scholarly journals Study of the sound radiation of a rectangular plate resting on a winkler elastic foundation

2016 ◽  
Author(s):  
Nicolás A. Bastián-Monarca ◽  
Jorge P. Arenas
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Sound Radiation ◽  
Winkler Elastic Foundation

Free Vibration of Orthotropic Plate on Foundation with Four Edges Free by Finite Integral Transform Method

2011 ◽  
Vol 243-249 ◽  
pp. 4253-4256
Author(s):  
Yong Zhong ◽  
Yuan Yuan Gao
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Integral Transform ◽  
Mode Shapes ◽  
Transform Method ◽  
Orthotropic Rectangular Plate ◽  
Winkler Elastic Foundation ◽  
Elasticity Equations ◽  
Finite Integral ◽  
Integral Transform Method

The double finite cosine integral transform method is exploited to obtain explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate on foundation with four edges free. In the analysis procedure, the classical Kirchhohh orthotropic rectangular plate is considered and the Winkler elastic foundation is utilized to represent the elastic foundation. Because only are the basic dynamic elasticity equations of the orthotropic thin plate on elastic foundation adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by present paper is reasonable and theoretical. In order to illuminate the correction of formulations, the numerical results are also presented to comparing with that of the other references.

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.

Stability Analysis of Cylindrical Shells Resting on Winkler Elastic Foundation Using Semi-Analytical Quadrature Element Method

2019 ◽  
Vol 821 ◽  
pp. 459-464
Author(s):  
Qi Gao Hu ◽  
Xu Dong Hu ◽  
Zhi Qiang Shen ◽  
Liang Yun Tao ◽  
Ze Tan
Keyword(s):  
Elastic Foundation ◽  
Cylindrical Shells ◽  
Longitudinal Direction ◽  
External Pressure ◽  
Element Formulation ◽  
Quadrature Element Method ◽  
Advanced Composite Materials ◽  
Winkler Elastic Foundation ◽  
Parametric Studies ◽  
Element Method

The buried pipelines or vessels and other similar structures made of homogeneous or advanced composite materials are commonly used in civil engineering and biotechnology. The radial stability problem of these structures was widely studied using the cylindrical shell model over the past years. In this paper, the linear stability of cylindrical shells resting on Winkler elastic foundation under uniformly distributed external pressure was analyzed with semi-analytical quadrature element method (QEM). As for the longitudinal direction, the radial deflection of shell was approximated by the quadrature element formulation. While the analytic trigonometric function was adopted for description of radial deflection in circumferential direction. The Numerical results of critical buckling load were compared with the semi-analytical FEM. It is found that the semi-analytical QEM possesses higher computational efficiency and applicability than semi-analytical FEM. Then, the effects of the shell length, radius, and thickness on the critical buckling pressures are systematically investigated through the parametric studies.

scholarly journals MODAL ANALYSIS OF TAPERED BEAM-COLUMN EMBEDDED IN WINKLER ELASTIC FOUNDATION

2015 ◽  
Vol 7 (1) ◽  
pp. 1-1 ◽  
Author(s):  
Engin Emsen ◽  
Kadir Mercan ◽  
Bekir Akgöz ◽  
Ömer Civalek
Keyword(s):  
Modal Analysis ◽  
Elastic Foundation ◽  
Tapered Beam ◽  
Winkler Elastic Foundation

Static and Dynamic Response of a Beam on a Winkler Elastic Foundation

2005 ◽  
Author(s):  
Timour M. A. Nusirat ◽  
M. N. Hamdan
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Initial Value Problem ◽  
Nonlinear Partial Differential Equation ◽  
Static Case ◽  
Initial Value ◽  
Characteristic Curves ◽  
System Parameters ◽  
Winkler Elastic Foundation ◽  
Dynamic Case

This paper is concerned with analysis of dynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation. The beam is assumed to be subjected to a uniformly distributed lateral static load, have an initial quarter-sine shape deflection. At one end, the beam is assumed to be restrained by a pin, while at the other end, the beam is assumed to be restrained by a torsional and a translational linear spring. The beam is modeled by a nonlinear partial differential equation where the nonlinearity enters the governing equation through the beam axial force. In the static case, because of a unique feature of governing equation, the analysis was carried out using the theory of linear differential equations, but takes into account the effect of actual deflection on the induced axial thrust. In the dynamic case, stability analysis of the beam is carried out by calculating the nonlinear frequencies of free vibration of the beam about its static equilibrium configuration. The assumed mode method is used to discretize and find an equivalent nonlinear initial value problem. Then the harmonic balance is used to obtain an approximate solution to the nonlinear oscillator described by the equivalent initial value problem. The analyses of results were carried out for a selected range of values of the system parameters: foundation elastic stiffness, lateral load, and maximum beam edge deflection. In the static case the results are presented as characteristic curves showing the variation of the beam static deflection and associated bending moment distribution with each of the above system parameters. In the dynamic case, the presented characteristic curves show the variation of the nonlinear natural frequency corresponding to the first and the second modes over a range of each of the above system parameters.

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