An Analytical and Experimental Evaluation of the Damping Capacity of Sandwich Beams With Viscoelastic Cores

1967 ◽  
Vol 89 (3) ◽  
pp. 438-443 ◽  
Author(s):  
I. W. Jones ◽  
V. L. Salerno ◽  
A. Savacchio
Keyword(s):  
Previous Investigation ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Vibration Damping ◽  
Damping Capacity ◽  
Sandwich Beams ◽  
Natural Boundary ◽  
Test Program ◽  
Test Procedures ◽  
Natural Boundary Conditions

A study is made of the free vibrations of sandwich beams with viscoelastic cores. The study, which is a generalization of a previous investigation by the authors [1] includes the equations of motion and natural boundary conditions, derivation of expressions for the modal distribution of damping based upon “small damping” assumptions, numerical examples, and a supporting test program. The generally high values calculated for beams of various materials indicate that this type of construction is efficient for vibration damping applications. It was found, however, that the calculated and test values were not in accord. This lack of agreement signifies the necessity for greater refinement in both analytical methods and test procedures.

Free Vibration of High-Order Curved Sandwich Beams

2001 ◽  
Author(s):  
Yeoshua Frostig ◽  
Elena Bozhevolnaya
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Free Vibrations ◽  
High Order ◽  
Design Parameters ◽  
Sandwich Beams ◽  
Natural Boundary Conditions ◽  
Thin Beams ◽  
Sandwich Core

Abstract A high-order model for free vibrations of singly curved sandwich beams is presented. The model takes into account the transverse flexibility of the sandwich core while the faces of the sandwich are treated as thin beams. Linear equations of motion as well as the natural boundary conditions are derived. It is shown for the curved sandwich beams, that there exist four eigen modes. A numerical analysis of free vibration of the simply supported beams is carried out. Effects of design parameters of the sandwich constituents on the eigen modes and their appropriate frequencies are investigated.

On the Vibrations of a Laminated Body

1968 ◽  
Vol 35 (4) ◽  
pp. 689-696 ◽  
Author(s):  
J. D. Achenbach ◽  
C. T. Sun ◽  
G. Herrmann
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Low Frequency ◽  
Continuum Theory ◽  
Acoustic Mode ◽  
Governing Equations ◽  
Natural Boundary ◽  
Natural Boundary Conditions ◽  
Laminated Layer

A continuum theory for a laminated medium is further developed in this paper. Constitutive equations, stress equations of motion, and natural boundary conditions are presented, and sufficient conditions for a unique solution are discussed. The governing equations and boundary conditions are employed to study the thickness-twist motion of a laminated layer. For every nodal number there is a low frequency acoustic mode and a high frequency optical mode. The frequencies of the acoustic modes are compared with the corresponding frequencies predicted by the effective modulus theory, and the relative magnitudes of the material parameters for which these frequencies are substantially at variance are indicated.

scholarly journals Eigenfrequencies of generally restrained beams

2003 ◽  
Vol 2003 (10) ◽  
pp. 503-516 ◽  
Author(s):  
Ricardo Oscar Grossi ◽  
Carlos Marcelo Albarracín
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Natural Boundary ◽  
Wide Range ◽  
Exact Determination ◽  
Natural Boundary Conditions ◽  
Elastic Constraints ◽  
Range Of Values ◽  
Intermediate Constraints

We deal with the exact determination of eigenfrequencies of a beam with intermediate elastic constraints and generally restrained ends. It is the purpose of this paper to use the calculus of variations to obtain the equations of motion and the natural boundary conditions, and particularly those at the intermediate constraints. Numerical values for the first five natural frequencies are presented in a tabular form for a wide range of values of the restraint parameters. Several particular cases are presented and some of these cases have been compared with those available in the literature.

Dynamic Variational Principles for Discontinuous Elastic Fields

1979 ◽  
Vol 23 (02) ◽  
pp. 115-122 ◽  
Author(s):  
M. Cengiz Dökmeci
Keyword(s):  
Variational Principles ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Governing Equations ◽  
Natural Boundary ◽  
Dimensional Theory ◽  
Elastic Fields ◽  
Complete Set ◽  
Natural Boundary Conditions

Various forms of variational principles are derived for the three-dimensional theory of elastodynamics. The continuity requirements on the fields of stresses or strains and/or displacements are relaxed through Friedrichs's transformation. Thus, the generalized forms of certain types of earlier variational principles' are systematically constructed using a basic principle of physics. The variational principles derived herein are shown to generate, as the appropriate Euler equations, the complete set of the governing equations of linear elastodynamics, that is, the stress equations of motion, the strain displacement relations, the mixed natural boundary conditions, the constitutive equations, the natural initial conditions, and the jump conditions. Similarly, generalized variational principles are established for the nonlinear theory of elastodynamics, for the incremental motions in linear elasticity, and for an elastic Cosserat continuum, as well.

scholarly journals Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Tatiana Odzijewicz ◽  
Agnieszka B. Malinowska ◽  
Delfim F. M. Torres
Keyword(s):  
Fractional Integral ◽  
Necessary Optimality Conditions ◽  
Variational Problems ◽  
Fractional Integrals ◽  
Natural Boundary ◽  
Free Boundary Value Problems ◽  
Fractional Variational Problems ◽  
Generalized Fractional Integral ◽  
Fractional Calculus Of Variations ◽  
Natural Boundary Conditions

We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

The Damping Study for Dammar Composites Reinforced with Natural Fibers

2015 ◽  
Vol 801 ◽  
pp. 188-193
Author(s):  
Dumitru Bolcu ◽  
Marius Marinel Stănescu ◽  
Cosmin Mihai Miriţoiu ◽  
Cristian Oliviu Burada
Keyword(s):  
External Force ◽  
Natural Fibers ◽  
Free Vibrations ◽  
Vibration Damping ◽  
Initial Deformation ◽  
Rectangular Section ◽  
Hemp Fibers ◽  
Free Length ◽  
Natural Resin

In this paper we have studied the vibration damping for composite bars made by dammar based natural resin, the reinforcement being made by flax, cotton, silk and hemp fibers. There were made rectangular section samples (5x10 mm) with 220 mm length. The bars were clamped, the free length being 100 mm, 120 mm, 140 mm, 160 mm and 180 mm. For each bar, the free vibrations made by an initial deformation, obtained by inserting an external force in the free end, were recorded. In each case, the measured vibration was under-damped.

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