Coupling between Transverse Vibrations and Instability Phenomena of Plates Subjected to In-Plane Loading

As it is known, the problems of free transverse vibrations and instability under in-plane loads of a plate are two different technological situations that have similarities in their approach to elastic solution. In fact, they are two eigenvalue problems in which we analyze the equilibrium situation of the plate in configurations which differ very slightly from the original, undeformed configuration. They are coupled in the event where in-plane forces are applied to the edges of the transversely vibrating plate. The presence of forces can have a significant effect on structural and mechanical performance and should be taken into account in the formulation of the dynamic problem. In this study, distributed forces of linear variation are considered and their influence on the natural frequencies and corresponding normal modes of transverse vibration is analyzed. It also analyzes their impact for the case of vibration control. The forces? magnitude is varied and the first natural frequencies of transverse vibration of rectangular thin plates with different combinations of edge conditions are obtained. The critical values of the forces which cause instability are also obtained. Due to the analytical complexity of the problem under study, the Ritz method is employed. Some numerical examples are presented.Fil: Bambill, Diana Virginia. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Free Vibrations of Beam System Structures with Elastic Boundary Conditions and an Internal Elastic Hinge

The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamilton's principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those obtained using the finite element method, with values of particular cases of the model available in the literature, and with measurements in an experimental device.Fil: Ratazzi, Alejandro R.. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Bambill, Diana Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Natural frequencies of thin, rectangular plates with holes or orthotropic "patches" carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh-Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or "patch", carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.Fil: Bambill, Diana Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Felix, Daniel Horacio. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Transverse, normal modes of vibration of a cantilever timoshenko beam with a mass elastically mounted at the free end

An exact solution for the title problem is obtained by means of the classical eigenfunction approach. The natural frequencies are computed for a wide range of the intervening mechanical and geometric parameters. Normal modes of transverse vibration are plotted for some cases of practical interest. The problem is technically important in several areas of applied science and technology.Fil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; ArgentinaFil: Laura, Patricio Adolfo Antonio. Universidad Nacional del Sur; Argentin

Unsteady thermoelastic analysis of a circular disk with a hot central core and subjected to adiabatic conditions

The unsteady thermoelastic analysis of a cooling circular disk or cylinder which is originally at uniform temperature is a classical problem of the theory of thermal stresses. More recent studies consider the case of composite structural configurations. The present paper deals with a situation which, apparently, has not been previously considered: unsteady thermal stresses caused by the presence of a hot, central nucleus. The temperature field is obtained in terms of a Fourier–Bessel expansion and then, radial and tangential stresses are evaluated analytically. The problem is of basic interest in mechanical and naval engineering systems.Fil: Rossit, Carlos Adolfo. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Laura, Patricio Adolfo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Eigenvalues of radially symmetric modes in composite spherical domains with a very small concentric cavity

In his study, Wang proved that the fundamental frequency coefficient of a circular annular membrane fixed at the outer radius ´b´ and at the inner radius ´a´, is the same eigenvalue as in the case of a solid circular membrane, when the inner radius of the annular membrane approaches zero. Related studies showed that the same rather unexpected conclusions holds true in the case of higher modes of vibrations and also in the case of composite membranes. The present work demonstrates that from a mathematical viewpoint, the same property holds when solving a Helmholtz differential-type system in the case of composite spherical domain when a/c approaches zero.Fil: Rossit, Carlos Adolfo. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Laura, Patricio Adolfo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Free vibrations of a cantilever beam with a spring-mass system attached to the free end

An exact solution for the title problem is obtained using the Bernoulli-Euler theory of beam vibrations. Natural frequencies are obtained for a wide range of the intervening physical parameters. The problem is of interest in naval and ocean engineering systems since in order to avoid dangerous resonance conditions the designer must be able to predict natural frequencies of the overall mechanical system: structure-motor and its elastic mounting.Fil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; ArgentinaFil: Laura, Patricio Adolfo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; Argentin

Free vibrations of anisotropic rectangular plates with holes and attached masses

Anisotropic materials are increasingly required in modern technological applications. Certainly, civil, mechanical and naval engineers frequently deal with the situation of analyzing the dynamical behaviour of structural elements being composed of such materials. For example, panels of anisotropic materials must sometimes support electromechanical engines, and besides, holes are performed in them for operational reasons e.g., conduits, ducts or electrical connections. This study is concerned with the natural frequencies and normal modes of vibration of rectangular anisotropic plates supported by different combinations of the classical boundary conditions: clamped, simply - supported and free, and with additional complexities such holes of free boundaries and attached concentrated masses. A variational approach (the well known Ritz method) is used, where the displacement amplitude is approximated by a set of beam functions in each coordinate direction corresponding to the sides of the rectangular plate. Consequently each coordinate function satisfies the essential boundary conditions at the outer edge of the plate. The influence of the position and magnitude of both hole and mass, on the natural frequencies and modal shapes of vibration are studied for a generic anisotropic material. The classical Ritz method with beam functions as spatial approximation proved to be a suitable procedure to solve a problem of such analytical complexity.Fil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Ciancio, Patricia Mónica. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ingeniería Olavarría; Argentin

Forced vibrations of a beam elastically restrained against rotation and carrying a spring-mass system

An exact solution for the title problem is obtained in closed form fashion in the case of a Bernoulli-Euler beam. It is assumed that the exciting force is applied to the mass which is elastically mounted on the beam. The mathematical model constitutes a first order approximation to a motor or engine elastically mounted on a structural element. The operation of the machine generates a transverse, sinusoidally varying force. The problem is of basic interest in mechanical, naval and ocean engineering systems from the point of view of the determination of dynamic displacements and stresses; sound radiation calculations, etc. The present problem arose in connection with the mounting of an engine on a structural beam in a small naval vessel and when excessive vibrational level was noted. This study was undertaken in order to understand the physical problem and to correct the mechanical situation.Fil: Bambill, Diana Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; ArgentinaFil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; Argentin

Comments on "faber series method for two-dimensional problems of an arbitrarily shaped inclusion in piezoelectric materials" by C.-F. Gao and N. Noda (Acta Mech. 171, 1-13, August 2004)

The writers wish to congratulate the authors for their rigorous treatment of an important anddifficult problem. As stated by Gao and Noda, the inclusion problem is of fundamentalimportance in engineering sciences and has received considerable attention from both theore-ticians and experimentalists.Fil: Laura, Patricio Adolfo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; ArgentinaFil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; ArgentinaFil: Maiz, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentin