Dynamics

Evaluate your design in real-time using SimSolid dynamics analysis.

Setup

  1. Specify the modal results to which the analysis is linked. The modal solution must exist in the current design study. In SimSolid, the time integration of the equations of motion is extremely fast and all modes are always included in the analysis.
  2. For Frequency and Random Response, specify the frequency span upper and lower limits. For Transient response, specify Time span.
  3. Specify damping using Rayleigh damping coefficients or Modal damping.
  4. Select the Evaluate peak responses during solving check box to evaluate peak responses during solving phase.

See Create Analysis for additional information.

Damping

Two methods to specify damping are supported.
Rayleigh Damping Coefficient
Assumes the damping matrix is proportional to the mass and stiffness matrices. You need to specify values for Mass (F1) and Stiffness (F2) in the Dynamics creation dialog to use this method.
Modal Damping
Creates critical damping ratio for each mode. You can specify this value in the Dynamics analysis creation dialog.

Notes for Dynamics Analysis

  1. When the base excitation type is displacement, the initial condition for displacement and velocity is always assumed to be zero.
  2. In SimSolid, the boundary compatibility is approximately met. The response at the constrained end is not going to be an absolute zero but is relatively small compared to the peak responses.
  3. Equivalent radiated power density is calculated as:(1)
    ERP Density = ERPRLF * (0 .5 * ERPC * ERPRHO) * v 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyraiaabk facaqGqbGaaGjbVlaabseacaqGLbGaaeOBaiaabohacaqGPbGaaeiD aiaabMhacaaMc8UaaeypaiaaykW7caqGfbGaaeOuaiaabcfacaqGsb GaaeitaiaabAeacaaMc8UaaeOkaiaaykW7caqGOaGaaeimaiaab6ca caqG1aGaaGPaVlaabQcacaaMc8UaaeyraiaabkfacaqGqbGaae4qai aaykW7caqGQaGaaGPaVlaabweacaqGsbGaaeiuaiaabkfacaqGibGa ae4taiaabMcacaaMc8UaaiOkaiaaykW7caWG2bWaaWbaaSqabeaaca aIYaaaaaaa@6594@
    Where:
    v MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaaaa@36EE@
    Normal velocity of the picked point
    ERPC (Speed of sound in air)
    343 m/s
    ERPRHO (Density of air)
    1.225 Kg/m3
    ERPRLF (Radiation loss factor)
    1

    Equivalent radiated power is calculated as an integral of ERP density over picked faces as:

    (2)
    ERP = ERPRLF * (0 .5 * ERPC * ERPRHO) S v 2 d s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyraiaabk facaqGqbGaaGPaVlaab2dacaaMc8UaaeyraiaabkfacaqGqbGaaeOu aiaabYeacaqGgbGaaGPaVlaabQcacaaMc8UaaeikaiaabcdacaqGUa GaaeynaiaaykW7caqGQaGaaGPaVlaabweacaqGsbGaaeiuaiaaboea caaMc8UaaeOkaiaaykW7caqGfbGaaeOuaiaabcfacaqGsbGaaeisai aab+eacaqGPaGaaGPaVlabgUIiYpaaBaaaleaacaWGtbaabeaakiaa yIW7caWG2bWaaWbaaSqabeaacaaIYaaaaOGaaGjcVlaadsgacaWGZb aaaa@633F@
  4. Phase for Absolute displacement can be queried using Pick Info for frequency dynamics.
  5. Relationship between relative and absolute displacement in frequency dynamics is as follows.
    Relative motion is calculated as:(3)
    x ¨ + 2 ζ ω n x ˙ + ω n 2 = b ¨ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmiEayaada GaaGPaVlabgUcaRiaaykW7caaIYaGaeqOTdONaeqyYdC3aaSbaaSqa aiaad6gaaeqaaOGabmiEayaacaGaaGPaVlabgUcaRiaaykW7cqaHjp WDdaWgaaWcbaGaamOBaaqabaGcdaahaaWcbeqaaiaaikdaaaGccaaM c8Uaeyypa0JaaGPaVlabgkHiTiqadkgagaWaaaaa@4F42@
    Where base excitation b MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaaaa@36DA@ is:(4)
    b ¨ = Y 0 ω e i ω t + ϕ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iabm OyayaadaGaaGPaVlabg2da9iaaykW7caWGzbWaaSbaaSqaaiaaicda aeqaaOWaaeWaaeaacqaHjpWDaiaawIcacaGLPaaacaWGLbWaaWbaaS qabeaacaWGPbWaaeWaaeaacqaHjpWDcaWG0bGaaGPaVlabgUcaRiaa ykW7cqaHvpGzaiaawIcacaGLPaaaaaaaaa@4D25@
    Solving this differential equation, the relative displacement can be calculated as:(5)
    x r t = Y 0 ω e i ϕ ω n 2 ω 2 ω n 2 ω 2 2 + 2 ζ ω n ω 2 i 2 ζ ω n ω ω n 2 ω 2 2 + 2 ζ ω n ω 2 e i ω t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGYbaabeaakmaabmaabaGaamiDaaGaayjkaiaawMcaaiaa ykW7cqGH9aqpcaaMc8UaamywamaaBaaaleaacaaIWaaabeaakmaabm aabaGaeqyYdChacaGLOaGaayzkaaGaamyzamaaCaaaleqabaGaamyA aiabew9aMbaakiaaykW7daqadaqaamaalaaabaGaeqyYdC3aaSbaaS qaaiaad6gaaeqaaOWaaWbaaSqabeaacaaIYaaaaOGaaGPaVlabgkHi TiaaykW7cqaHjpWDdaahaaWcbeqaaiaaikdaaaaakeaadaqadaqaai abeM8a3naaBaaaleaacaWGUbaabeaakmaaCaaaleqabaGaaGOmaaaa kiaaykW7cqGHsislcaaMc8UaeqyYdC3aaWbaaSqabeaacaaIYaaaaa GccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOGaaGPaVlabgUca RiaaykW7daqadaqaaiaaikdacqaH2oGEcqaHjpWDdaWgaaWcbaGaam OBaaqabaGccqaHjpWDaiaawIcacaGLPaaadaahaaWcbeqaaiaaikda aaaaaOGaaGPaVlabgkHiTiaaykW7caWGPbWaaSaaaeaacaaIYaGaeq OTdONaeqyYdC3aaSbaaSqaaiaad6gaaeqaaOGaeqyYdChabaWaaeWa aeaacqaHjpWDdaWgaaWcbaGaamOBaaqabaGcdaahaaWcbeqaaiaaik daaaGccaaMc8UaeyOeI0IaaGPaVlabeM8a3naaCaaaleqabaGaaGOm aaaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaakiaaykW7cq GHRaWkcaaMc8+aaeWaaeaacaaIYaGaeqOTdONaeqyYdC3aaSbaaSqa aiaad6gaaeqaaOGaeqyYdChacaGLOaGaayzkaaWaaWbaaSqabeaaca aIYaaaaaaaaOGaayjkaiaawMcaaiaadwgadaahaaWcbeqaaiaadMga cqaHjpWDcaWG0baaaaaa@9C3E@
    Absolute motion is calculated as:(6)
    x ¨ + 2 ζ ω n x ˙ + ω n 2 = 2 ζ ω n b ˙ + ω n 2 b MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmiEayaada GaaGPaVlabgUcaRiaaykW7caaIYaGaeqOTdONaeqyYdC3aaSbaaSqa aiaad6gaaeqaaOGabmiEayaacaGaaGPaVlabgUcaRiaaykW7cqaHjp WDdaWgaaWcbaGaamOBaaqabaGcdaahaaWcbeqaaiaaikdaaaGccaaM c8Uaeyypa0JaaGPaVlaaikdacqaH2oGEcqaHjpWDdaWgaaWcbaGaam OBaaqabaGcceWGIbGbaiaacaaMc8Uaey4kaSIaaGPaVlabeM8a3naa BaaaleaacaWGUbaabeaakmaaCaaaleqabaGaaGOmaaaakiaadkgaaa a@5C8B@
    Where, (7)
    b = Y 0 ω ω 2 e i ω t + ϕ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyaiaayk W7cqGH9aqpcaaMc8+aaSaaaeaacaWGzbWaaSbaaSqaaiaaicdaaeqa aOWaaeWaaeaacqaHjpWDaiaawIcacaGLPaaaaeaacqaHjpWDdaahaa WcbeqaaiaaikdaaaaaaOGaamyzamaaCaaaleqabaGaamyAamaabmaa baGaeqyYdCNaamiDaiaaykW7cqGHRaWkcaaMc8Uaeqy1dygacaGLOa Gaayzkaaaaaaaa@4EFE@
    Solving this equation, the absolute displacement can be calculated as:(8)
    x a t = ω n ω 2 +i2ζ ω n ω x r t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGHbaabeaakmaabmaabaGaamiDaaGaayjkaiaawMcaaiaa ykW7cqGH9aqpcaaMc8+aaeWaaeaadaqadaqaamaalaaabaGaeqyYdC 3aaSbaaSqaaiaad6gaaeqaaaGcbaGaeqyYdChaaaGaayjkaiaawMca amaaCaaaleqabaGaaGOmaaaakiaaykW7cqGHRaWkcaaMc8UaamyAai aaikdacqaH2oGEdaWcaaqaaiabeM8a3naaBaaaleaacaWGUbaabeaa aOqaaiabeM8a3baaaiaawIcacaGLPaaacaWG4bWaaSbaaSqaaiaadk haaeqaaOWaaeWaaeaacaWG0baacaGLOaGaayzkaaaaaa@5860@
  6. In Frequency and Random dynamics, the Complex Function Method is used to solve differential equations. Displacement, velocity, and acceleration results have complex components.
    Given complex values of displacement as:(9)
    D x = a x + i b x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWG4baabeaakiaaykW7cqGH9aqpcaaMc8UaamyyamaaBaaa leaacaWG4baabeaakiaaykW7cqGHRaWkcaaMc8UaamyAaiaadkgada WgaaWcbaGaamiEaaqabaaaaa@451A@
    D y = a y + i b y MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWG5baabeaakiaaykW7cqGH9aqpcaaMc8UaamyyamaaBaaa leaacaWG5baabeaakiaaykW7cqGHRaWkcaaMc8UaamyAaiaadkgada WgaaWcbaGaamyEaaqabaaaaa@451D@
    D z = a z + i b z MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWG6baabeaakiaaykW7cqGH9aqpcaaMc8UaamyyamaaBaaa leaacaWG6baabeaakiaaykW7cqGHRaWkcaaMc8UaamyAaiaadkgada WgaaWcbaGaamOEaaqabaaaaa@4520@
    Displacement magnitude is calculated as:(10)
    D x 2 + D x 2 + D x 2 = D x 2 + D x 2 + D x 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaada GcaaqaaiaadseadaWgaaWcbaGaamiEaaqabaGcdaahaaWcbeqaaiaa ikdaaaGccaaMc8Uaey4kaSIaaGPaVlaadseadaWgaaWcbaGaamiEaa qabaGcdaahaaWcbeqaaiaaikdaaaGccaaMc8Uaey4kaSIaaGPaVlaa dseadaWgaaWcbaGaamiEaaqabaGcdaahaaWcbeqaaiaaikdaaaaabe aaaOGaay5bSlaawIa7aiaaykW7cqGH9aqpcaaMc8+aaOaaaeaadaab daqaaiaadseadaWgaaWcbaGaamiEaaqabaGcdaahaaWcbeqaaiaaik daaaGccaaMc8Uaey4kaSIaaGPaVlaadseadaWgaaWcbaGaamiEaaqa baGcdaahaaWcbeqaaiaaikdaaaGccaaMc8Uaey4kaSIaaGPaVlaads eadaWgaaWcbaGaamiEaaqabaGcdaahaaWcbeqaaiaaikdaaaaakiaa wEa7caGLiWoaaSqabaGccaaMc8oaaa@638D@
  7. When a Transient Dynamics analysis is linked to a prestressed modal analysis, a new result type is offered called Total Displacement. Total Displacement is the combination of the prestressed and dynamic displacements. Therefore, displacement magnitude is the displacement caused by the dynamic analysis.