The Support Reaction of a Simply Supported and Uniformly Loaded Thin Circular Aeolotropic Plate

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Kjell Eriksson
Keyword(s):  
Analytical Solution ◽  
Series Solution ◽  
Lateral Load ◽  
Anisotropic Materials ◽  
Higher Order ◽  
Simply Supported ◽  
Support Reaction ◽  
Degree Of Anisotropy

A previous analytical solution of the deflection of a thin circular aeolotropic plate, with simply supported edge and uniform lateral load, has been used to derive approximate series expressions for the plate support reaction, which are directly applicable in practice. The support reaction, which has been calculated for some typical anisotropic materials of varying degree of anisotropy, varies significantly along the plate perimeter and strongly anisotropic materials require in general a higher order series solution. Certain solution constants of previous deflection approximations were not found to harmonize and are therefore recalculated.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

An analytical solution of the Gibbs–Dehem equation in multicomponent systems

1970 ◽  
Vol 48 (5) ◽  
pp. 752-763 ◽  
Author(s):  
A. D. Pelton
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Multicomponent Systems ◽  
Duhem Equation ◽  
Number Of Components ◽  
Analytical Power

A general analytical power-series solution of the Gibbs–Duhem equation in multicomponent systems of any number of components has been developed. The simplicity and usefulness of the solution is made possible through the choice of a special set of composition variables.

scholarly journals On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Saad Ilyas ◽  
Feras K. Alfosail ◽  
Mohammad I. Younis
Keyword(s):  
Analytical Solution ◽  
Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Equation Of Motion ◽  
Higher Order ◽  
Resonance Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Electrostatically Actuated

We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.

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