scholarly journals On the Modeling of Periodic Sandwich Structures with the Use of the Broken Line Hypothesis

2020 ◽  
Vol 22 (3) ◽  
pp. 761-774 ◽  
Author(s):  
Jakub Marczak
Keyword(s):  
Vibration Analysis ◽  
Sandwich Plate ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
System Of Equations ◽  
Governing Equations ◽  
Fem Model ◽  
Constant Coefficients ◽  
Plate Strip ◽  
Periodic Plate

AbstractIn this paper a dynamic analysis of sandwich plate with a certain periodic microstructure is considered. The initial system of governing equations is derived basing on the classic broken line hypothesis. As a result of transformations one can obtain a system of three differential equations of motion with periodic, highly oscillating and non-continuous coefficients. In order to derive a system of equations with constant coefficients tolerance averaging technique is applied. Eventually, in the calculation example a free vibration analysis of certain periodic plate strip is performed with the use of both the derived model and a FEM model. It can be observed that the consistency of obtained results is highly dependent on the calculation assumptions.

On the Free Vibration Analysis of a Sandwich Beam With Tip Mass

2018 ◽  
Author(s):  
E. F. Joubaneh ◽  
O. R. Barry
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Design Parameters ◽  
Governing Equations ◽  
Tip Mass

This paper presents the free vibration analysis of a sandwich beam with a tip mass using higher order sandwich panel theory (HSAPT). The governing equations of motion and boundary conditions are obtained using Hamilton’s principle. General Differential Quadrature (GDQ) is employed to solve the system governing equations of motion. The natural frequencies and mode shapes of the system are presented and Ansys simulation is performed to validate the results. Various boundary conditions are also employed to examine the natural frequencies of the sandwich beam without tip mass and the results are compared with those found in the literature. Parametric studies are conducted to examine the effect of key design parameters on the natural frequencies of the sandwich beam with and without tip mass.

scholarly journals Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
D. A. Maturi ◽  
A. J. M. Ferreira ◽  
A. M. Zenkour ◽  
D. S. Mashat
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Transverse Displacement ◽  
Laminated Shells ◽  
Radial Basis

The static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to Murakami’s zig-zag (ZZ) function (MZZF) theory . The MZZF theory accounts for through-the-thickness deformation, by considering a ZZ evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

2017 ◽  
Vol 24 (14) ◽  
pp. 3026-3035 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi ◽  
Mohsen Irani-Rahagi ◽  
Keivan Torabi ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Fiber Metal Laminate ◽  
Circular Cylindrical Shells ◽  
Fiber Metal

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

The Flapwise Bending Free Vibration Analysis of Micro-rotating Timoshenko Beams Using the Differential Transform Method

2017 ◽  
Vol 24 (20) ◽  
pp. 4868-4884 ◽  
Author(s):  
Hadi Arvin
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Slenderness Ratio ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Model ◽  
Transform Method ◽  
Differential Transform ◽  
Material Length Scale ◽  
Material Length

The flapwise bending free vibration analysis of isotropic rotating Timoshenko microbeams, including the size effects, is presented in this paper. A nonclassical theory, i.e. the Modified Couple Stress theory, has been employed to include the size effect in the presented formulation. By consideration of the Timoshenko beam assumptions the shear deformation and the rotary inertia effects are taken into account. The Hamilton’s principle is applied to the obtained strain and kinetic energy relations to derive the nonlinear equations of motion and the associated boundary conditions. After nondimensionalization of the equations of motion and the corresponding boundary conditions, the linearized form of the equations of motion and the accompanied boundary conditions are developed. A semi-analytical approach, i.e. the differential transform method, is implemented to achieve the flapping and axial frequencies. The achieved results are validated via comparison with the available results in the literature. The material length scale, shear deformation consideration, rotating speed and the slenderness ratio influences on the natural frequencies are examined. The results demonstrate that the slenderness ratio and the thickness to the material length scale parameter quotient are the dominant indicators in determining the usage of the nonclassical theories against classical theories. On the other hand, the precision in determination of the higher modes frequencies motivates us to implement the Timoshenko beam model instead of the Euler–Bernoulli beam model.

Analytic Study of Discreteness Effects in a String Resting on a Periodic Array of Vibro-Impact Supports

1997 ◽  
Author(s):  
Gary D. Salenger ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Boundary ◽  
Equations Of Motion ◽  
Forced Oscillations ◽  
System Of Equations ◽  
Solitary Wave Solutions ◽  
Governing Equations ◽  
Nonlinear Boundary Value Problems ◽  
Regular Perturbation ◽  
Discrete Nature ◽  
Infinite String

Abstract We analyze the forced oscillations of an infinite string supported by an array of vibro-impact supports. The envelope of the excitation possesses ‘slow’ and ‘fast’ scales and is periodic with respect to the ‘fast’ scale. The ‘fast’ spatial scale is defined by the distance between adjacent nonlinear supports. To eliminate the singularities from the governing equations of motion that arise due to the discrete nature of the supports, we employ the nonsmooth transformations of the spatial variable first introduced in (Pilipchuk, 1985) and (Pilipchuk, 1988). Thus, we convert the problem to a set of two nonhomogeneous nonlinear boundary value problems which we solve by means of perturbation theory. The boundary conditions of these problems arise from ‘smoothness conditions’ that are imposed to guarantee sufficient differentiability of the results. The transformed system of equations is simplified using regular perturbation and harmonic balancing. Standing solitary wave solutions reflecting the discreteness effects inherent in the discrete foundation are calculated numerically for the unforced system.

Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation

2017 ◽  
Vol 29 (5) ◽  
pp. 774-786 ◽  
Author(s):  
M Arefi ◽  
MH Zamani ◽  
M Kiani
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
First Order ◽  
Size Dependent ◽  
Inhomogeneity Parameter ◽  
Exponentially Graded

This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.

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