Transverse Vibrations of Clamped Rectangular Plates of Generalized Orthotropy Subjected To In-Plane Forces

1980 ◽  
Vol 102 (2) ◽  
pp. 399-404 ◽  
Author(s):  
P. A. A. Laura ◽  
L. E. Luisoni
Keyword(s):  
Exact Solution ◽  
Variational Method ◽  
Forced Vibrations ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Structural Element ◽  
Transverse Vibrations ◽  
Free And Forced Vibrations ◽  
Title Problem ◽  
Algorithmic Procedure

An exact solution of the title problem is probably out of the question. It is shown in the present study that a very simple solution can be obtained using simple polynomials and a variational method. Free and forced vibrations of the structural element are analyzed in a unified manner. The algorithmic procedure can be implemented in a microcomputer. The problem is of particular interest in certain filamentary plates as well as of obliquely stiffened plates.

scholarly journals Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

2013 ◽  
Vol 225 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Michele Ducceschi ◽  
Cyril Touzé ◽  
Stefan Bilbao ◽  
Craig J. Webb
Keyword(s):  
Nonlinear Dynamics ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Modal Interaction ◽  
Free And Forced Vibrations

CONTROL OF STEADY-STATE VIBRATIONS OF RECTANGULAR PLATES

2011 ◽  
Vol 11 (03) ◽  
pp. 535-562 ◽  
Author(s):  
K. A. ALSAIF ◽  
M. A. FODA
Keyword(s):  
Steady State ◽  
Function Method ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Selected Lines ◽  
Numerical Examples ◽  
Nodal Lines ◽  
Free And Forced Vibrations ◽  
Concentrated Masses ◽  
The Given

The focus of the present research is to eliminate the undesired steady-state vibrations at selected lines or locations in a vibrating plate by means of adding attachments at arbitrary selected locations. These attachments can be either added concentrated masses and/or translational or rotational springs which are connected to the plate at one end and grounded at the other. The case of attachment of translational and/or rotational oscillators systems is examined. In addition, imposing lines of zero displacements (nodal lines) at selected locations are also investigated. The dynamic Green's function method is employed. Several numerical examples are cited to verify the utility of the proposed method. In addition, sample experiments to measure the plate free and forced vibrations for the given boundary conditions are conducted and the experimental measurements are compared with the analytical results.

On the Transverse Vibrations of Rectangular Orthotropic Plates

1958 ◽  
Vol 25 (3) ◽  
pp. 389-395
Author(s):  
N. J. Huffington ◽  
W. H. Hoppmann
Keyword(s):  
Boundary Value Problems ◽  
Orthotropic Material ◽  
Boundary Value ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Energy Functions ◽  
Transverse Vibrations ◽  
Flexural Vibrations ◽  
Kinetic And Potential Energies

Abstract Frequency equations and modal eigenfunctions have been determined for the flexural vibrations of rectangular plates of orthotropic material, for those cases which may be treated by the method of M. Lévy (1). In addition, for a broader class of boundary-value problems, an orthogonality criterion for the eigenfunctions has been established and relations for the kinetic and potential energies derived. The value of these energy functions in dealing with forced vibrations is demonstrated.

Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations

Ultrasonics ◽  
2017 ◽  
Vol 73 ◽  
pp. 96-106 ◽  
Author(s):  
Rongxing Wu ◽  
Wenjun Wang ◽  
Guijia Chen ◽  
Hui Chen ◽  
Tingfeng Ma ◽  
...  
Keyword(s):  
Quartz Crystal ◽  
Forced Vibrations ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
First Order ◽  
Free And Forced Vibrations ◽  
Plate Equations

On Elastic Continua With Hereditary Characteristics

1951 ◽  
Vol 18 (3) ◽  
pp. 273-279
Author(s):  
Enrico Volterra
Keyword(s):  
Equations Of Motion ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Degree Of Freedom ◽  
Elastic Media ◽  
Stress Strain ◽  
Radial Vibrations ◽  
Damping Characteristics ◽  
Transverse Vibrations ◽  
Free And Forced Vibrations

Abstract In a previous paper (1) the free and forced vibrations of systems of one degree of freedom with hereditary damping characteristics were discussed. In the present paper the classical equations of motion for elastic media are extended on the basis of the general linear stress-strain law involving hereditary damping. These equations are applied to the case of free radial vibrations of a sphere. Furthermore, the free vibrations of strings, the free transverse vibrations of beams, and the free vibrations of rectangular and circular membranes are studied under the assumption of hereditary damping.

Exact Modal Analysis and Its Applications to Transverse Vibrations of Axially Travelling Strings

2004 ◽  
Author(s):  
Yuefang Wang ◽  
Xichun Ren ◽  
Lihua Huang
Keyword(s):  
Critical Speed ◽  
Hamiltonian Dynamics ◽  
Hamiltonian Function ◽  
Forced Vibrations ◽  
Expansion Theorem ◽  
Transverse Vibrations ◽  
Free And Forced Vibrations ◽  
Orthogonality Conditions ◽  
Divergence Instability ◽  
Linear And Nonlinear

The Hamiltonian dynamics based on symplectic mathematics is used to solve the transverse vibration of axially traveling strings. The Hamiltonian function is formulated and the canonical equation is developed. The exact modal functions are obtained through a linear eigenvalue analysis, and the symplectic-type orthogonality conditions of modes are derived. The expansion theorem is applied to solve the displacement response to free and forced vibrations. Unlike traditional modes of transporting strings, the exact modal functions do not suffer divergence instability, or singularity, at the critical speed, and can be easily used as the base or trial functions for solving linear and nonlinear vibration.

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