Planar Flexural Vibrations and Dissipative Heating of Laminated Rectangular Plates (original) (raw)
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Dynamic Behaviour of Laminated Plates Subjected to Thermomechanical Loads
Proceedings of the 3rd South-East European Conference on Computational Mechanics – SEECCM III, 2013
The engineering structures may be subjected to the dynamic loads such as blast. Therefore, in the design of such structures, the effect of the blast loading should be taken into account. There are two possible effects of the blast: sudden pressure and the temperature rise. In this study, a closed form solution is presented for the thermomechanical transient analysis of the simply supported laminated composite plates subjected to blast loading. In-plane stiffness and inertia effects are considered in the formulation of the problem and transverse shear stresses are ignored. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. The Galerkin method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations. The displacement-time and strain-time histories are obtained for critical cases and compared the isothermal condition. The method presented here can be used for the dynamic response analysis of laminated plates in preliminary design.
Composite Structures, 2003
This paper deals with the dynamic response of shear deformable laminated plates exposed to thermomechanical loading and resting on a two-parameter (Pasternak-type) elastic foundation. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties are assumed to be independent of temperature. The formulations are based on ReddyÕs higher order shear deformable plate theory and include the plate-foundation interaction and thermal effects due to temperature rise. All four edges of the plate are assumed to be simply supported with no inplane displacements. Analytical solutions of dynamic response for symmetric cross-ply and antisymmetric angle-ply laminated plates subjected to a transverse dynamic load and exposed to a uniform temperature rise are obtained by using the state variable approach. The numerical illustrations concern the free vibration and dynamic response of shear deformable laminated plates resting on Pasternak-type elastic foundations with the Winkler elastic foundations being a limiting case. Effects of foundation stiffness, plate side-to-thickness ratio, and temperature rise on the dynamic response are also studied.
Non-linear response of laminated composite plates under thermomechanical loading
International Journal of Non-Linear Mechanics, 2005
The non-linear response of laminated composite plates under thermomechanical loading is studied using the third-order shear deformation theory (TSDT) that includes classical and first-order shear deformation theories (CLPT and FSDT) as special cases. Geometric non-linearity in the von Kármán sense is considered. The temperature field is assumed to be uniform in the plate. Layers of magnetostrictive material, Terfenol-D, are used to actively control the center deflection. The negative velocity feedback control is used with the constant gain value. The effects of lamination scheme, magnitude of loading, layer material properties, and boundary conditions are studied under thermomechanical loading.
Thermoelastic vibrations in a thin elliptic annulus plate with elastic supports
Theoretical and Applied Mechanics Letters, 2018
The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. • The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. • The thermal moment is derived on the basis of temperature distribution, and its stresses are derived based on resultant bending moments per unit width. • The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.
Thermoelastic damping in an auxetic rectangular plate with thermal relaxation: forced vibrations
Journal of Mechanics of Materials and Structures, 2013
This work describes an extended thermodynamical model to represent coupled thermomechanical interactions in continuum media having negative Poisson's ratio. In particular, the Zener thermoelastic damping effect is considered for a plate with auxetic characteristics undergoing free vibrations. The extended thermodynamical model is characterized by a thermal relaxation time to avoid the propagation of thermal waves at infinite velocity. The thermal relaxation time used in this work is not Zener's characteristic time constant. Strong dependence of the thermoelastic damping is observed for auxetic configurations, various plate thicknesses and ambient temperatures.
Open Engineering, 2014
This study presents the thermoelastic analysis of laminated composite plates subjected to sinusoidal thermal load linearly varying across the thickness. Analytical solutions for thermal displacements and stresses are investigated by using a uniied plate theory which includes diferent functions in terms of thickness coordinate to represent the efect of shear deformation. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Governing equations of equilibrium and associated boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates has been developed. Numerical results are presented to demonstrate the thermal response of the laminated composite plates.
… journal of emerging in engineering and …, 2012
Visco-elastic plates are widely used in various mechanical structures, aircraft and industries. For a proper design of plate structures and efficient use of material, the behavior and strength characteristics of plates should be accurately determined. In the modern technology, the plates of variable thickness are widely used in engineering applications i.e. nuclear reactor, aeronautical field, naval structure, submarine, earth-quake resistors etc. A mathematical model is presented for the use of engineers, technocrats and research workers in space technology, mechanical sciences have to operate under elevated temperatures. In this paper, the effect of thermal gradient on the vibration of Square plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal effect on vibration of such plate has been taken as linear in one direction and parabolic in another direction. An approximate but quite convenient frequency equation is derived for a by using Rayleigh-Ritz technique with a two-term deflection function. Both the modes of the frequency are calculated by the latest computational technique, MATLAB, for the various values of taper parameters and temperature gradient. All the results are presented in the graphs.
Modelling and Nonlinear Dynamics of Third-Order Thermomechanically Coupled Laminated Plates
2016
Thermomechanically coupled, geometrically nonlinear, laminated plates are addressed through a unified 2D formulation that integrates mechanical and thermal aspects and consistently accounts for cubic variations along the thickness of both in-plane displacement components and temperature. It allows to address a variety of thermal boundary conditions on the plate upper and lower surfaces. Minimal dimension reduction of the problem is pursued for symmetric cross-ply laminates. A numerical case study provides hints on the potential of the reduced model for the analysis of thermomechanical coupling effects on the system nonlinear dynamics
Applied Mathematical Modelling, 2012
This paper deals with large amplitude vibration of hybrid laminated plates containing piezoelectric layers resting on an elastic foundation in thermal environments. The motion equation of the plate that includes plate-foundation interaction is based on a higher order shear deformation plate theory and solved by a two-step perturbation technique. The thermo-piezoelectric effects are also included and the material properties of both orthotropic layers and piezoelectric layers are assumed to be temperature-dependent. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions. The results show that the foundation stiffness and stacking sequence have a significant effect on the nonlinear vibration characteristics of the hybrid laminated plate. The results also reveal that the temperature rise reduces the natural frequency, but it only has a small effect on the nonlinear to linear frequency ratios of the hybrid laminated plate. The results confirm that the effect of the applied voltage on the natural frequency and the nonlinear to linear frequency ratios of the hybrid laminated plate is marginal except the plate is sufficiently thin.
Vibrations and Buckling of Annular and Circular Plates Subjected to a Thermal Load
44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2003
We consider the behavior of annular plates with clamped-clamped immovable boundary conditions to axisymmetric in-plane thermal loads. We model the plate using the dynamic analogue of Saint-Venant plate theory and solve the steady-state heat conduction equation for the radial temperature distribution. We investigate the influence of key thermal and geometric parameters on the free vibrations and buckling of the annulus. As a special case, we also investigate the behavior of clamped thermally loaded circular plates.