-fixed end conditions are in excellent agreement with those for a tensioned single beam with the same end conditions. The asynchronous mode frequencies are not observed, and believed to be due to the existence of damping properties in the elastic foundation, which suppressed the out-of-phase (asynchronous) mode frequencies.

Axial–bending coupling vibration of mass eccentric double-beam system with discrete elastic connections

2016 ◽  
Vol 231 (2) ◽  
pp. 555-568
Author(s):  
Jinpeng Su ◽  
Zhiyang Lei ◽  
Hongxing Hua
Keyword(s):  
Timoshenko Beam ◽  
Forced Vibration ◽  
Coupled System ◽  
Spectral Element ◽  
Coupling Vibration ◽  
System A ◽  
Beam System ◽  
Mass Eccentricity ◽  
Double Beam ◽  
Lower Beam

The existence of mass eccentricity will lead to the energy transfer between axial and flexural vibrations of a beam. To study the coupling properties of a double-Timoshenko beam system, a non-uniform coupled double-beam system is modeled in which the upper beam is typical and the lower beam is mass eccentric simulated by a non-uniform two-layer Timoshenko beam. By incorporating Hamilton’s principle and spectral element method, the axial–bending coupled governing equations of the system are derived and the approach can also be easily used to analyze the influences of the parameters and other coupled beam systems. Both the free and forced vibration results of a double-beam system by this method are consistent with the corresponding finite element model’s and thus this method is validated. The coupled properties and their mechanism are revealed. The influences of axial and transverse flexible connection on the coupling properties including free and forced vibration are investigated. A systematic matching principle of reducing the vibration of the coupled system is proposed.

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