scholarly journals Transverse Vibrations and Stability of Axially Traveling Sandwich Beam With Soft Core

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Li-Qun Chen
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Axial Loading ◽  
Core Layer ◽  
Soft Core ◽  
Axially Moving Beam ◽  
Transverse Vibrations ◽  
Axially Moving ◽  
The Galerkin Method

The transverse vibrations and stability of an axially moving sandwich beam are studied in this investigation. The face layers are assumed to be in the membrane state, which bears only axial loading but no bending. Only shear deformation is considered for the soft core layer. The governing partial equation is derived using Newton's second law and then transferred into a dimensionless form. The Galerkin method and the complex mode method are employed to study the natural frequencies. In comparison with the classical homogenous axially moving beam, the gyroscopic matrix is no longer skew-symmetric because of the introduction of the soft core. The critical speed for the divergence of the axially moving sandwich beam is analytically obtained. The contribution of the core layer shear modulus to the natural frequencies and critical speed is discussed.

Computing Natural Frequencies and Mode Shapes of an Axially Moving Non-Uniform Beam

2020 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Cross Sections ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Linear Time ◽  
Mode Shapes ◽  
Axially Moving Beam ◽  
Time Varying Systems ◽  
Axially Moving ◽  
The Galerkin Method ◽  
Spatially Varying

Abstract The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam’s cross section.

Computing Natural Frequencies and Mode Shapes of an Axially Moving Non-Uniform Beam

2021 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Cross Sections ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Linear Time ◽  
Mode Shapes ◽  
Axially Moving Beam ◽  
Time Varying Systems ◽  
Axially Moving ◽  
The Galerkin Method ◽  
Spatially Varying

Abstract The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems and numerical optimization, a general algorithm has been developed to compute complex eigenvalues/natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam's cross section.

The Vibration of Two Axially Translating Strings Interconnected by Winkler Elastic Foundation

2006 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Muftu
Keyword(s):  
Elastic Foundation ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Elastic Stiffness ◽  
Gyroscopic System ◽  
First Order ◽  
Axial Tension ◽  
Transverse Vibrations ◽  
Winkler Elastic Foundation

The transverse vibrations of two translating strings interconnected by a Winkler elastic foundation, and subjected to axial loading are investigated. The system of governing partial differential equations of this gyroscopic system is cast in the first order canonical form. It is shown that the natural frequencies are composed of two infinite sets, representing in-phase and out-of-phase vibrations of the two strings. The effects of the axial tension ratios of the two continuous media, as well as the effects of the elastic foundation stiffness are investigated. In general, it is found that the natural frequencies increase with increasing elastic stiffness of the foundation. It is found that the elastic foundation does not alter the critical speed, but different mass and tension ratios do.

Nonlinear Dynamics and Bifurcations of an Axially Moving Beam

1999 ◽  
Vol 122 (1) ◽  
pp. 21-30 ◽  
Author(s):  
F. Pellicano ◽  
F. Vestroni
Keyword(s):  
High Dimensional ◽  
Axially Moving Beam ◽  
Dimensional System ◽  
Global Dynamics ◽  
Dimensional Phase Space ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability ◽  
The Galerkin Method ◽  
Sample Case

The present paper analyzes the dynamic behavior of a simply supported beam subjected to an axial transport of mass. The Galerkin method is used to discretize the problem: a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and super-critical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning the convergence of the series expansion, linear subcritical behavior, bifurcation analysis and stability, and direct simulation of global postcritical dynamics. A homoclinic orbit is found in a high dimensional phase space and its stability and collapse are studied. [S0739-3717(00)00501-8]

Finite Width Effects on the Critical Speed of Axially Moving Materials

1998 ◽  
Vol 120 (2) ◽  
pp. 633-634 ◽  
Author(s):  
C. C. Lin
Keyword(s):  
Critical Speed ◽  
Beam Theory ◽  
Axially Moving Beam ◽  
Finite Width ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Simply Supported ◽  
Moving Beam ◽  
Two Dimensional Model ◽  
Axially Moving

An exact solution is provided to determine the effects of the free end boundary conditions and the slenderness ratios on the critical speed of two dimensional, axially moving materials. The axially moving beam theory and the mathematical, two-dimensional model with all edges simply supported are also considered for comparison.

Effects of carbon nanotube reinforcements on vibration suppression of magnetorheological fluid sandwich beam

2019 ◽  
Vol 30 (7) ◽  
pp. 1053-1069 ◽  
Author(s):  
M Talebitooti ◽  
M Fadaee
Keyword(s):  
Carbon Nanotube ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Differential Quadrature Method ◽  
Sandwich Beam ◽  
Core Layer ◽  
Magnetorheological Fluid ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fluid Core

Vibration suppression of a carbon nanotube–reinforced sandwich beam with magnetorheological fluid core is numerically investigated by employing the differential quadrature method. The beam has functionally graded carbon nanotube–reinforced composite base and constraining layers while its core layer is made of magnetorheological fluid. Four different types of distribution of carbon nanotubes along the thickness direction are considered. The extended rule of mixture is used to explain the effective material properties of the base and constraining layers of the beam. The equations of motion and corresponding boundary conditions are derived by applying Hamilton’s principle, and then these coupled differential equations are transformed into a set of algebraic equation applying the differential quadrature method. Natural frequencies and loss factors are extracted and compared with those available in literature. Convergence study has been performed to verify stability of the method. Effects of various parameters such as magnetic field intensity, mode number, and thickness of the magnetorheological fluid core layer on the natural frequencies and loss factors are studied.

Analysis of Transverse Vibration of Axially Moving Viscoelastic Sandwich Beam with Time-Dependent Velocity

2011 ◽  
Vol 338 ◽  
pp. 487-490 ◽  
Author(s):  
Hai Wei Lv ◽  
Ying Hui Li ◽  
Qi Kuan Liu ◽  
Liang Li
Keyword(s):  
Transverse Vibration ◽  
Multiple Scales ◽  
Sandwich Beam ◽  
Core Layer ◽  
Response Elimination ◽  
Response Curves ◽  
Mean Velocity ◽  
State Response ◽  
Axially Moving ◽  
The Stability

Transverse vibration of an axially moving viscoelastic sandwich beam is investigated in this paper. Based on the Kelvin constitutive equation, transverse controlling equation is established. First of all, the multiple scales method is applied to obtained steady-state response. Elimination of scales terms will give us the amplitude of vibrations. Additionally, the stability conditions of trivial and non-trivial solutions are analyzed using Routh-Hurwitz criterion. Eventually, numerical results are obtained to show the thickness of core layer, mean velocity, the amplitude of fluctuation effects on natural frequencies and response curves.

Dynamic Characteristic of Axially Moving Soft Sandwich Beam

2013 ◽  
Vol 702 ◽  
pp. 275-279
Author(s):  
Hai Wei Lv ◽  
Ying Hui Li ◽  
Liang Li
Keyword(s):  
Governing Equation ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Soft Core ◽  
Independent Variables ◽  
The Third ◽  
Second Mode ◽  
Galerkin Truncation ◽  
Axially Moving ◽  
State Of Tension

A new sandwich beam theory is proposed by introducing independent variables of the displacements of face sheets, middle plane of soft core according to the incompression in transverse direction of traditional sandwich beam theory. Based on Hamilton principal, the governing equation of the system is established. Galerkin truncation method was used to solve the governing equation. It was found that (1) the first mode of the system displays that it is consistent with the traditional sandwich beam theory; (2) the second mode of the system shows that the soft core is in the state of tension or in compression; (3) the third mode of the system displays that the upper part and lower part of soft core are in different state (tension or compression); (4) The incompressible model of sandwich beam is the special form of soft sandwich beam we establish in this paper.

scholarly journals Thermal Effects on Nonlinear Vibrations of an Axially Moving Beam with an Intermediate Spring-Mass Support

2013 ◽  
Vol 20 (3) ◽  
pp. 385-399 ◽  
Author(s):  
Siavash Kazemirad ◽  
Mergen H. Ghayesh ◽  
Marco Amabili
Keyword(s):  
Thermal Loading ◽  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Time Integration ◽  
Harmonic Excitation ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving ◽  
The Galerkin Method ◽  
Continuation Technique

The thermo-mechanical nonlinear vibrations and stability of a hinged-hinged axially moving beam, additionally supported by a nonlinear spring-mass support are examined via two numerical techniques. The system is subjected to a transverse harmonic excitation force as well as a thermal loading. Hamilton's principle is employed to derive the equations of motion; it is discretized into a multi-degree-freedom system by means of the Galerkin method. The steady state resonant response of the system for both cases with and without an internal resonance between the first two modes is examined via the pseudo-arclength continuation technique. In the second method, direct time integration is employed to construct bifurcation diagrams of Poincaré maps of the system.

Sign in / Sign up

Export Citation Format

Share Document