An Inverse Mode Problems for Simply Connected Central Symmetric Spring-Mass Systems

2012 ◽  
Vol 166-169 ◽  
pp. 3399-3402
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Numerical Methods ◽  
Total Mass ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Mass ◽  
Mass System ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Given the odd /even degree eigenpair and the even degree eigenpair of a simply connected central symmetric spring-mass system respectively. The inverse mode problem of constructing the physical elements of the system from two eigenpairs and the total mass of the system is considered. The necessary and sufficient conditions for constructing of a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the simply connected central symmetric spring-mass system may be constructed uniquely. The numerical methods and examples are given finally.

An Inverse Eigenvalue Problem for Spring-Mass Systems with Partial Mass Connected to the Ground

2013 ◽  
Vol 353-356 ◽  
pp. 3308-3311
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Total Mass ◽  
Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Inverse Eigenvalue ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Consider the simply connected spring-mass system with partial mass connected to the ground. The inverse mode problem of constructing the physical elements of the system from two eigenpairs, the grounding spring stiffness and total mass of the system is considered. The necessary and sufficient conditions for constructing a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the grounding spring-mass system may be constructed uniquely. The numerical methods and examples are given finally.

An Inverse Mode Problem for the Rod on Elastic Foundation

2013 ◽  
Vol 353-356 ◽  
pp. 3198-3201
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Numerical Methods ◽  
Elastic Foundation ◽  
Discrete Model ◽  
Sufficient Conditions ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Consider the rod on elastic foundation. Its discrete model is the simply connected spring-mass system with partial mass connected to the ground. The inverse mode problem of constructing the physical elements of the system from two eigenpairs, the spring stiffness of the system is considered. The necessary and sufficient conditions for constructing a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the rod on the elastic foundation may be constructed uniquely. The numerical methods and examples are given finally.

An Inverse Eigenvalue Problem for Star Spring-Mass System

2012 ◽  
Vol 166-169 ◽  
pp. 3348-3351
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Stiffness Matrix ◽  
Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Inverse Eigenvalue ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Arrowhead Matrix

The mass-normalized stiffness matrix of the star spring-mass system is an arrowhead matrix. Given two eigenpairs of the arrowhead matrix. It is assumed that the total mass of a star spring-mass system is known. The problem of constructing the physical elements of the system from the known data is considered. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and spring stiffness are established. If these conditions are satisfied, the system may be constructed uniquely.

An Inverse Mode Problem for the Continuous Model of an Axially Vibrating Rod

1994 ◽  
Vol 61 (3) ◽  
pp. 624-628 ◽  
Author(s):  
Y. M. Ram
Keyword(s):  
Modal Analysis ◽  
Total Mass ◽  
Sufficient Conditions ◽  
Continuous Model ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

An inverse mode problem for the continuous model of an axially vibrating rod is formulated and solved. It is shown that the density and axial rigidity functions are determined by two eigenvalues, their corresponding eigenfunctions, and the total mass of the rod. The necessary and sufficient conditions for the construction of a physically realizable rod with positive parameters are given. It is shown that when these conditions are satisfied, the solution is unique. Since the data required for the construction may be available from measurements, the presented approach is well-suited for modal analysis applications.

scholarly journals Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1887
Author(s):  
Sharief Deshmukh ◽  
Amira Ishan ◽  
Olga Belova ◽  
Suha B. Al-Shaikh
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Simply Connected

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.

scholarly journals MOSER–TRUDINGER INEQUALITY ON CONFORMAL DISCS

2010 ◽  
Vol 12 (06) ◽  
pp. 1055-1068 ◽  
Author(s):  
G. MANCINI ◽  
K. SANDEEP
Keyword(s):  
Connected Domain ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Poincaré Metric ◽  
Simply Connected Domain ◽  
Trudinger Inequality ◽  
Necessary And Sufficient ◽  
Simply Connected

We prove that a sharp Moser–Trudinger inequality holds true on a conformal disc if and only if the metric is bounded from above by the Poincaré metric. We also derive necessary and sufficient conditions for the validity of a sharp Moser–Trudinger inequality on a simply connected domain in ℝ2.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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