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

Vibration analysis of rotating Timoshenko beams by means of the differential quadrature method

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering. The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.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: Rossi, Raul Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; 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

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 "Free vibration analysis of arbitrarily shaped plates with clamped edges using wave-type functions"

The purpose of the present discussion is twofold: " rst to congratulate the authors for their interesting paper and extension of the non-dimensional dynami cin # uence function in order to deal with vibrating arbitrarily shaped plates with clamped edges [1] and, in the second place, to present additional methods and references dealing with the subject matter and which have been inadvertently omitted by the authors.Fil: Laura, Patricio Adolfo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. 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; Argentin

Comments on "Free vibration of super elliptical plates with constant and variable thickness by Ritz method"

Free vibration of super elliptical plates with constant and variable thickness by Ritz method has been reported. the shape of the plate in the x y plane can be defined by the super elliptical function. Calculating the area and perimeter of the region may give an idea about the convergence of the integration. the discussers also obtained the area sand perimeters using a finite element code, to be sure about the good precision of their values. The re-calculated values are in excellent agreement with Wang's results. The calculations have been performed for simply supported and clamped super elliptical plates with aspect ratio a/b=1, 1.2, 2, 3; with n=8 and n=10.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: Maiz, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Rossi, Raul Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Free vibrations of AFG cantilever tapered beams carrying attached masses

The free transverse vibrations of axially functionally graded (AFG) cantilever beams with concentrated masses attached at different points are studied in this paper. The material properties of the AFG beam, consisting of metal and ceramic, vary continuously in the axial direction according to an established law form. Approximated solutions for the title problem are obtained by means of the Ritz Method. The influence of the material variation on the natural frequencies of vibration of the functionally graded beam is investigated and compared with the influence of the variation of the cross section. The phenomenon of dynamic stiffening of beams can be observed in various situations. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study.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: 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: Gilardi, Gonzalo José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentin

Forced vibrations of a clamped-free beam with a mass at the free end with an external periodic disturbance acting on the mass with applications in ships' structures

An exact, analytical solution is obtained for the title problem which constitutes a classical one although no solution is available in well known textbooks and handbooks normally used by the structural engineer in several fields of technology: ocean and naval engineering, aerospace applications, etc. The authors performed this study motivated by a situation where excessive displacements were noticed in a structural element carrying a relatively small motor at the free end and placed at the engine room of a naval vessel. The Bernoulli-Euler model has been employed. © 2002 Elsevier Science Ltd. All rights reserved.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: Escanes, Samanta Jorgelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. 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