Shallow Spherical Shells Research Articles

Nonlinear Thermal Vibrations on Elastic Shallow Spherical Shell Under Linear and Parabolic Temperature Distributions

Brief Notes Nonlinear Thermal Vibrations on Elastic Shallow Spherical Shell Under Linear and Parabolic Temperature Distributions U. K. Mandal, U. K. Mandal Jalpaiguri Government Engineering College, Jalpaiguri 735102, West Bengal, India Search for other works by this author on: This Site PubMed Google Scholar P. Biswas P. Biswas P. D. Women’s College, Jalpaiguri 725101, West Bengal, India Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information U. K. Mandal Jalpaiguri Government Engineering College, Jalpaiguri 735102, West Bengal, India P. Biswas P. D. Women’s College, Jalpaiguri 725101, West Bengal, India J. Appl. Mech. Sep 1999, 66(3): 814-815 (2 pages) https://doi.org/10.1115/1.2791762 Published Online: September 1, 1999 Article history Online: October 25, 2007

Determination of the stressed-strained state of nonthin transversally isotropic spherical shells with elastically stiffened curvilinear holes

An approximate analytical method has been developed for determining the stressed-strained state of nonthin transversally isotropic shallow spherical shells with noncircular elastic inclusions or stiffened holes, under both ideal and nonideal contact at the interface. The method is based on two tried and tested analytical methods—the method of Fourier expansion of the required functions using Legendre polynomials and the second version of the perturbation method for the boundary shape.

Axisymmetric shells and plates on tensionless elastic foundations

This paper first describes a finite element method for the large deflection analysis of axisymmetric shells and plates on a nonlinear tensionless elastic foundation. Through the use of discrete data points, any form of nonlinear elastic foundation behaviour can be easily modelled. The analysis is then validated by comparison with existing results for circular plates and beams as the only existing results for shells on tensionless foundations are found to be in error. Following this verification, the analysis is applied to investigate the behaviour of shallow spherical shells subject to a central concentrated load on tensionless linear elastic foundations. A number of insightful conclusions regarding the behaviour of such structure-foundation systems are drawn. The numerical results for shells are believed to be the first correct results, which may be useful in benchmarking results from other sources in the future.

Modeling, Design, and Zero Gravity Testing of a Doubly Curved Aperture Antenna

A smart aperture antenna whose reflector is deformed by curved piezoelectric actuators is modeled and the results are experimentally verified in a microgravity environment. The reflector is modeled as a shallow spherical shell with a small hole at the apex for mounting. Using Reissner's shallow spherical shell theory, five equations governing the mechanical behavior of the reflector structure are reduced to two equations. These are described in terms of a stress function and the axial deflection. As actuators, four PZT strip actuators are attached along the meridians separated by 90 degrees respectively. The forces developed by the actuators are modeled as distributed pressure loads on the reflector surface. In addition to the analytical model, a finite element model is generated to verify the analytical model on the various surface positions of the reflector. Finally, an actual model of the reflector is built and tested in a zero gravity environment. The experimental data show good agreement with those obtained from the analytical and the finite element models.

Static-geometric duality and stress concentration in twisted and sheared shallow spherical shells

Static-geometric duality and stress concentration in twisted and sheared shallow spherical shells

Piezoelectrically driven speakers for active aircraft interior noise suppression

This paper presents results from an experimental study of light weight piezoelectrically driven speakers developed in the Smart Trim Technology Laboratory (SMARTTLAB) at University of Delaware. The speakers are of direct radiator type and are driven by shallow spherical shell piezoceramic actuators. Two implementations – an acoustic piston and a cone – have been tested. Results from small signal characteristics measurements performed in a semi-reverberant environment are presented. While most of the tests have been performed using RAINBOW actuators as driving elements, some results for the THUNDER actuator are also presented. The possible use of these devices as controllable acoustic sources in active noise control applications is discussed. The low weight of these actuators makes them highly suitable for aircraft interior noise control applications with severe space and weight restrictions.

On the stressed state of a non-thin transversally isotropic spherical shell with a circular hole

On the basis of a generalized theory constructed using the Fourier-series expansion of the unknowns in Legendre polynomials of the thickness coordinate we give a representation of the general solution of the equilibrium equations of a transversally isotropic spherical shell for an arbitrary approximation. On this basis we study the problem of the stressed state of a shallow spherical shell with a circular cavity on whose boundary surface there are tangential stresses varying nonlinearly over the thickness.

Iterative analytical solution of nonlinear analysis of shallow spherical shell with computer algebra systems—MapleV

This paper is concerned with the application of Computer Algebra System—MapleV to the nonlinear analysis of shallow spherical shells. In the present paper, the nonlinear equations of the shell to the nonlinear problem could be solved by using CASes method. Detailed high-order iterative solution expressions and analytical results for the third iteration are given in CASes forms. The numerical results show that the solutions of this paper contain other cases where the solutions were the second iteration. The effects of various inner radius parameters have been investigated in detail. The results of the third iterative expressions are obtained firstly. It has been shown that the adoption of CASes method would be useful in nonlinear problems.

Experimental studies of shallow spherical shell piezoceramic actuators as acoustic boundary control elements

This paper presents an experimental study of the shallow spherical shell piezoceramic RAINBOW actuator, to follow up the theoretical modeling and numerical studies of this actuator reported in a previous paper. A comparison of theoretically predicted and experimentally determined natural frequencies of the RAINBOW actuator with free edge boundary conditions is presented in the paper. Also presented are results from experiments performed on a prototype of a low profile piezoelectrically driven baffled acoustic piston developed at the Smart Trim Technology Laboratory. Experimentally generated volume velocity curves of the piston are presented. The possible use of this device in active noise control applications is discussed.

Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells

In this paper, a model of cusped catastrophe at nonlinear dynamic buckling of a symmetrically laminated cylindrically orthotropic shallow spherical shell is presented. The shell is subjected to an axisymmetrical load. Effects of transverse shear are taken into account. Effects of the shear modulus, geometry and parameters of the material on the nonlinear dynamic buckling are discussed.

Well-posedness for a nonlinear shallow spherical shell

Well-posedness for a nonlinear shallow spherical shell

Effect of transverse shear on static and dynamic buckling of antisymmetrically laminated polar orthotropic shallow spherical shells

This paper deals with the static and dynamic buckling of polar orthotropic antisymmetrically laminated, moderately thick shallow spherical shells under uniformly distributed loading. Considering the effects of transverse shear and rotatory inertia, the governing equations of motion for shells undergoing large deformations are derived and expressed in terms of normal deflection W, slope ϑ and stress function Ψ. the Chebyshev series technique is used for spatial discretization and the Houbolt scheme is used for temporal discretization. Considering step function loading, both clamped and simply supported immovable laminated spherical shells are analyzed. The effects of transverse shear, rotatory inertia, shell rise, base-radius-to-thickness ratio and material properties on the static and dynamic snap-through buckling of antisymmetrically laminated shells have been studied.

Nonlinear stability of truncated shallow spherical shell with variable thickness under uniformly distributed load

In this paper, to begin with, the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformly distributed load are linearized by step-by-step loading method. The linear differential equations can be solved by spline collocation method. Critical loads have been obtained accordingly.

Finite element simulation of electromagnetic induction transducers for impulsive intense sound

A finite element approach to the simulation of the dynamic responses of electromagnetic induction transducers is presented. The electromagnetic induction transducer for intense sound radiation is considered as a transient coupled magneto-mechano-acoustic system, in which nonlinear effect of the acoustic field is also included. The axisymmetric finite element formulation is developed and solved in the time domain. Some numerical examples are demonstrated for the transducers with a circular plate radiator and a shallow spherical shell radiator. Experimental verification is then made for the fabricated models of small scale. The comparison proves the validity and the capability of the present numerical modelling.

Nonlinear free vibration of orthotropic shallow shells of revolution under the static loads

In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.

THE NON-LINEAR VIBRATION AND DYNAMIC INSTABILITY OF THIN SHALLOW SHELLS

In this paper, the non-linear vibration and dynamic instability of thin shallow spherical and conical shells subjected to periodic transverse and in-plane loads are investigated. The Marguerre type dynamic equations used for the analysis of shallow shells, when treated by the Galerkin method, will result in a system of total differential equations in the time functions, known as Duffing and Mathieu equations, from which the various kinds of non-linear vibration and dynamic instability are determined by using numerical methods. Numerical results are presented for axisymmetric vibrations and dynamic instabilities of shallow spherical and conical shells with (a) clamped and (b) supported edge conditions. As numerical examples, non-linear vibration frequencies and instability regions for shells are determined. The effects of static load as well as static snap-through buckling on the instability are also investigated.

Influence functions of a thin shallow meniscus-shaped mirror

Thin shallow spherical shell theory is used to derive the general influence function, owing to uniform and/or discrete (actuators) loads, for a thin shallow meniscus-shaped mirror of uniform thickness with a central hole and supported at discrete points. Small elastic deformations are considered. No symmetry on the load distribution constrains the model. Explicit analytical expressions of the set of equations are given for calculating the influence functions. Results agree with the finite element analysis (FEA) to within 1%. When the FEA requires megabytes of RAM memory, the analytical method needs only kilobytes and typically runs 30 times faster. This is a crucial advantage for the iterative optimization of mirror supports such as large passive or active meniscus-shaped primary mirror supports or Cassegrain/Gregorian adaptive secondary actuator configurations. References are given on estimating the shear effects (thick mirror), the thickness variation effect, and the influence of the size of the support pads.

Orthotropic Shallow Spherical Shell on a Kerr Foundation

Parametric study involving foundation parameters and shell geometry is carried out for nonlinear static behavior of an orthotropic shallow spherical shell on a Kerr foundation. Study shows that the deflection reduces if the shell curvature or the foundation parameters of the shear layer and the lower spring layer are increased. Shells with immovable edges are found to be more prone and vulnerable to changes in various parameters than those with movable edges.

Revised analysis of the thermal stresses in a shallow spherical shell with a foreign inclusion

We carry out a revised analysis of the concentration of thermal stresses in a shallow spherical shell with a small foreign inclusion. We show that near the interface of the materials the stressed state has a sharply expressed three-dimensional character; thus the stresses differ significantly (both qualitatively and quantitatively) from the shells predicted by the standard theories.

Geometrically nonlinear analysis of the shallow shell by the displacement-based boundary element formulation

In this paper, the boundary element method is used to solve the problem of a shallow shell undergoing finite deflections. Four coupled integral equations of the in-plane and transverse displacements are obtained through the use of the weighted residual method. The resulting equations are then linearized and an incremental solution procedure is discussed. Numerical results of the shallow spherical shell are given to demonstrate the computational efficiency of the method.