scholarly journals Analysis of Lamellar Structures with Application of Generalized Functions

2016 ◽  
Vol 16 (2) ◽  
pp. 49-60
Author(s):  
Gela Kipiani ◽  
Nika Botchorishvili
Keyword(s):  
Differential Equations ◽  
Variable Stiffness ◽  
Generalized Functions ◽  
Functional Area ◽  
Load Bearing ◽  
Elastic Links ◽  
Lamellar Structures ◽  
Basic Concepts ◽  
Theory Of Generalized Functions

Abstract Theory of differential equations in respect of the functional area is based on the basic concepts on generalized functions and splines. There are some basic concepts related to the theory of generalized functions and their properties are considered in relation to the rod systems and lamellar structures. The application of generalized functions gives the possibility to effectively calculate step-variable stiffness lamellar structures. There are also widely applied structures, in that several in which a number of parallel load bearing layers are interconnected by discrete-elastic links. For analysis of system under study, such as design diagrams, there are applied discrete and discrete-continual models.

scholarly journals Dynamically variable negative stiffness structures

2016 ◽  
Vol 2 (2) ◽  
pp. e1500778 ◽  
Author(s):  
Christopher B. Churchill ◽  
David W. Shahan ◽  
Sloan P. Smith ◽  
Andrew C. Keefe ◽  
Geoffrey P. McKnight
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Variable Stiffness ◽  
Negative Stiffness ◽  
Load Bearing ◽  
Vibration Isolators ◽  
Wide Range ◽  
Engineered Systems ◽  
Tunable Stiffness

Variable stiffness structures that enable a wide range of efficient load-bearing and dexterous activity are ubiquitous in mammalian musculoskeletal systems but are rare in engineered systems because of their complexity, power, and cost. We present a new negative stiffness–based load-bearing structure with dynamically tunable stiffness. Negative stiffness, traditionally used to achieve novel response from passive structures, is a powerful tool to achieve dynamic stiffness changes when configured with an active component. Using relatively simple hardware and low-power, low-frequency actuation, we show an assembly capable of fast (<10 ms) and useful (>100×) dynamic stiffness control. This approach mitigates limitations of conventional tunable stiffness structures that exhibit either small (<30%) stiffness change, high friction, poor load/torque transmission at low stiffness, or high power active control at the frequencies of interest. We experimentally demonstrate actively tunable vibration isolation and stiffness tuning independent of supported loads, enhancing applications such as humanoid robotic limbs and lightweight adaptive vibration isolators.

scholarly journals A remark on convergence of test functions

1975 ◽  
Vol 20 (1) ◽  
pp. 73-76 ◽  
Author(s):  
W. F. Moss
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Generalized Functions ◽  
Test Functions ◽  
Definition Of ◽  
Theory Of Generalized Functions

In this note it is shown in the most frequently encountered spaces of test functions in the theory of generalized functions that the customary definitions of convergence are equivalent to apparently much weaker definitions. For example, in the space g the condition of uniform convergence of the functions together with all derivatives (which appears in the definition of convergence) is equivalent to the condition of pointwise convergence of the functions alone. Thus verification of convergence is simplified somewhat.

Free vibration analysis of two parallel beams connected together through variable stiffness elastic layer with elastically restrained ends

2016 ◽  
Vol 20 (3) ◽  
pp. 275-287 ◽  
Author(s):  
Alborz Mirzabeigy ◽  
Reza Madoliat ◽  
Mehdi Vahabi
Keyword(s):  
Differential Equations ◽  
Elastic Layer ◽  
Flexural Rigidity ◽  
Free Vibration Analysis ◽  
Variable Stiffness ◽  
Differential Transform Method ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Transform Method ◽  
Differential Transform

In this study, free transverse vibration of two parallel beams connected together through variable stiffness Winkler-type elastic layer is investigated. Euler–Bernoulli beam hypothesis has been applied and the support is considered to be translational and rotational elastic springs in each ends. Linear and parabolic variation has been considered for connecting layer. The equations of motion have been derived in the form of coupled differential equations with variable coefficients. The differential transform method has been applied to obtain natural frequencies and normalized mode shapes of system. Differential transform method is a semi-analytical approach based on Taylor expansion series which converts differential equations to recursive algebraic equations and does not need domain discretization. The results obtained from differential transform method have been validated with the results reported by well-known references in the case of two parallel beams connected through uniform elastic layer. The effects of variation type and total stiffness of connecting layer, flexural rigidity ratio of beams, and boundary conditions on behavior of system are investigated and discussed in detail.

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