scholarly journals Steady-state linear harmonic vibrations of multiple-stepped Euler-Bernoulli beams under arbitrarily distributed loads carrying any number of concentrated elements

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Michael Klanner ◽  
Katrin Ellermann
Keyword(s):  
Steady State ◽  
Harmonic Vibrations

REACTANTS AND OTHER PARAMETERS OF MECHANICAL SYSTEMS

2020 ◽  
pp. 4-12
Author(s):  
I. P. Popov ◽  
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Electrical Engineering ◽  
Mechanical Systems ◽  
Phase Relations ◽  
Calculation Algorithm ◽  
Steady State Mode ◽  
Harmonic Oscillations ◽  
Harmonic Vibrations ◽  
Algebraic Operations

The traditional calculation of mechanisms for forced harmonic oscillations is often a difficult task. Most often, calculators are interested in the steady-state modes of harmonic oscillations. The purpose of this paper is to significantly simplify calculations by replacing the need to solve differential equations with simpler algebraic methods. A complex representation of harmonic and related quantities is used. This approach is widely used in theoretical electrical engineering. Parallel and serial connections of mechanical power consumers are considered. The velocities of elements of mechanical systems and the forces applied to them are determined algebraically from the known parameters of systems and the disturbing harmonic effect. The use of a symbolic (complex) description of mechanical systems under forced harmonic vibrations (in steady-state mode) allowed us to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations, and replace it with simpler and more visual algebraic operations. Due to this, the time of calculations is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems under harmonic influences, have substantial methodological significance, since they show quantitative and phase relations between the parameters of systems.

Harmonic Vibrations in Thermoelasticity of Microstretch Materials

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Marin Marin
Keyword(s):  
Steady State ◽  
Lateral Surface ◽  
Boundary Data ◽  
Heat Supply ◽  
Critical Frequency ◽  
Body Force ◽  
Decay Estimate ◽  
Angular Frequency ◽  
Plane Boundary ◽  
Harmonic Vibrations

Consider a cylinder made of a microstretch thermoelastic material for which one plane end is subjected to plane boundary data varying harmonically in time. On the lateral surface and other base, we have zero body force and heat supply. By using a Toupin type measure associated with the corresponding steady-state vibration, and by assuming that the angular frequency of oscillations is lower than a certain critical frequency, we show that the amplitude of the vibrations decays exponentially with the distance to the base. This decay estimate is similar to that of the Saint-Venant type.

CALCULATION OF PARAMETERS OF MECHANICAL SYSTEMS WITH HARMONIC VIBRATION

2021 ◽  
pp. 29-35
Author(s):  
I. P. Popov
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Mechanical Systems ◽  
Harmonic Vibration ◽  
Calculation Algorithm ◽  
Calculation Of Parameters ◽  
Harmonic Vibrations ◽  
Resonant Modes ◽  
Algebraic Operations ◽  
Phase Relationships

Parallel and series connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. Attention is paid to resonant modes, incl. resonance of forces and resonance of speeds. The use of a symbolic (complex) description of mechanical systems with forced harmonic vibrations (in a steady state) made it possible to abandon the extremely cumbersome and laborious calculation algorithm associated with solving differential equations and replace it with simple and visual algebraic operations. Due to this, the calculation time is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.

Robust Boundary Control for an Euler Bernoulli Beam Subject to Unknown Harmonic Disturbances With a Focus on Resonance

2017 ◽  
Author(s):  
Dimitri Karagiannis ◽  
Verica Radisavljevic-Gajic
Keyword(s):  
Steady State ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Open Loop ◽  
Bernoulli Beam ◽  
Harmonic Vibrations ◽  
The Face ◽  
State Position ◽  
Backstepping Controller ◽  
Euler Bernoulli Beam

In this paper, a sliding mode backstepping controller for a pinned-pinned Euler-Bernoulli beam is briefly reviewed and its efficacy in the presence of unknown bounded harmonic disturbances at arbitrary frequencies is analyzed. A brief discussion of the open-loop unstable response to harmonic excitations at resonant frequencies is provided. Motivated by this, particular attention is given to excitations at the natural frequencies of the system. It is shown that in the face of such resonant disturbances, the sliding mode backstepping controller is able to eliminate the vibrations in the beam system where backstepping control alone cannot. Indeed it is shown that if the disturbances are not accounted for, the closed loop system exhibits large (relative to the initial conditions) steady state harmonic vibrations. When the unknown resonant harmonic disturbances are accounted for via the sliding mode backstepping technique, the steady state position is constant and does not exhibit any vibrations, and furthermore it reaches this steady state exponentially at an arbitrarily selected rate.

On Steady-State Harmonic Vibrations of Nonlinear Systems With Many Degrees of Freedom

1966 ◽  
Vol 33 (2) ◽  
pp. 406-412 ◽  
Author(s):  
W. M. Kinney ◽  
R. M. Rosenberg
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Degrees Of Freedom ◽  
Forced Vibrations ◽  
Geometrical Method ◽  
Mass System ◽  
Harmonic Vibrations ◽  
Forcing Functions ◽  
Exciting Forces ◽  
The Stability

A nonlinear spring-mass system with many degrees of freedom, and subjected to periodic exciting forces, is examined. The class of admissible systems and forcing functions is defined, and a geometrical method is described for deducing the steady-state forced vibrations having a period equal to that of the forcing functions. The methods used combine the geometrical methods developed earlier in the problem of normal mode vibrations and Rauscher’s method. The stability of these steady-state forced vibrations is examined by Hsu’s method. The results are applied to an example of a system having two degrees of freedom.

Studies on Water in the Hydration Chamber of a Modified Electron Microscope

1970 ◽  
Vol 28 ◽  
pp. 544-545
Author(s):  
R. C. Moretz ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Electron Microscope ◽  
Steady State ◽  
Room Temperature ◽  
Small Mass ◽  
Equilibrium Pressure ◽  
Biological Objects ◽  
Mechanical Pump ◽  
Differential Pumping

Use of the electron microscope to examine wet objects is possible due to the small mass thickness of the equilibrium pressure of water vapor at room temperature. Previous attempts to examine hydrated biological objects and water itself used a chamber consisting of two small apertures sealed by two thin films. Extensive work in our laboratory showed that such films have an 80% failure rate when wet. Using the principle of differential pumping of the microscope column, we can use open apertures in place of thin film windows.Fig. 1 shows the modified Siemens la specimen chamber with the connections to the water supply and the auxiliary pumping station. A mechanical pump is connected to the vapor supply via a 100μ aperture to maintain steady-state conditions.

Continuous hydrogenolysis of acetal-stabilized lignin in flow

2021 ◽  
Author(s):  
Wu Lan ◽  
Yuan Peng Du ◽  
Songlan Sun ◽  
Jean Behaghel de Bueren ◽  
Florent Héroguel ◽  
...  
Keyword(s):  
Steady State ◽  
Challenges And Opportunities

We performed a steady state high-yielding depolymerization of soluble acetal-stabilized lignin in flow, which offered a window into challenges and opportunities that will be faced when continuously processing this feedstock.

Network reconstruction based on steady-state data

2008 ◽  
Vol 45 ◽  
pp. 161-176 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
Reverse Engineering ◽  
Theoretical Method ◽  
Network Reconstruction ◽  
Quasi Steady State ◽  
State Data

This paper discusses a theoretical method for the “reverse engineering” of networks based solely on steady-state (and quasi-steady-state) data.

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