Dissertations / Theses on the topic 'Shells (Engineering) Vibration. Elastic plates and shells'

Almost all of the analytical solution techniques presented for composite plates and shells deal with either simply supported conditions or boundary conditions with at least a pair of opposite edges simply supported. In the present study, an alternative general approach, combining superposition and state space techniques is developed for the free vibration analysis of laminated orthotropic composite plates and shells having arbitrary boundary conditions. This study concentrates on the antisymmetric angle-ply laminated plates and cross-ply laminated plates and shells. Three commonly adopted theories, i.e., classical theory, first-order shear deformation theory and third-order shear deformation theory, have been employed and compared with one another to investigate the influence of transverse shear deformation, structural aspect ratio, length-to-thickness ratio, degree of anisotropy and the number of layers on natural frequency. Convergence tests have been carried out to guarantee the accuracy of the closed-form solutions. Wherever possible, numerical results generated by the present approach are compared with those reported in the published references. Accurate non-dimensional fundamental frequencies are presented for laminated plates and shells with two adjacent edges, three edges and four edges clamped and other edges simply supported. Such analyses have not been reported in the literature previously. Also, vibration analysis of a cantilever angle-ply antisymmetric plate with a point support is conducted to demonstrate the applicability of the present technique. It has been shown that the method works extremely well and excellent agreements are found between the present results and those generated by previous researchers. It has also been shown that more complicated boundary-value problems can be solved by this technique without any difficulty.

First-order transverse shear-deformation Mindlin theory has been used to predict the free vibration frequencies and modal shapes for isotropic, laminated and composite plates or shells. A finite element model based on the small deflection linear theory has been developed to obtain numerical solutions for this class of problems. The results for some of the degenerate cases are compared with other results available in the literature. These analyses involve a wide number of variables, namely; material properties, aspect ratios, support conditions and also radius to base ratio. The cracked base plates, shells and blades are idealized as partially supported models with varying support lengths. The effects of the detached base length on natural frequencies, modal shapes and nodal lines of these types of structures are investigated. Although the expected decrease in frequency with increase in the detached base length is observed almost for all modes it is seen that this behavior is very pronounced for higher modes in both plates and shells. Analysis also showed that the variation of the detached base length has a small effect on the natural frequencies of plates and shells with large aspect ratios ( b/a > 2, r/a > 2).

Thesis (M.S.)--West Virginia University, 1999.
Title from document title page. Document formatted into pages; contains iv, 87 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 86-87).

The research work presented here deals with the problems of geometrically nonlinear analysis of thin shell structures. The specific objective was to develop geometrically nonlinear formulations, using Discrete-Kirchhoff Curved Triangular (DKCT) thin shell elements. The DKCT elements, formulated in the natural curvilinear coordinates, based on arbitrary deep shell theory and representing explicit rigid body modes, were successfully applied to linear elastic analysis of composite shells in an earlier research work. A detailed discussion on the developments of classical linear and nonlinear shell theories and the Finite Element applications to linear and nonlinear analysis of shells has been presented. The difficulties of developing converging shell elements due to Kirchhoff's hypothesis have been discussed. The importance of formulating shell elements based on deep shell theory has also been pointed out. The development of shell elements based on Discrete-Kirchhoff's theory has been discussed. The development of a simple 3-noded curved triangular thin shell element with 27 degrees-of-freedom in the tangent and normal displacements and their first-order derivatives, formulated in the natural curvilinear coordinates and based on arbitrary deep shell theory, has been described. This DKCT element has been used to develop geometrically nonlinear formulation for the nonlinear analysis of thin shells. A detailed derivation of the geometrically nonlinear (GNL) formulation, using the DKCT element based on the Total Lagrangian approach and the principles of virtual work has been presented. The techniques of solving the nonlinear equilibrium equations, using the incremental methods has been described. This includes the derivation of the Tangent Stiffness matrix. Various Newton-Raphson solution algorithms and the associated convergence criteria have been discussed in detail. Difficulties of tracing the post buckling behavior using these algorithms and hence the necessity of using alternative techniques have been mentioned. A detailed numerical evaluation of the GNL formulation has been carried out by solving a number of standard problems in the linear buckling and GNL analysis. The results compare well with the standard solutions in linear buckling cases and are in general satisfactory for the GNL analysis in the region of large displacements and small rotations. It is concluded that this simple and economical element will be an ideal choice for the expensive nonlinear analysis of shells. However, it is suggested that the element formulation should include large rotations for the element to perform accurately in the region of large rotations.

Active control of vibration in structures has been investigated by an increasing number of researchers in recent years. There has been a great deal of theoretical work and some experiment examining the use of point forces for vibration control, and more recently, the use of thin piezoelectric crystals laminated to the surfaces of structures. However, control by point forces is impractical, requiring large reaction masses, and the forces generated by laminated piezoelectric crystals are not sufficient to control vibration in large and heavy structures. The control of flexural vibrations in stiffened structures using piezoceramic stack actuators placed between stiffener flanges and the structure is examined theoretically and experimentally in this thesis. Used in this way, piezoceramic actuators are capable of developing much higher forces than laminated piezoelectric crystals, and no reaction mass is required. This thesis aims to show the feasibility of active vibration control using piezoceramic actuators and angle stiffeners in a variety of fundamental structures. The work is divided into three parts. In the first, the simple case of a single actuator used to control vibration in a beam is examined. In the second, vibration in stiffened plates is controlled using multiple actuators, and in the third, the control of vibration in a ring-stiffened cylinder is investigated. In each section, the classical equations of motion are used to develop theoretical models describing the vibration of the structures with and without active vibration control. The effects of the angle stiffener(s) are included in the analysis. The models are used to establish the quantitative effects of variation in frequency, the location of control source(s) and the location of the error sensor(s) on the achievable attenuation and the control forces required for optimal control. Comparison is also made between the results for the cases with multiple control sources driven by the same signal and with multiple independently driven control sources. Both finite and semi-finite structures are examined to enable comparison between the results for travelling waves and standing waves in each of the three structure types. This thesis attempts to provide physical explanations for all the observed variations in achievable attenuation and control force(s) with varied frequency, control source location and error sensor location. The analysis of the simpler cases aids in interpreting the results for the more complicated cases. Experimental results are given to demonstrate the accuracy of the theoretical models in each section. Trials are performed on a stiffened beam with a single control source and a single error sensor, a stiffened plate with three control sources and a line of error sensors and a ring-stiffened cylinder with six control sources and a ring of error sensors. The experimental results are compared with theory for each structure for the two cases with and without active vibration control.
Thesis (Ph.D.)--Mechanical Engineering, 1995.

In modern engineering there is a considerable interest in predicting the behavior of post-buckled structures. With current lightweight, aerospace, and high performance applications, structural elements frequently operate beyond their buckled load. This is especially true of plates, which are capable of maintaining stability at loads several times their critical buckling load. Additionally, even structures such as cylindrical shells may be pushed into a post-buckled range in these extreme applications.

Because of the nature of these problems, continuation methods are particularly well suited as a solution method. Continuation methods have been extensively applied to a range of problems in mathematics and physics but have been used to a lesser extent in engineering problems. In the present work, continuation methods are used to solve a variety of buckling and stability problems of discrete dynamical systems, plates and cylinders. The continuation methods, when applied to dynamic mechanical systems, also provide very useful information regarding the modal behavior of the structure, including linearized natural frequencies and mode shapes as a by-product of the solution method.

To verify the results of the continuation calculations, the commercial finite element code ANSYS is used as an independent check. To confirm previously unseen stable equilibrium shapes for square plates, a set of experiments on polycarbonate plates is also presented.

Dissertation

This work aims at dimensional reduction of nonlinear material models in an asymptotically accurate manner. The three-dimensional(3-D) nonlinear material models considered include isotropic, orthotropic and dielectric compressible hyperelastic material models. Hyperelastic materials have potential applications in space-based inflatable structures, pneumatic membranes, replacements for soft biological tissues, prosthetic devices, compliant robots, high-altitude airships and artificial blood pumps, to name a few. Such structures have special engineering properties like high strength-to-mass ratio, low deflated volume and low inflated density. The majority of these applications imply a thin shell form-factor, rendering the problem geometrically nonlinear as well. Despite their superior engineering properties and potential uses, there are no proper analysis tools available to analyze these structures accurately yet efficiently. The development of a unified analytical model for both material and geometric nonlinearities encounters mathematical difficulties in the theory but its results have considerable scope. Therefore, a novel tool is needed to dimensionally reduce these nonlinear material models. In this thesis, Prof. Berdichevsky’s Variational Asymptotic Method(VAM) has been applied rigorously to alleviate the difficulties faced in modeling thin shell structures(made of such nonlinear materials for the first time in the history of VAM) which inherently exhibit geometric small parameters(such as the ratio of thickness to shortest wavelength of the deformation along the shell reference surface) and physical small parameters(such as moderate strains in certain applications). Saint Venant-Kirchhoff and neo-Hookean 3-D strain energy functions are considered for isotropic hyperelastic material modeling. Further, these two material models are augmented with electromechanical coupling term through Maxwell stress tensor for dielectric hyperelastic material modeling. A polyconvex 3-D strain energy function is used for the orthotropic hyperelastic model. Upon the application of VAM, in each of the above cases, the original 3-D nonlinear electroelastic problem splits into a nonlinear one-dimensional (1-D) through-the-thickness analysis and a nonlinear two-dimensional(2-D) shell analysis. This greatly reduces the computational cost compared to a full 3-D analysis. Through-the-thickness analysis provides a 2-D nonlinear constitutive law for the shell equations and a set of recovery relations that expresses the 3-D field variables (displacements, strains and stresses) through thethicknessintermsof2-D shell variables calculated in the shell analysis (2-D). Analytical expressions (asymptotically accurate) are derived for stiffness, strains, stresses and 3-D warping field for all three material types. Consistent with the three types of 2-D nonlinear constitutive laws,2-D shell theories and corresponding finite element programs have been developed. Validation of present theory is carried out with a few standard test cases for isotropic hyperelastic material model. For two additional test cases, 3-Dfinite element analysis results for isotropic hyperelastic material model are provided as further proofs of the simultaneous accuracy and computational efficiency of the current asymptotically-correct dimensionally-reduced approach. Application of the dimensionally-reduced dielectric hyperelastic material model is demonstrated through the actuation of a clamped membrane subjected to an electric field. Finally, the through-the-thickness and shell analysis procedures are outlined for the orthotropic nonlinear material model.