Vibration of Beam-Mass Systems With Time-Dependent Boundary Conditions

1959 ◽  
Vol 26 (3) ◽  
pp. 353-356
Author(s):  
T. C. Yen ◽  
S. Kao
Keyword(s):  
Boundary Conditions ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Simply Supported ◽  
Vibration Problems ◽  
Fixed End

Abstract Vibration problems of beams with time-dependent boundary conditions are solved by the method of Laplace transforms. The problems treated include the simply supported, cantilevered, and fixed beams carrying a single arbitrarily placed mass; two equal masses symmetrically placed on a simply supported or fixed-end beam and a beam carrying a mass at the center and two equal masses at tips, striking a spring.

Beam Vibrations With Time-Dependent Boundary Conditions

1950 ◽  
Vol 17 (4) ◽  
pp. 377-380
Author(s):  
R. D. Mindlin ◽  
L. E. Goodman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Time Dependent ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Vibration Problems

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.

Dynamics of Initially Stressed Plates

1976 ◽  
Vol 43 (2) ◽  
pp. 304-308 ◽  
Author(s):  
H. Reismann ◽  
Z. A. Tendorf
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Stable State ◽  
Time Dependent ◽  
Membrane Stress ◽  
Simply Supported

A formalism is presented for the solution of supported plates of bounded extent, subjected to time-dependent transverse forces and boundary conditions. Initially, and during the course of the motion, the plate is assumed to be in an arbitrary (stable) state of membrane stress. An example of a suddenly loaded, simply supported rectangular plate is presented. The membrane prestress, in the example problem, is assumed to be constant and parallel to two opposite edges of the plate.

scholarly journals On the use of variable-separation method for the analysis of vibration problems with time-dependent boundary conditions

2012 ◽  
Vol 226 (12) ◽  
pp. 2912-2924 ◽  
Author(s):  
Josué Aranda-Ruiz ◽  
José Fernández-Sáez
Keyword(s):  
Boundary Conditions ◽  
Solution Method ◽  
Separation Method ◽  
Time Dependent ◽  
Proper Solution ◽  
Variable Separation ◽  
Harmonic Force ◽  
Vibration Problems ◽  
Transversal Vibrations ◽  
Variable Separation Method

In this article, the axial vibrations of a rod with a clamped end and the transversal vibrations of a cantilever beam, both with a time-dependent and non-harmonic force applied on their free ends, are analysed. These are problems in which the traction and the shear, for the rod and the beam, respectively, prescribed in the boundaries of the bodies vary with time. The problems can be solved by the method proposed by Mindlin and Goodman. However, it is usual to solve this problem by the classic variable-separation method (which does not properly fulfil the time-dependent boundary conditions). The displacements and the forces along the systems are derived from both cited methods, and the results are compared. These results highlight the importance of using the proper solution method for the vibration problems with time-dependent boundary conditions.

scholarly journals Analysis of a 4-span continuous plate in one direction using Matlab programming

2021 ◽  
Vol 27 (2) ◽  
pp. 203-207
Author(s):  
E. I. Adah ◽  
S. E Ubi ◽  
F. O. Idagu ◽  
P. A. Ubi
Keyword(s):  
Boundary Conditions ◽  
Bending Moments ◽  
Shape Functions ◽  
Study Program ◽  
Simply Supported ◽  
Maximum Value ◽  
Percentage Difference ◽  
Fixed End ◽  
Matlab Programming ◽  
Continuous Plate

The present study presents a computer approach based on polynomial shape functions application for analysis of continuous plate in one direction using Matlab. A 4-span continuous plate in the x-direction comprises of boundary conditions SSSC, SCSC, SCSC and SCSS single panels’ plate was analyzed. It was assumed that, the external edges were simply supported while the internal edges of each panel were clamped. The bending moments of the clamped edges were calculated for each panel using appropriate boundary conditions which formed the fixed end moments (FEMs). Stiffness method was used based on beam analogy to analyze the continuous plate. Matlab codes were applied to develop a computer program for this analysis. To validate the results of this present study, the values of the moments obtained were compared with those of earlier studies using manual method. The percentage difference for fixed end moments were all 0.00% and that of support moments had the maximum value of 0.016%. Thus, it was concluded that the present study program based on Matlab is adequate and a faster approach for a 4-span continuous plate in one direction analysis. Keywords: Matlab Programming, Continuous Plate, Polynomial Shape Functions, Beam Analogy, Fixed Edge Moment.

The response of an oscillatory system to excitation by a transient displacement

1971 ◽  
Vol 324 (1556) ◽  
pp. 63-77 ◽  
Keyword(s):  
Linear System ◽  
Boundary Conditions ◽  
Oscillatory System ◽  
Physical Significance ◽  
Applied Force ◽  
Time Dependent ◽  
The Past ◽  
Vibration Problems ◽  
Modal Mass

The response of a conservative linear system to a transient applied force of some prescribed form is shown, with suitable interpretation, to be the same as that due to excitation by a transient displacement of the same form. Consequently the solution of practical vibration problems involving ‘time-dependent boundary conditions’ (with their attendant mathematical complexity) is greatly simplified and given a readily understood physical significance. In the development of the theory, the concepts of ‘effective modal stiffness’ and ‘effective modal mass’ (which have occasionally been invoked in the past, and in more senses than one) are elucidated.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

scholarly journals Geometries with mismatched branes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Andreas Karch ◽  
Lisa Randall
Keyword(s):  
Boundary Conditions ◽  
Effective Action ◽  
Cosmological Models ◽  
Time Dependent ◽  
De Sitter ◽  
Stabilization Mechanism ◽  
New Class ◽  
Vacuum Solutions ◽  
Single Coordinate

Abstract We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

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