Free vibrations of conical shells for various boundary conditions

1972 ◽  
Vol 8 (1) ◽  
pp. 25-29
Author(s):  
A. A. Repin
Keyword(s):  
Boundary Conditions ◽  
Free Vibrations ◽  
Conical Shells ◽  
Various Boundary Conditions

A Nonlinear Shear Deformable Nanoplate Model Including Surface Effects for Large Amplitude Vibrations of Rectangular Nanoplates with Various Boundary Conditions

2015 ◽  
Vol 07 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Reza Ansari ◽  
Mostafa Faghih Shojaei ◽  
Vahid Mohammadi ◽  
Raheb Gholami ◽  
Mohammad Ali Darabi
Keyword(s):  
Boundary Conditions ◽  
Surface Stress ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Free Vibrations ◽  
Model Parameters ◽  
Geometrically Nonlinear ◽  
Residual Surface Stress ◽  
Various Boundary Conditions ◽  
Shear Deformable

In this paper, a geometrically nonlinear first-order shear deformable nanoplate model is developed to investigate the size-dependent geometrically nonlinear free vibrations of rectangular nanoplates considering surface stress effects. For this purpose, according to the Gurtin–Murdoch elasticity theory and Hamilton's principle, the governing equations of motion and associated boundary conditions of nanoplates are derived first. Afterwards, the set of obtained nonlinear equations is discretized using the generalized differential quadrature (GDQ) method and then solved by a numerical Galerkin scheme and pseudo arc-length continuation method. Finally, the effects of important model parameters including surface elastic modulus, residual surface stress, surface density, thickness and boundary conditions on the vibration characteristics of rectangular nanoplates are thoroughly investigated. It is found that with the increase of the thickness, nanoplates can experience different vibrational behavior depending on the type of boundary conditions.

Distributed Sensing Signals of Truncated Conical Shells With Clamped-Free Boundary Conditions

2009 ◽  
Author(s):  
H. Li ◽  
Z. B. Chen ◽  
H. S. Tzou
Keyword(s):  
Boundary Conditions ◽  
Conical Shell ◽  
Vibration Isolation ◽  
Free Vibrations ◽  
Distributed Sensing ◽  
The Other ◽  
Helical Line ◽  
Circular Membrane ◽  
Conical Shells ◽  
Truncated Conical Shell

In aerospace structures, vehicles, civil structures, conical shells are used to support a part or connect different parts, such as spacecraft adaptors, fixtures of machine tools. This type of structures has the possibility of vibration isolation. The final purpose of the on-going research is to isolate the supported part from the vibration transferred from the other end. As a phase of the research, the present paper emphasizes on the distributed sensing signals and modal voltages of the truncated conical shell. To simulate free vibrations of supported part, one end of the truncated conical shell is clamped and the other end is free. The piezoelectric patches are attached on top skin of the shell along diagonal helical line. This paper presents an analytical procedure of sensing of truncated conical shell supporting a mass. The displacement functions satisfying the special boundary conditions are given. Based on the thin-shell theory and Donnel-Mushtari-Valsov theory, sensing equations of the piezoelectric stripes are derived. The sensing signals consist of four components, i.e. sensing signals due to meridional and circular membrane strains, meridional and circular bending strains. These components are studied separately to show their distributions to the sensing signals. Finally, a case study is carried out using a sample truncated conical shell model with laminated piezoelectric stripes.

In-plane free vibrations of functionally graded sandwich arches using shear and quasi-3D deformation theories

2021 ◽  
pp. 109963622110219
Author(s):  
Ke Xie ◽  
Yuewu Wang ◽  
Hongpan Niu ◽  
Hongyong Chen
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Various Boundary Conditions ◽  
Shear Deformation Theories ◽  
3D Deformation ◽  
First Time ◽  
Stress Free Boundary

The in-plane vibration problem of functionally graded (FG) sandwich circular arch made up of two layers of power law FGM face sheet and one layer of homogeneous core is investigated. A framework for the vibration analysis of FG sandwich circular arches is presented, and the quasi-3D theories for the arch structures compatible with this framework are established for the first time. The quasi-3D theories take into account the changes of displacement through the thickness of the arch, and satisfy the stress-free boundary conditions naturally. The Lagrange equation is employed to derive the equation of motion, and various boundary conditions are implemented by applying simple algebraic polynomials as admissible functions to discrete the displacement fields of the FG sandwich arches. The comparison study of various high-order shear deformation theories and quasi-3D deformation theories for the FG sandwich circular arches is carried out via different numerical examples. The influences of material distributions and geometric parameters on the vibration characteristics of the FG sandwich circular arches are also presented and discussed for the first time.

scholarly journals Numerical analysis of free vibrations of open cylindrical shells with elliptical cross section

2019 ◽  
pp. 52-59
Author(s):  
A. Grigorenko ◽  
M. Borysenko ◽  
O. Boychuk
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Numerical Solutions ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Elliptical Cross Section ◽  
Opening Angle ◽  
Elliptical Cross ◽  
Various Boundary Conditions ◽  
Finite Element Package

The natural frequencies and the corresponding vibration modes of open cylindrical shells with an elliptical cross-section and variable thickness are analyzed. Various opening angle of the shell along both the minor and major axes are allowed and various boundary conditions are considered. The numerical solutions are obtained using the finite element package FEMAP with the NASTRAN solver. A number of lowfrequency vibrations are investigated in terms of their dependence on the opening angle along major and minor axes of the shell. The vibration forms for the first ten frequencies with different boundary conditions at the same opening angles are shown.

Free Vibrations of Spinning Beams Under Nonclassical Boundary Conditions Using Adomian Modified Decomposition Method

2014 ◽  
Vol 14 (07) ◽  
pp. 1450027 ◽  
Author(s):  
Qibo Mao
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation System ◽  
Free Vibrations ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Straightforward Method

This study employs the Adomian modified decomposition method (AMDM) for the dynamic analysis of Euler–Bernoulli beams spinning about their longitudinal axes under various boundary conditions. Based on the AMDM, the governing differential equations for the spinning beam become a recursive algebraic equation system. By using the boundary condition equations, the natural frequencies can be readily obtained. The computed results under different classical and nonclassical boundary conditions as well as spinning speeds are presented. The accuracy is assured from comparison with published results. It is shown that the AMDM offers an accurate and straightforward method of free vibration analysis of spinning beams with arbitrary boundary conditions.

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