Nonlinear Vibration of a Rectangular Plate Arbitrarily Laminated of Anisotropic Material

1973 ◽  
Vol 40 (2) ◽  
pp. 452-458 ◽  
Author(s):  
C. W. Bert
Keyword(s):  
Composite Material ◽  
Nonlinear Vibration ◽  
Rectangular Plate ◽  
Anisotropic Material ◽  
Present Theory ◽  
Practical Case ◽  
Orthotropic Plates ◽  
Simplified Approach ◽  
Isotropic Plates ◽  
Special Cases

A new simplified approach is presented for calculating the flexural frequencies of a composite-material plate undergoing moderately large, normal deflections. The plate may be arbitrarily laminated with respect to the midplane, so that bending-stretching coupling is present. The approach used is a generalization of the work of Wah for homogeneous, isotropic plates. In the case of orthotropic plates, it differs from various orthotropic extensions of the popular Berger hypothesis. The present theory is applied to the practical case of a clamped rectangular plate with finite in-plane restraint. The results are compared satisfactorily with those of previous analyses for various special cases.

scholarly journals When to Substitute a Missing Upper Lateral With a Canine: A Simplified Approach

2021 ◽  
pp. 030157422098054
Author(s):  
Renu Datta
Keyword(s):  
Anterior Segment ◽  
Specific Treatment ◽  
Simplified Approach ◽  
Special Cases ◽  
Randomized Control ◽  
The One ◽  
Individual Presentation ◽  
Available Information ◽  
Missing Tooth ◽  
Made In

Introduction: The upper lateral incisor is the most commonly missing tooth in the anterior segment. It leads to esthetic and functional imbalance for the patients. The ideal solution is the one that is most conservative and which fulfills the functional and esthetic needs of the concerned individual. Canine substitution is evolving to be the treatment of choice in most of the cases, because of its various advantages. These are special cases that need more time and effort from the clinicians due to space discrepancy in the upper and lower arches, along with the presentation of individual malocclusion. Aims and Objectives: Malocclusion occurring due to missing laterals is more complex, needing more time and effort from the clinicians because of space discrepancy, esthetic compromise, and individual presentation of the malocclusion. An attempt has been made in this article to review, evaluate, and tabulate the important factors for the convenience of clinicians. Method: All articles related to canine substitution were searched in the electronic database PubMed, and the important factors influencing the decision were reviewed. After careful evaluation, the checklist was evolved. Result: The malocclusions in which canine substitution is the treatment of choice are indicated in the tabular form for the convenience of clinicians. Specific treatment-planning considerations and biomechanics that can lead to an efficient and long-lasting result are also discussed. Conclusion: The need of the hour is an evidence-based approach, along with a well-designed prospective randomized control trial to understand the importance of each factor influencing these cases. Until that time, giving the available information in a simplified way can be a quality approach to these cases.

Vibration control of an unbalanced system using a quasi-zero stiffness vibration isolator with fluidic actuators and composite material: An experimental study

2022 ◽  
pp. 107754632110514
Author(s):  
Sivakumar Solaiachari ◽  
Jayakumar Lakshmipathy
Keyword(s):  
Composite Material ◽  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Basalt Fiber ◽  
Experimental Investigations ◽  
Vibration Isolator ◽  
Coil Spring ◽  
Linear Type ◽  
Fluidic Actuators ◽  
Isolation Performance

In this study, a new type of vibration isolator based on fluidic actuators and a composite slab was tested experimentally with an unbalanced disturbance. Quasi-zero stiffness vibration isolation techniques are advanced and provide effective isolation performance for non-nominal loads. The isolation performance of the proposed isolator was compared to that of a nonlinear vibration isolator equipped with fluidic actuators and a mechanical coil spring (NLVIFA). The NLVIFA system is better suited to non-nominal loads; however, the mechanical spring axial deflection leads to limited amplitude reduction in the system. To address this issue, a cross buckled slab was developed to replace a mechanical coil spring for absorbing vertical deflection by transverse bending, which is made of a specially developed composite material of Basalt fiber reinforced with epoxy resin and enhanced with graphene nano pellets. This current study was concerned with the theoretical analysis and experimental investigations of the proposed nonlinear vibration isolator with fluidic actuators and composite material (NLVIFA-CM), which performs under quasi-zero stiffness characteristics. Because of its reduced axial deflection, the theoretical and experimental results show that the NLVIFA-CM system outperforms the NLVIFA system and other linear type vibration isolators in terms of isolation performance. Furthermore, the proposed vibration isolator makes a significant contribution to low-frequency vibration.

scholarly journals COMPARATIVE STUDY OF STRESSES AND STRAINS THAT OCCUR IN STRUCTURAL ELEMENTS MADE OF COMPOSITE MATERIALS CONSIDERING THE MODEL WITH AND WITHOUT LAYERS

2016 ◽  
Vol 18 (4) ◽  
Author(s):  
FLORENTINA TOCU ◽  
COSTEL IULIAN MOCANU
Keyword(s):  
Mechanical Properties ◽  
Composite Material ◽  
Mechanical Characteristics ◽  
Building Industry ◽  
Careful Study ◽  
Structural Elements ◽  
Ship Building ◽  
Isotropic Plates ◽  
Layer Composite ◽  
Collective Experience

<p>Fibreglass-reinforced polyester (GRP) is the most widely used composite material in the ship building industry and requires careful study in point of mechanical characteristics. This article presents the collective experience related to behaviour in different situations of GRP loading. We considered three cases manufacturing for GRP: layers with mechanical characteristics for each layer, composite (the material is considered isotropic but with layers and same mechanical properties for all layers), and isotropic plates.</p>

Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method

2000 ◽  
Vol 68 (1) ◽  
pp. 3-10 ◽  
Author(s):  
H. M. Shodja ◽  
A. S. Sarvestani
Keyword(s):  
Elastic Constants ◽  
Present Method ◽  
Present Theory ◽  
Actual Distribution ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Ellipsoidal Inhomogeneity ◽  
Equivalent Inclusion ◽  
Comparison Results ◽  
Special Cases

Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to single-inclusion problems by means of superposition. The present theory is the first to obtain the actual distribution rather than the averages of the field quantities over the double inhomogeneity using Eshelby’s EIM. The present method is precise and is valid for thin as well as thick layers of coatings, and accommodates eccentric heterogeneity of arbitrary size and orientation. To establish the accuracy and robustness of the present method and for the sake of comparison, results on some of the previously reported problems, which are special cases encompassed by the present theory, will be re-examined. The formulations are easily extended to treat multi-inhomogeneity cases, where an inhomogeneity is surrounded by many layers of coatings. Employing an averaging scheme to the present theory, the average consistency conditions reported by Hori and Nemat-Nasser for the evaluation of average strains and stresses are recovered.

The distribution of stress and velocity in glaciers and ice-sheets

1957 ◽  
Vol 239 (1216) ◽  
pp. 113-133 ◽  
Keyword(s):  
Steady Flow ◽  
Longitudinal Velocity ◽  
Present Theory ◽  
Surface Velocity ◽  
General Flow ◽  
Glacier Valley ◽  
Compressive Flow ◽  
Special Cases ◽  
Flow Law ◽  
Distribution Of Stress

A block of ice resting upon a rough slope forms a theoretical model of a glacier or an ice-sheet, the sides of the glacier valley being ignored. Previous papers have described two types of steady flow in this model: ( a ) laminar flow, in which the longitudinal velocity gradient r is zero, and ( b ) extending or compressive flow, in which r is non-zero, ( a ) was derived under the assumption of a general flow law for ice, but ( b ) was only derived under the assumption of perfect plasticity. In the present paper a general flow law is used throughout, and the equations for steady flow, with r allowed to be non-zero, are found. The previous results ( a ) and ( b ) appear as special cases. Possible variations of density, temperature or flow law with depth are allowed for. If the density and the flow law are known as functions of depth in any region, and if the surface slope, the surface velocity, and the value of r are known, the equations give the stresses and velocity as functions of depth. The borehole experiment on the Jungfraufirn (1948-50) allows an experimental test. From the observed value of r , and Glen’s laboratory flow law for ice, a theoretical curve for the result of the experiment is calculated which is compared with the experimental curve. At a depth of 50 m the effect of ignoring r , as has been done hitherto, is to underestimate the shear rate by a factor of 50; on the present theory it is overestimated by a factor of 1∙33. The remaining discrepancy is probably mainly due to the effect of the glacier sides.

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

Phase and signal velocities of eigenwaves in a binary dissipative plasma

1974 ◽  
Vol 11 (2) ◽  
pp. 269-298 ◽  
Author(s):  
M. Kranyš ◽  
J. Teichmann
Keyword(s):  
Electromagnetic Wave ◽  
Bulk Viscosity ◽  
Present Theory ◽  
Speed Of Light ◽  
Longitudinal Diffusion ◽  
Front Speed ◽  
Phase Velocities ◽  
Special Cases ◽  
Complete Set ◽  
The Given

The signal and phase velocities of the possible waves (eigenwaves) in a dissipative binary plasma have been studied on the basis of the linearized thirteenmoment theory. The complete set of eigenmodes for the given system is formed using approximations in the range of frequencies high compared with typical collision or plasma frequencies. There are twenty non-trivial propagation modes. Four of them are modes with signal-front speed c associated with the induced electromagnetic wave. Eight modes belong to each of the gas constituents, among them two longitudinal diffusion modes (±WI), four transverse viscosity modespolarized respectively along two transverse axes ±W⊥ in the direction x1 and ±W⊥ in the direction x2) and two longitudinal thermal modes (±WII). The signalfront speed of all eigenwaves is lower than the speed of light, so that the system is hyperbolic. The ultra-relativistic plasma is also briefly discussed. In this case, all the mixture constituents will have the same set of signal-front speeds as a single gas, irrespective of the bulk viscosity. Comparison is made of the present theory and results with other theories (for some special cases).

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