On the Vibration of Layered Sandwich Elastic Plates

2008 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku
Keyword(s):  
Plate Theory ◽  
Impact Damage ◽  
Local Buckling ◽  
Recent Analysis ◽  
Sandwich Plates ◽  
Elastic Plates ◽  
Interface Pressure ◽  
Engineering Structures ◽  
Thin Plate Theory ◽  
Operational Methods

Sandwich elastic plates have found increasing applications in civil, aerospace, military and offshore industries to enhance superior resistance to fatigue crack propagation, impact damage, local buckling and are very effective for vibration damping and noise reduction. Such structural application has significantly led to reduction in vulnerability of warships to blasts, ballistics, bomb and fire attacks. In engineering structures, one of the effective ways of damping vibration and noise attenuation, is to exploit the occurrence of slip at the interface of structural laminates where such members are held together in a pressurised environment. Recent analysis and experimental investigation of vibration characteristics and damping properties of layered sandwich structures, are mostly limited to elastic beams. This paper is an attempt to extend such analytical investigations to layered sandwich plates. By employing contact mechanics and laminated thin plate theory, the generalised equation governing the vibration of two layered sandwich plates that are held together in pressurised environment is presented. In particular, by invoking operational methods for the case of linear interface pressure distribution, closed form analytical results for the system natural frequency and dynamic response under external excitation are reported for design analysis and applications.

Local Buckling Coefficient of Thin-Walled Pultruded FRP Compression Members

2007 ◽  
Vol 334-335 ◽  
pp. 377-380 ◽  
Author(s):  
Joo Hyung Joo ◽  
Soon Jong Yoon ◽  
Ju Kyung Park ◽  
Sun Kyu Cho
Keyword(s):  
Civil Engineering ◽  
Plate Theory ◽  
Low Cost ◽  
Local Buckling ◽  
Approximate Equation ◽  
Material Strength ◽  
Structural Members ◽  
Engineering Structures ◽  
Buckling Coefficient ◽  
Thin Walled

Recently there has been an increased demand in the use of FRP materials as load-bearing structural elements for the civil engineering applications, since FRP composite materials offer superior properties to conventional structural materials used in civil engineering structures. Among various production techniques, the pultrusion process has enabled the production of structural profiles with large cross sections at relatively low cost. Pultruded structural members are generally manufactured in the form of thin-walled member composed of plate elements and material properties can often be assumed as orthotropic. Due to the relatively low geometrical stiffness, often combined with low elastic modulus, the design of pultruded profiles is governed by the deflection or buckling rather than the material strength. In this paper, the elastic local buckling coefficient of the pultruded structural member having L-, T- and box-shape under the uniform in-plane compression was investigated and approximate equation to find the local buckling strength was proposed by using the classical orthotropic plate theory and energy method. The suggested equation can be used in the development of the design criteria and local buckling analysis of pultruded structural members.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Thin Plate ◽  
Strain Gradient ◽  
Plate Theory ◽  
Laminated Composite ◽  
Equilibrium Equations ◽  
Thin Plate Theory ◽  
Bending Behavior ◽  
Hygrothermal Environment ◽  
Load Types ◽  
Novel Applications

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Study on Gradual Deformation and Prediction Model of the Mined Overburden

2012 ◽  
Vol 524-527 ◽  
pp. 699-704
Author(s):  
Xiao Gang Xia ◽  
Yun Feng Yang
Keyword(s):  
Boundary Condition ◽  
Plate Theory ◽  
Surface Expression ◽  
Rock Deformation ◽  
Double Trigonometric Series ◽  
Mechanics Model ◽  
Thin Plate Theory ◽  
Gradual Deformation ◽  
Exchange Condition ◽  
Gradual Transformation

Based on the overburden three caving feature, the deformation of mining rock process was devided and the criterion of gradual transformation of each stages deformation were given. Then , combined the thin-plate theory, the differential models were derived for rock deformation in level and similar to level bured condition. The boundary condition of each models and exchange condition between different models were put forward and the gradual mechanics model was set up.The subsidence model before roof collapse was solved by Navier double trigonometric series and the deflection surface expression of rock deformation was put forword. At last, the reliability and practicality of the models was verified by engineering examples.

Normal Loading on a Wedge-Shaped Plate

1955 ◽  
Vol 6 (3) ◽  
pp. 196-204 ◽  
Author(s):  
D. E. R. Godfrey
Keyword(s):  
Thin Plate ◽  
Mellin Transform ◽  
Plate Theory ◽  
Normal Loading ◽  
Thin Plate Theory

SummaryThe equations of thin plate theory are expressed in polar co-ordinates and transformed using the Mellin transform. Problems involving discontinuous and isolated normal loadings may then be solved in the case of the built-in or freely supported wedge-shaped boundary.

Calculation for Elastic Global Buckling of Sandwich Plates with Ribs

2012 ◽  
Vol 188 ◽  
pp. 25-30 ◽  
Author(s):  
Qi Chao Xue ◽  
Guang Ping Zou ◽  
Ye Wu ◽  
Hai Lin Xiong ◽  
Meng Chai
Keyword(s):  
Energy Method ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Sandwich Plates ◽  
Buckling Stress ◽  
Global Buckling ◽  
Simple Support ◽  
Rectangular Sandwich Plate ◽  
Two Sides ◽  
Rectangular Sandwich Plates

Based on Reissner’s sandwich plate theory, the critical globlal buckling equation of sandwich plate with ribs is deduced by energy method under simple support boundary conditions. And the critical buckling solution is obtained and discussed here. Afterwards a rectangular sandwich plate with steel faceplate and polyurthane core is taken as an example. The influence on critical global buckling stress with different inertia moments in rectangular sandwich plates are discussed. simularly the effect of the lengh ratio of two sides and the thickness of rectangular sandwich plate are also studied.

General Solutions for the Statics of Anisotropic, Transversely Inhomogeneous Elastic Plates in Terms of Complex Functions

2006 ◽  
Vol 11 (6) ◽  
pp. 596-628 ◽  
Author(s):  
Kostas P. Soldatos
Keyword(s):  
General Solution ◽  
Elastic Plate ◽  
Plate Theory ◽  
High Order ◽  
Transverse Strain ◽  
Elastic Plates ◽  
General Solutions ◽  
Material Inhomogeneity ◽  
Complex Functions ◽  
Anisotropic Elastic

This paper develops the general solution of high-order partial differential equations (PDEs) that govern the static behavior of transversely inhomogeneous, anisotropic, elastic plates, in terms of complex functions. The basic development deals with the derivation of such a form of general solution for the PDEs associated with the most general, two-dimensional (“equivalent single-layered”), elastic plate theory available in the literature. The theory takes into consideration the effects of bending–stretching coupling due to possible un-symmetric forms of through-thickness material inhomogeneity. Most importantly, it also takes into consideration the effects of both transverse shear and transverse normal deformation in a manner that allows for a posteriori, multiple choices of transverse strain distributions. As a result of this basic and most general development, some interesting specializations yield, as particular cases, relevant general solutions of high-order PDEs associated with all of the conventional, elastic plate theories available in the literature.

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