Multi-Modal Nonlinear Forced Vibrations of Circular Cylindrical Shells of Arbitrary Shapes

2011 ◽  
Author(s):  
Galyna Pilgun ◽  
Marco Amabili
Keyword(s):  
Strain Energy ◽  
Cylindrical Panel ◽  
Forced Vibrations ◽  
Second Step ◽  
Natural Modes ◽  
Nonlinear Responses ◽  
Mesh Free ◽  
Circular Cylindrical Shells ◽  
Spectral Neighborhood ◽  
Admissible Functions

Large-amplitude nonlinear forced vibrations of a circular cylindrical panel with a complex base, clamped at the edges are investigated. The Sanders-Koiter and the Donnell nonlinear shell theories are used to calculate the strain energy; in-plane inertia is retained. A mesh-free technique based on classic approximate functions and the R-function theory is used to build the discrete model of the nonlinear vibrations. This allows for constructing the sequences of admissible functions that satisfy given boundary conditions in domains with complex geometries. The problem is solved in two steps: a linear analysis is conducted to identify natural frequencies and corresponding natural modes to be used in the second step as a basis for nonlinear displacements. The system of ordinary differential equations is obtained by using the Lagrange approach on both steps. Numerical responses are obtained in the spectral neighborhood of the lowest natural frequency. The convergence of nonlinear responses is investigated.

Analysis of Nonlinear Forced Vibrations of Shallow Shells With Cut-Outs by Using the R-Function Method

2011 ◽  
Author(s):  
Galyna Pilgun ◽  
Marco Amabili
Keyword(s):  
Equations Of Motion ◽  
Continuation Method ◽  
Forced Vibrations ◽  
Second Step ◽  
Geometrically Nonlinear ◽  
Shallow Shells ◽  
Natural Modes ◽  
Mesh Free ◽  
Nonlinear Equations Of Motion ◽  
Admissible Functions

Geometrically nonlinear forced vibrations of shells based on the domains with cut-outs are investigated. Classical nonlinear shallow-shell theories retaining in-plane inertia is used to calculate the strain energy; the shear deformation is neglected. A mesh-free technique based on classic approximate functions and the R-function theory is used to build the discrete model of the nonlinear vibrations. This allowed for constructing the sequences of admissible functions that satisfy given boundary conditions in domains with complex geometries. Shell displacements are expanded by using Chebyshev orthogonal polynomials. A two-step approach is implemented to solve the problem: first a linear analysis is conducted to identify natural frequencies and corresponding natural modes to be used in the second step as a basis for nonlinear displacements. The system of ordinary differential equations is obtained by using Lagrange approach on both steps. The convergence of the solution is studied by using different multimodal expansions. The pseudo-arclength continuation method and bifurcation analysis are used to study the nonlinear equations of motion. Numerical responses are obtained in the spectral neighbourhood of the lowest natural frequency. When possible, obtained results are compared to those available in the literature.

A Two Step Damage Prognosis Method for Beam-Like Truss Structures

2014 ◽  
Vol 578-579 ◽  
pp. 1092-1095
Author(s):  
Hao Kai Jia ◽  
Ling Yu
Keyword(s):  
Finite Element Method ◽  
Strain Energy ◽  
Truss Structure ◽  
Truss Structures ◽  
Second Step ◽  
The Finite Element Method ◽  
Modal Strain Energy ◽  
Damage Prognosis ◽  
Modal Curvature ◽  
Simulation Results

In this study, a two step damage prognosis method is proposed for beam-like truss structures via combining modal curvature change (MCC) with modal strain energy change ratio (MSECR). Changes in the modal curvature and the elemental strain energy are selected as the indicator of damage prognosis. Different damage elements with different damage degrees are simulated. In the first step, the finite element method is used to model a beam-like truss structure and the displacement modes are got. The damage region is estimated by the MCC of top and bottom chords of a beam-like truss structure. In the second step, the elemental MSECR in the damage region is calculated and the maximum MSECR element is deemed as the damage element. The simulation results show that this method can accurately locate the damage in the beam-like truss structure.

Forced vibrations of an elongated cylindrical panel on a unilateral elastic foundation

1985 ◽  
Vol 21 (8) ◽  
pp. 768-772
Author(s):  
V. A. Bazhenov ◽  
E. A. Gotsulyak ◽  
V. I. Gulyaev ◽  
G. S. Kondakov
Keyword(s):  
Elastic Foundation ◽  
Cylindrical Panel ◽  
Forced Vibrations

The BFS Method Combined with Chemical Cluster Interactions for the Study of Order-Disorder Transitions

2007 ◽  
Vol 263 ◽  
pp. 129-134
Author(s):  
Maarten Schurmans ◽  
Jan Luyten ◽  
Claude Creemers
Keyword(s):  
First Principles ◽  
Strain Energy ◽  
Local Environment ◽  
Second Step ◽  
Atom Pair ◽  
Atomic Displacements ◽  
Modeling Techniques ◽  
Structural Contribution ◽  
Alloying Effects ◽  
Number Of Particles

First Principles (FP) methods are invoked to improve the accuracy of Bozzolo-Ferrante- Smith (BFS) model, one of the quantum-approximate modeling techniques for the computation of thermodynamic properties that involve a large number of particles. The BFS method calculates the energy of an atom in an alloy in two steps [1]. A first term pertains to the structural contribution. A recent improvement [2] allows to calculate the strain energy depending on the local environment [1,2] and this involves only pure element properties of the different atomic species. In the second step, binary chemical interactions are taken into account. This was originally done by only two interaction parameters for each atom pair in an alloy. In contrast, the adaptable parameterization of Cluster Expansion Methods (CEM) routinely incorporates any number of FP data to describe ordering in alloy systems. But in standard CEM calculations, no explicit information on local atomic displacements is used. In this work, the BFS chemical energy term is successfully replaced by a CEM chemical term to combine the ability of BFS to account for local displacements and the ability of CEM to include as many FP results as needed for the correct evaluation of alloying effects.

Frequency Tuning Characteristics of Multi-Layered Micro-Resonators Using Thermal and Piezoelectric Actuation

2006 ◽  
Vol 324-325 ◽  
pp. 647-650
Author(s):  
Il Kwon Oh ◽  
Dong Hyun Kim
Keyword(s):  
Thermal Loading ◽  
Frequency Tuning ◽  
Plane Deformation ◽  
Initial Imperfection ◽  
Piezoelectric Actuation ◽  
Natural Modes ◽  
Nonlinear Responses ◽  
Geometric Nonlinear ◽  
Out Of Plane ◽  
Selection Of

Frequency tuning characteristics of the multi-layered micro-resonators have been extensively investigated by using thermal and piezoelectric actuations. Based on the layerwise displacement theory and geometric nonlinear formulation, the nonlinear deformation and its attendant vibration characteristics of un-symmetrically deposited camped-camped micro-beams under piezoelectric and thermal actuations have been analyzed. The effects of the eccentric piezoelectric actuation and uniform thermal loading on the large deflection and natural modes were discussed with respect to geometric nonlinear responses and initial imperfection. Present results show that both piezoelectric and thermal actuations can effectively tune the resonant frequencies as increasing and decreasing desired values by the alternative selection of the dominance between in-plane deformation and out-of-plane deformation.

Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation

2017 ◽  
Vol 24 (11) ◽  
pp. 2327-2343 ◽  
Author(s):  
Rasool Moradi-Dastjerdi ◽  
Hamed Momeni-Khabisi
Keyword(s):  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Free And Forced Vibrations ◽  
Mesh Free ◽  
Pasternak Elastic Foundation

In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

Forced Vibrations of Rotating Circular Cylindrical Shells.

1995 ◽  
Vol 61 (586) ◽  
pp. 2190-2194 ◽  
Author(s):  
Hirotaka Igawa ◽  
Yoshiyuki Maruyama ◽  
Mitsuru Endo
Keyword(s):  
Cylindrical Shells ◽  
Forced Vibrations ◽  
Circular Cylindrical Shells

scholarly journals A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Issam El Hantati ◽  
Ahmed Adri ◽  
Hatim Fakhreddine ◽  
Said Rifai ◽  
Rhali Benamar
Keyword(s):  
Approximate Method ◽  
Forced Vibration ◽  
Algebraic System ◽  
Strain Energy ◽  
Dynamic Behaviour ◽  
Forced Vibrations ◽  
Geometrical Parameters ◽  
Geometrically Nonlinear ◽  
Free And Forced Vibrations ◽  
Nonlinear Algebraic System

The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation.

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