Principle of Linear Superposition and Complex Notation

2013 ◽  
Keyword(s):  
Linear Superposition ◽  
Principle Of Linear Superposition

Synthesis of Seven-Link Mechanisms

1973 ◽  
Vol 95 (2) ◽  
pp. 533-540 ◽  
Author(s):  
D. Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Nonlinear Equations ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Superposition ◽  
Two Degrees Of Freedom ◽  
Closed Form Solutions ◽  
Highly Nonlinear ◽  
Principle Of Linear Superposition

The mechanisms derived from the seven-link chains with five links in their two loops and having two degrees of freedom are examined for six synthesis problems. Using displacement matrices, closed form synthesis equations are derived. It is shown that three synthesis problems may be solved using the principle of linear superposition, and closed form solutions may be obtained. The other three synthesis problems involve highly nonlinear equations and must be solved numerically.

scholarly journals ANALISA LINEAR SUPERPOSITION DALAM KELOLA GETARAN TANAH HASIL PELEDAKAN PADA PERTAMBANGAN BATUBARA

2020 ◽  
Vol 1 (1) ◽  
pp. 349-356
Author(s):  
Dhion Pradatama. DM ◽  
Chani Pradasara ◽  
Syarif Nurdiansyah
Keyword(s):  
Wave Propagation ◽  
Delay Time ◽  
Ground Vibration ◽  
Analysis Method ◽  
Linear Superposition ◽  
Service Company ◽  
Engineering Approach ◽  
Vibration Signature ◽  
Waste Energy ◽  
Principle Of Linear Superposition

ABSTRAK Getaran tanah merupakan getaran yang ditimbulkan akibat dari proses peledakan tambang. Selama ini getaran tanah dianggap sebagai waste energy yang dapat merusak dan menjadi isu terhadap lingkungan di sekitar area tambang. PT. Multi Nitrotama Kimia sebagai perusahaan jasa peledakan dan penjualan bahan peledak di Indonesia memiliki kustomer dengan isu demikian, salah satunya adalah PT Adaro Indonesia. Guna menanggulangi isu tersebut, maka dilakukan rekayasa teknik terhadap getaran tanah yang dihasilkan dengan merubah waste energy menjadi work energy dengan prinsip linear superposition menggunakan metode signature hole analysis (SHA) dan dioptimalkan dengan aplikasi inter-deck delay pada lubang double-deck untuk meminimalisir getaran tanah yang ditimbulkan. Penelitian dan percobaan dilakukan menggunakan metode Signature Hole Analisys (SHA) untuk merekam perambatan gelombang di setiap range blok – strip tertentu terhadap area konsen. Gelombang yang telah terekam selanjutnya dianalisis dengan fitur Linear Superposition untuk mendapatkan rekomendasi waktu tunda beserta prediksi getaran yang ditimbulkan. Rekomendasi waktu tunda yang didapat adalah waktu tunda pada inter-hole, inter-row, dan inter-deck yang mana akan diterapkan untuk peledakan selanjutnya. Berdasarkan analisis menggunakan metode Signature Hole Analysis, rekomendasi waktu tunda yang diberikan dapat diterapkan untuk mengakomodir prinsip linear superposition gelombang. Penerapannya dapat dioptimalkan menggunakan inter-deck delay sehingga meminimalisir getaran tanah yang dihasilkan. Dibuktikan oleh getaran tanah yang dihasilkan menggunakan rekomendasi tersebut selalu di bawah standar yang ditetapkan (PVS = < 2.00 mm/s). Kaca Kunci : Getaran Tanah, Signature Hole Analysis, Linear Superposition   ABSTRACT One of the blasting process effect is ground vibration. Ground vibration currently consider as waste energy which it can infere and be an issue to the environment. PT. Multi Nitrotama Kimia as blasting service company and explosives sales in Indonesia has customers dealing with that issues, one of them is PT Adaro Indonesia. To overcome the issue, engineering approach is done to the ground vibration by changing waste energy into work energy with the principle of linear superposition using the signature hole analysis (SHA) method and optimized with the application of inter-deck delay on the double-deck hole to minimize the ground vibration. Researches and experiments are carried out using the Signature Hole Analysis (SHA) method to record wave propagation in each range of certain blocks - strips to the concern area. The recorded waves are analyzed with the Linear Superposition feature to obtain delay time recommendation along with the predicted vibration. The recommended delay time obtained is the delay time on inter-hole, inter-row, and inter-deck which will be applied for next blasting. Based on the Signature Hole Analysis method, the recommended delay time given can be applied to accommodate the linear superposition wave principle. Its application can be optimized using inter-deck delay to minimize ground vibration produced. Its proven by ground vibrations produced using the recommendations always below the specified standard (PVS = <2.00 mm / s). Keywords: Ground Vibration, Signature Hole Analysis, Linear Superposition

scholarly journals CALCULATING THE POSITRON – ELECTRON CORRELATION ENERGY IN ZnO WITH THE MODIFIED SINGLE WAVE FUNCTION FOR POSITRON

2011 ◽  
Vol 14 (4) ◽  
pp. 77-85
Author(s):  
Tao Van Chau ◽  
Lang Hoa Trinh ◽  
Tuan Anh Nguyen ◽  
Chien Hoang Le ◽  
Loc Huu Nguyen
Keyword(s):  
Wave Function ◽  
Electron Correlation ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Correlation Energy ◽  
Linear Superposition ◽  
Single Wave ◽  
Electron Correlation Energy ◽  
Quantum Monte Carlo Method ◽  
Principle Of Linear Superposition

The ZnO – positron system is studied and its positron – electron correlation energy is estimated in its ground state. The positron binds with the outer shell electrons of Zinc and Oxigen to form the pseudo ZnO – positron molecule before it anihilates with one of these electrons. In this work, the single wave function for positron is modified according to the principle of linear superposition, and by using Variational Quantum Monte – Carlo method (VQMC) the correlation energy of this system is estimated with the value Ec e-p = - 9.3 ± 1.1 eV. It turns out that the value is closer to results estimated by other methods than the value that we had done before.

scholarly journals Linier Superposition Analysis on Managing Blasting Ground Vibration in Coal Mining

2019 ◽  
Vol 1 (1) ◽  
pp. 22-28
Author(s):  
Dhion Pradatama ◽  
Chani Pradasara ◽  
Syarif Nurdiansyah
Keyword(s):  
Wave Propagation ◽  
Coal Mining ◽  
Delay Time ◽  
Ground Vibration ◽  
Analysis Method ◽  
Ground Vibrations ◽  
Linear Superposition ◽  
Engineering Approach ◽  
Waste Energy ◽  
Principle Of Linear Superposition

One of the blasting process effect is ground vibration. Ground vibration currently consider as waste energy which it can infere and be an issue to the environment. PT. Multi Nitrotama Kimia as blasting service and explosives sales in Indonesia has customers dealing with that issues, one of them is PT Adaro Indonesia. To overcome the issue, engineering approach is done to the ground vibration by changing waste energy into work energy with the principle of linear superposition using the signature hole analysis (SHA) method to minimize the ground vibration. Researches and experiments are carried out using the Signature Hole Analysis (SHA) method to record wave propagation in each range of certain blocks - strips to the concern area. The recorded waves are analyzed with the Linear Superposition feature to obtain delay time recommendation along with the predicted vibration. The recommended delay time obtained is the delay time on inter-hole and inter-row which will be applied for next blasting.Based on the Signature Hole Analysis method, the recommended delay time given can be applied to accommodate the linear superposition wave principle. Its application can be optimized using inter-deck delay to minimize ground vibration produced. Its proven by ground vibrations produced using the recommendations always below the specified standard (PVS = &#60;2.00 mm / s).

Second-Order Directional Seas and Associated Wave Forces

1981 ◽  
Vol 21 (01) ◽  
pp. 129-140 ◽  
Author(s):  
J.N. Sharma ◽  
R.G. Dean
Keyword(s):  
Hybrid Method ◽  
Time Domain ◽  
Pile Group ◽  
Second Order ◽  
Wave Forces ◽  
Linear Superposition ◽  
Directional Characteristics ◽  
Water Particle Kinematics ◽  
The Time Domain ◽  
Principle Of Linear Superposition

Abstract Most methods for wave force computation incorporate either the nonlinearities of the ocean surface for a single fundamental component or the random and/or directional characteristics using superposition of linear wave components. One exception is the intuitive "hybrid" method, which combines elements of linear and nonlinear waves. This paper describes and applies a method correct to the second order in wave height for calculating waves and wave forces caused by a directional wave spectrum on an offshore structure.Starting with a prescribed linear spectrum of directional waves, a set of random phases is generated and the second-order spectrum computed with phases defined by all contributing pairs of first-order components. Thus, with one realization of the spectrum complete up to the second order, the wave profile and water particle kinematics can be profile and water particle kinematics can be simulated in the time domain. The wave forces also are computed in the time domain, taking full account of their nonlinear and directional properties. The resulting wave forces at any level vary in direction and magnitude. The total wave forces summed over all piling of a structure are less than those for a unidirectional train of waves with the same one-dimensional spectrum.Several examples are presented to illustrate reductions in maximum wave forces caused by the directional distribution of waves. We found that for a single piling the maximum force decreases by a factor ranging from 1.0 to 0.61 as the directional spread increases from unidirectional to uniformity over a half plane. For a four-pile group on a square array of 300-ft (91.4-m) spacing, the corresponding decrease in the factor is 1.0 to 0.51 for a Bretschneider spectrum with a peak period of approximately 12 seconds. The results of this complete model are compared with the more intuitive and approximate hybrid method and are found to agree quite well. Force spectra are presented and discussed for the inline and transverse directions. Introduction The nonlinearity, randomness, and directionality of a real sea preclude a simple but realistic determination of wave loading on a single- or multiple-pile group. Presently, there are two essentially different but complementary methods for computing wave loadings. One method represents nonlinearities of a single wave composed of a characteristic fundamental period and its higher harmonics. A number period and its higher harmonics. A number of such theories have been-developed. Dalrymple extended the stream function approach of Dean, to waves on a shear current. Some of these theories adequately account for the nonlinearities; however, they avoid the random and directional characteristics of the sea surface. The second method uses the principle of linear superposition of an infinite principle of linear superposition of an infinite number of waves with given frequencies, amplitudes, and directions of propagation but independent phases; the total energy is distributed over a phases; the total energy is distributed over a continuum of frequencies and directions. In this manner, a three-dimensional Gaussian sea can be represented fully. However, ignoring the nonlinearities makes the random Gaussian model unrealistic - especially for large waves. SPEJ P. 129

INVESTIGATION OF SUITABILITY FOR THE LINEAR SUPERPOSITION MODEL

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1631-1634
Author(s):  
DA HUANG ◽  
GENXIN WU
Keyword(s):  
Angle Of Attack ◽  
Large Angle ◽  
Unsteady Aerodynamics ◽  
Mathematic Model ◽  
Linear Superposition ◽  
Unsteady Aerodynamic ◽  
Aerodynamic Model ◽  
Aerodynamic Parameters ◽  
Principle Of Linear Superposition ◽  
Low Speed Wind Tunnel

An aircraft model was tested at the 3-meter low speed wind tunnel as it was oscillated with large amplitude. The unsteady aerodynamic behavior was acquired during the oscillation in yawing, rolling and yawing-rolling. The lateral-directional dynamic derivative was obtained using the mathematic model of unsteady aerodynamics and the dynamic derivative simulation. According to the principle of linear superposition, the unsteady aerodynamic parameters of the model about yaw-roll coupled motion can be obtained by the quasi-steady aerodynamic model and the result was compared with the experimental test. It was found that for the quasi-steady aerodynamic model the unsteady aerodynamic characteristic was in agreement with the test at the middle and large angle of attack (for example α ≤ 45°), but was opposite at the extremely large angle of attack (α > 45°).

A Study of Midship Bending Moments in Irregular Head Seas

1957 ◽  
Vol 1 (02) ◽  
pp. 43-54
Author(s):  
Edward V. Lewis
Keyword(s):  
Exploratory Study ◽  
Irregular Waves ◽  
Statistical Characteristics ◽  
Bending Moments ◽  
Linear Superposition ◽  
Principle Of Linear Superposition ◽  
Marine Engineers ◽  
Model Agreement

In this article an exploratory study on behalf of the S-3 Panel of The Society of Naval Architects and Marine Engineers is reported, in which the statistical characteristics of model bending moments in irregular head seas have been predicted on the basis of the principle of linear superposition of responses to the component waves. It is shown that for the case of a T2-SEA1 tanker model, agreement between predicted and observed bending moments in irregular waves is reasonably good. The method is then applied to predicting the trend of bending moments with severity of sea and speed of ship.

scholarly journals Failure Analysis for a Low Pressure Aeroengine Turbine Vane

2017 ◽  
Vol 11 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Roberto Citarella ◽  
Venanzio Giannella ◽  
Edoardo Vivo ◽  
Massimo Mazzeo
Keyword(s):  
Boundary Conditions ◽  
Global Analysis ◽  
Initial Crack ◽  
Fe Model ◽  
Classical Approach ◽  
Linear Superposition ◽  
Turbine Vane ◽  
Principle Of Linear Superposition ◽  
Crack Faces ◽  
Stress Analyses

Background & Objective In this work, a thermo-mechanical fatigue application related to a fracture process simulation in a turbine vane is implemented, using a submodelling approach based on the principle of linear superposition. Method The proposed crack propagation approach leverages on a combined use of FEM and DBEM methodologies: the global analysis is solved by using FEM whereas the fracture problem is demanded to DBEM. In particular, a DBEM submodel is extracted from a global uncracked FE model and, in the new proposed formulation, boundary conditions are applied just on crack faces rather than loading subdomain boundaries with displacements/tractions and temperatures, as in the classical approach. Results & Conclusion The adopted approach solves the fracture problem by using simpler pure stress analyses rather than by thermal-stress analyses, as requested by the classical approach. Boundary conditions applied on the submodel crack faces come from the solution of a FE uncracked global model. The computational advantages of such alternative approach are highlighted and, in addition, a fatigue assessment is provided for a turbine vane, considering as initial crack the maximum design defect dictated by GE-Avio regulations for such kind of components.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

scholarly journals Chaos for communication

2021 ◽  
Author(s):  
Murilo S. Baptista
Keyword(s):  
Information Content ◽  
Lyapunov Exponents ◽  
Communication System ◽  
Linear Superposition ◽  
Chaotic Signals ◽  
Physical Medium ◽  
Periodic Signals ◽  
Low Probability ◽  
Chaotic Interference ◽  
Source Signals

AbstractThis work shows that chaotic signals with different power spectrum and different positive Lyapunov exponents are robust to linear superposition, meaning that the superposition preserves the Lyapunov exponents and the information content of the source signals, even after being transmitted over non-ideal physical medium. This work tackles with great detail how chaotic signals and their information content are affected when travelling through medium that presents the non-ideal properties of multi-path propagation, noise and chaotic interference (linear superposition), and how this impacts on the proposed communication system. Physical media with other non-ideal properties (dispersion and interference with periodic signals) are also discussed. These wonderful properties that chaotic signals have allow me to propose a novel communication system based on chaos, where information composed from and to multiple users each operating with different base frequencies and that is carried by chaotic wavesignals, can be fully preserved after transmission in the open air wireless physical medium, and it can be trivially decoded with low probability of errors.

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