Vibrations of a Rectangular Plate With Concentrated Mass, Spring, and Dashpot

1963 ◽  
Vol 30 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Y. C. Das ◽  
D. R. Navaratna
Keyword(s):  
Rectangular Plate ◽  
Composite System ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Double Series ◽  
Concentrated Mass ◽  
Orthogonal Functions ◽  
Isotropic Rectangular Plate ◽  
Mass Spring

An analytical method, developed by Young [1], is here extended to the determination of the natural frequencies of a composite system which consists of an isotropic rectangular plate with a concentrated mass, spring, and dashpot attached at any point of the plate. This method makes use of a double series expansion in terms of two sets of orthogonal functions which represent the normal modes of the vibration of the plate alone. Numerical examples for a square plate with (a) a combined concentrated mass and spring, (b) two concentrated masses, and (c) an attached dashpot have been presented.

Vibration of a Beam With Concentrated Mass, Spring, and Dashpot

1948 ◽  
Vol 15 (1) ◽  
pp. 65-72
Author(s):  
Dana Young
Keyword(s):  
Analytical Method ◽  
Composite System ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Concentrated Mass ◽  
Orthogonal Functions ◽  
Numerical Examples ◽  
Modes Of Vibration ◽  
Concentrated Masses ◽  
Mass Spring

Abstract An analytical method is developed for determining the natural frequencies of a composite system which consists of a uniform beam with a concentrated mass, spring, and dashpot attached at any point along the length of the beam. The method makes use of a series expansion in terms of the set of orthogonal functions which represent the normal modes of vibration of the beam alone. Numerical examples are given for a beam with a combined concentrated mass and spring, for a beam with two concentrated masses, and for a beam with an attached dashpot.

The Natural Frequencies of Free and Constrained Non-Uniform Beams

1960 ◽  
Vol 64 (599) ◽  
pp. 697-699 ◽  
Author(s):  
R. P. N. Jones ◽  
S. Mahalingam
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Normal Modes ◽  
Iteration Process ◽  
Conservative System ◽  
Basic System ◽  
Orthogonal Functions ◽  
Added Masses ◽  
The Given

The Rayleigh-Ritz method is well known as an approximate method of determining the natural frequencies of a conservative system, using a constrained deflection form. On the other hand, if a general deflection form (i.e. an unconstrained form) is used, the method provides a theoretically exact solution. An unconstrained form may be obtained by expressing the deflection as an expansion in terms of a suitable set of orthogonal functions, and in selecting such a set, it is convenient to use the known normal modes of a suitably chosen “ basic system.” The given system, whose vibration properties are to be determined, can then be regarded as a “ modified system,” which is derived from the basic system by a variation of mass and elasticity. A similar procedure has been applied to systems with a finite number of degrees of freedom. In the present note the method is applied to simple non-uniform beams, and to beams with added masses and constraints. A concise general solution is obtained, and an iteration process of obtaining a numerical solution is described.

Free Vibration of Continuous Skin-Stringer Panels

1960 ◽  
Vol 27 (4) ◽  
pp. 669-676 ◽  
Author(s):  
Y. K. Lin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Structural Configuration ◽  
Modes Of Vibration ◽  
Fuselage Skin

The determination of the natural frequencies and normal modes of vibration for continuous panels, representing more or less typical fuselage skin-panel construction for modern airplanes, is discussed in this paper. The time-dependent boundary conditions at the supporting stringers are considered. A numerical example is presented, and analytical results for a particular structural configuration agree favorably with available experimental measurements.

scholarly journals ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC RECTANGULAR PLATE ON WINKLER’S FOUNDATION USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL

2017 ◽  
Vol 36 (3) ◽  
pp. 724-728
Author(s):  
EI Ogunjiofor ◽  
CU Nwoji
Keyword(s):  
Differential Equation ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Winkler Foundation ◽  
Rectangular Plates ◽  
Deflection Coefficient ◽  
Percentage Difference ◽  
Governing Differential Equation ◽  
Isotropic Rectangular Plate

The analytical bending solution of all clamped rectangular plate on Winkler foundation using characteristic orthogonal polynomials (COPs) was studied. This was achieved by partially integrating the governing differential equation of rectangular plate on elastic foundation four times with respect to its independents x and y axis. The foundation was assumed to be homogeneous, elastic and isotropic. The governing differential equation was non-dimensionalised to make it consistent. The deflection polynomials functions were formulated. Thereafter, the Galerkin’s works method was applied to the governing differential equation of the plate on Winkler foundation to obtain the deflection coefficient, . Numerical example was presented at the end to compare the results obtained by this method and those from earlier studies. The percentage difference obtained for central deflection of all clamped rectangular plate loaded with UDL using the method and earlier research works  for K = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are: 0.000042, 0.000052, 0.000043, -0.000011, -0.000068, 0.000001, 0.000001, 0.000001, -0.000001, 0.000000, 0.000001. 0.000033, 0.000035, 0.000033, -0.000018, -0.000072, -0.000003, -0.000003, -0.000003, 0.000002, -0.000002, -0.000001. The result showed that an easy to use and understandable model was developed for determination of deflections of all clamped rectangular plates on Winkler’s elastic foundation using principle of COPs. http://dx.doi.org/10.4314/njt.v36i3.9

Rates of Change of Eigenvalues, With Reference to Buckling and Vibration Problems

1962 ◽  
Vol 66 (621) ◽  
pp. 590-591 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Rectangular Plate ◽  
Concentrated Mass ◽  
Rates Of Change ◽  
Side Ratio ◽  
Buckling Stress ◽  
Edge Conditions ◽  
Basic Parameters ◽  
Vibration Problems ◽  
Elastic Constraint

There are many problems in practice, particularly in the fields of buckling and vibration, where the required end result is a curve showing the relation between the eigenvalue and one or more of the basic parameters of the physical system. For example, the curve relating the buckling stress and side ratio of a rectangular plate, with some specified set of edge conditions, under uni-axial compression may be required. Or the problem may be the buckling of a rectangular plate of given proportions, under combined compression and shear, and the determination of the relation between the two types of load at buckling. Alternatively, the effect on the frequency of vibration of varying a concentrated mass, or the stiffness of an elastic constraint at a given point in an elastic system may be required.

Natural Frequency Determination of Long Span Floor Slabs

1972 ◽  
Vol 94 (2) ◽  
pp. 660-664 ◽  
Author(s):  
J. Chadha ◽  
D. L. Allen
Keyword(s):  
Rectangular Plate ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
General Procedure ◽  
Beam Structure ◽  
Plate Structures ◽  
Long Span ◽  
Floor Slabs ◽  
Experimental Values

This paper presents a general procedure for calculating the natural frequencies of rectangular plate structures which have beam stiffeners in the interior and at the boundaries. The technique of analysis accounts for shear deflections and rotary inertia of the plate. The effect of torsional and flexural reactions of the supporting beams on the plate-beam structure has also been included. The natural frequencies are compared with experimental values and also with those obtained by orthotropic plate approximation and Rayleigh’s method.

scholarly journals Enhancement of a New Methodology Based on the Impulse Excitation Technique for the Nondestructive Determination of Local Material Properties in Composite Laminates

2020 ◽  
Vol 11 (1) ◽  
pp. 101
Author(s):  
Carlo Boursier Niutta
Keyword(s):  
Resonant Frequency ◽  
Elastic Properties ◽  
Composite Laminates ◽  
Concentrated Mass ◽  
Modal Shape ◽  
Nondestructive Determination ◽  
Material Orientation ◽  
Impulse Excitation ◽  
Clamping System

A new approach for the nondestructive determination of the elastic properties of composite laminates is presented. The approach represents an improvement of a recently published experimental methodology based on the Impulse Excitation Technique, which allows nondestructively assessing local elastic properties of composite laminates by isolating a region of interest through a proper clamping system. Different measures of the first resonant frequency are obtained by rotating the clamping system with respect to the material orientation. Here, in order to increase the robustness of the inverse problem, which determines the elastic properties from the measured resonant frequencies, information related to the modal shape is retained by considering the effect of an additional concentrated mass on the first resonant frequency. According to the modal shape and the position of the mass, different values of the first resonant frequency are obtained. Here, two positions of the additional mass, i.e., two values of the resonant frequency in addition to the unloaded frequency value, are considered for each material orientation. A Rayleigh–Ritz formulation based on higher order theory is adopted to compute the first resonant frequency of the clamped plate with concentrated mass. The elastic properties are finally determined through an optimization problem that minimizes the discrepancy on the frequency reference values. The proposed approach is validated on several materials taken from the literature. Finally, advantages and possible limitations are discussed.

Statistical determination of normal modes

1987 ◽  
Vol 64 (5) ◽  
pp. 425 ◽  
Author(s):  
John F. Geldard ◽  
Lawrence R. Pratt
Keyword(s):  
Normal Modes ◽  
Statistical Determination
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