Increase of the first natural frequency and buckling load of plates by optimal fields of initial stresses

1977 ◽  
Vol 27 (1-4) ◽  
pp. 217-238 ◽  
Author(s):  
F. G. Rammerstorfer
Keyword(s):  
Natural Frequency ◽  
Buckling Load ◽  
Initial Stresses

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Free vibration and buckling of heavy column with regular polygon cross-section

2021 ◽  
pp. 095440622110293
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Natural Frequency ◽  
Cross Section ◽  
Buckling Load ◽  
Mode Shapes ◽  
Equilibrium Equations ◽  
Direct Integration Method ◽  
Solution Methods ◽  
Buckling Length

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

scholarly journals Torsional vibration of irregular single-walled carbon nanotube incorporating compressive initial stress effects

2021 ◽  
Vol 37 ◽  
pp. 260-269
Author(s):  
Mahmoud M Selim
Keyword(s):  
Carbon Nanotube ◽  
Natural Frequency ◽  
Initial Stress ◽  
Torsional Vibration ◽  
Initial Stresses ◽  
Surface Irregularity ◽  
Torsional Vibrations ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Stress Effects

Abstract This study is an attempt to show the impacts of surface irregularity and compressive initial stresses on the torsional vibration of a single-walled carbon nanotube (SWCNT). The governing equation and corresponding closed-form solutions were derived with the aid of Hamilton's principle. Then, the natural frequencies were obtained analytically and the influences of surface irregularity and compressive initial stresses on the torsional vibration were studied in detail. Numerical results analyzing the torsional vibration incorporating compressive initial stress effects were discussed and presented graphically. The effects of surface irregularity on the natural frequency of torsional vibrations of nanomaterials, especially for SWCNTs, have not been investigated before, and most of the previous research works have been carried for a regular carbon nanotube. Therefore, it must be emphasized that the torsional vibrations of irregular SWCNTs are novel and applicable for the design of nano-oscillators and nanodevices, in which SWCNTs act as the most prevalent nanocomposite structural element. The analytical solutions and numerical results revealed that the surface irregularity and compressive initial stress have notable effects on the natural frequency of torsional vibrations. It has been observed that, as the surface irregularity and compressive initial stress parameters increase, the torsional natural frequency of vibrations of SWCNTs also increases. Since SWCNTs have very small size, they are always subject to initial stresses from different resources; therefore, understanding the influences of compressive initial stresses on the torsional frequency of nanotubes helps the engineers and researchers to design proper nanodevices for different applications with irregular shapes.

scholarly journals Vibration Analysis of Cross-Ply Plates Under Initial Stress Using Refined Theory

2018 ◽  
Vol 14 (4) ◽  
pp. 34-44
Author(s):  
Ibtehal Abbas Sadiq ◽  
Kani Hussein Bawa
Keyword(s):  
Natural Frequency ◽  
Initial Stress ◽  
Plate Thickness ◽  
Laminated Plates ◽  
Initial Stresses ◽  
Transverse Shear Strain ◽  
Refined Theory ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Eigen Value

Natural frequency under initial stresses for simply supported cross-ply composite laminated plates (E glass- fiber) are obtained using Refind theory (RPT). This theory accounts for parabolic distribution of the transverse shear strain through the plate thickness and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. The governing equations for Eigen value problem under initial stress are derived using Hamilton’s principle and solved using Navier solution for simply supported cross-ply symmetric and antisymmetric laminated plates. The effect of many design factors such as modulus ratio, thickness ratio and number of laminates on the Natural frequency and buckling stresses of orthotropic plates are studied. The results are compared with other researcher.

Free Vibration of Initially Stressed Circular Disks

1965 ◽  
Vol 87 (2) ◽  
pp. 258-264 ◽  
Author(s):  
C. D. Mote
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Variable Thickness ◽  
Transverse Vibration ◽  
Fundamental Mode ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Vibration Characteristics ◽  
Initial Stresses ◽  
Circular Disks

The approximate free vibration characteristics of centrally clamped, variable thickness disks are analyzed by the Rayleigh-Ritz technique. Natural frequencies of transverse vibration are computed, taking into consideration rotational and thermal in-plane stresses as well as purposely induced initial stresses. Initial stresses can significantly raise the minimum disk natural frequency throughout a prescribed rotational and thermal environment. The fundamental mode of disk vibration is one of zero nodal circles and either zero, one, or two nodal diameters, depending upon the disk geometry and the rotational-thermal environment.

scholarly journals Multiobjective Design Optimization of Reentrant Auxetic Model Using Lichtenberg Algorithm Based on Metamodel

2022 ◽  
Author(s):  
Matheus Brendon Francisco ◽  
João Luiz Junho Pereira ◽  
Lucas Antonio de Oliveira ◽  
Sebastião Da Cunha ◽  
Guilherme Ferreira Gomes
Keyword(s):  
Natural Frequency ◽  
Performance Optimization ◽  
Poisson’S Ratio ◽  
Failure Load ◽  
Buckling Load ◽  
Poisson's Ratio ◽  
Critical Buckling Load ◽  
Compression Performance ◽  
Multi Objective ◽  
Multiobjective Design

Abstract The optimization of five different responses of an auxetic model was considered: mass; critical buckling load under compression effort; natural frequency; Poisson’s ratio; and failure load. The Response Surface Methodology was applied, and a new meta-heuristic of optimization called the Multi-Objective Lichtenberg Algorithm was used to find the optimized configuration of the model. It was possible to increase the failure load by 26,75% in compression performance optimization. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, the failure load by 28.70% and reduce the mass and Poisson’s ratio by 15.97% and 11%, respectively. This paper shows something unprecedented in the literature to date when evaluating in a multi-objective optimization problem, the compression and modal performance of an auxetic reentrant model.

Influence of axial compressive loads on buckling and free vibration response of surface-modified fly ash cenosphere/epoxy syntactic foams

2018 ◽  
Vol 52 (19) ◽  
pp. 2621-2630 ◽  
Author(s):  
Sunil Waddar ◽  
P Jeyaraj ◽  
Mrityunjay Doddamani
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Testing Machine ◽  
Syntactic Foam ◽  
Compressive Load ◽  
Buckling Load ◽  
Superior Performance ◽  
Syntactic Foams ◽  
Critical Buckling Load ◽  
Compressive Loads

This work deals with experimental buckling and free vibration behavior of silane-treated cenosphere/epoxy syntactic foams subjected to axial compression. Critical buckling loads are computed from compressive load–deflection plots deduced using universal testing machine. Further, compressive loads are applied in the fixed intervals until critical loading point on different set of samples having similar filler loadings to estimate natural frequency associated with the first three transverse bending modes. Increasing filler content increases critical buckling load and natural frequency of syntactic foam composites. Increasing axial compressive load reduce structural stiffness of all the samples under investigation. Syntactic foams registered higher stiffness compared to neat epoxy for all the test loads. Similar observations are noted in case of untreated cenosphere/epoxy foam composites. Silane-modified cenosphere embedded in epoxy matrix registered superior performance (rise in critical buckling load and natural frequencies to the tune of 23.75% and 11.46%, respectively) as compared to untreated ones. Experimental results are compared with the analytical solutions that are derived based on Euler–Bernoulli hypothesis and results are found to be in good agreement. Finally, property map of buckling load as a function of density is presented by extracting values from the available literature.

Vibration Analysis of Nanoplate with the Effects of Surface Irregularity and Initial Stresses

2021 ◽  
Vol 16 (1) ◽  
pp. 48-53
Author(s):  
Mahmoud. M. Selim ◽  
Sherif A. El-Safty
Keyword(s):  
Natural Frequency ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Initial Stresses ◽  
Surface Irregularity ◽  
Closed Form Solutions ◽  
Stress Effects ◽  
Vibration Properties ◽  
Stress Parameters

Based on Kirchhoff plate theory, the vibration behavior of irregular nanoplate with consideration of initial compressive stress effects is investigated. The equations of motion are derived and the closed form solutions for the natural frequency of the nanoplate are obtained. The analytical solutions reveal that, the natural frequency of the nanoplate, are found to be significantly dependent on the irregularity and compressive initial stresses present in the nanoplate. Numerical results show that, the natural frequency of nanoplates increases with increase of surface irregularity and initial stress parameters. To the author best knowledge, the effects of surface irregularity and initial stresses on the vibration behaviour of nanoplates have not yet been studied, and the present work is an attempt to find out this effectiveness. The results of this work is expected to be useful to design and analyze the vibration properties of nanostructures and Devices in NEMS.

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