Harmonic Analysis.docx

Harmonic Response Analysis Harmonic analyses are used to determine the steady-state response of a linear structure to loads that vary sinusoidally (harmonically) with time, thus enabling you to verify whether or not your designs will successfully overcome resonance, fatigue, and other harmful effects of forced vibrations. Introduction In a structural system, any sustained cyclic load will produce a sustained cyclic or harmonic response. Harmonic analysis results are used to determine the steady-state response of a linear structure to loads that vary sinusoidally (harmonically) with time, thus enabling you to verify whether or not your designs will successfully overcome resonance, fatigue, and other harmful effects of forced vibrations. This analysis technique calculates only the steady-state, forced vibrations of a structure. The transient vibrations, which occur at the beginning of the excitation, are not accounted for in a harmonic analysis. In this analysis all loads as well as the structure’s response vary sinusoidally at the same frequency. A typical harmonic analysis will calculate the response of the structure to cyclic loads over a frequency range (a sine sweep) and obtain a graph of some response quantity (usually displacements) versus frequency. “Peak” responses are then identified from graphs of response vs. frequency and stresses are then reviewed at those peak frequencies. Points to Remember A Harmonic Analysis is a linear analysis. Some nonlinearities, such as plasticity will be ignored, even if they are defined. All loads and displacements vary sinusoidally at the same known frequency (although not necessarily in phase). If the Reference Temperature is set as By Body and that temperature does not match the environment temperature, a thermally induced harmonic load will result (from the thermal strain assuming a nonzero thermal expansion coefficient). This thermal harmonic loading is ignored for all harmonic analysis. Mechanical offers the following solution methods for harmonic analyses: Mode-Superposition (default) For the Mode-Superposition (MSUP) method, the harmonic response to a given loading condition is obtained by performing the necessary linear combinations of the eigensolutions obtained from a Modal analysis. For MSUP, it is advantageous for you to select an existing modal analysis directly (although Mechanical can automatically perform a modal analysis behind the scene) since calculating the eigenvectors is usually the most computationally expensive portion of the method. In this way, multiple harmonic analyses with different loading

conditions could effectively reuse the eigenvectors. For more details, refer to Harmonic Response Analysis Using Linked Modal Analysis System. Acceleration and/or Displacement applied as a base excitation uses the Enforced Motion Method. See the Enforced Motion Method for Mode-Superposition Transient and Harmonic Analyses section of the Mechanical APDL Structural Analysis Guide for additional information. Full Using the Full method, you obtain harmonic response through the direct solution of the simultaneous equations of motion. In addition, a Harmonic Response analysis can be linked to, and use the structural responses of, a Static-Structural analysis. See the Harmonic Analysis Using Pre-Stressed Structural System section of the Help for more information. Include Residual Vector This property is available when the Solution Method is set to Mode Superposition. You can turn the Include Residual Vector property On to execute the RESVEC command and calculate residual vectors. Note: The following boundary conditions do not support residual vector calculations:   

Nodal Force Remote Force scoped to a Remote Point (created via Model object) Moment scoped to a Remote Point (created via Model object)

Variational Technology This property is available when the Solution Method is set to Full. When this property is set to No, the Harmonic Response analysis uses the Full method. The direct solution of the simultaneous equations of motion is solved for each excitation frequency, i.e., frequency steps defined in the Solution Intervals. When this property is set to Yes, it uses Variational Technology to evaluate harmonic response for each excitation frequency based on one direct solution. This property is set to Program Controlled by default allowing the application to select the best solution method based on the model. For more technical information about Variational Technology, see the Harmonic Analysis Variational Technology Method section of the Mechanical APDL Theory Reference. This option is an alternate Solution Method that is based on the harmonic sweep algorithm of the Full method. For additional information, see the HROPT command in the MAPDL Command Reference. If a Command object is used with the MSUP method, object content is sent twice; one for the modal solution and another for the harmonic solution. For that reason, harmonic responses are double if a load command is defined in the object, e.g., F command.

Preparing the Analysis Create Analysis System Basic general information about this topic ... for this analysis type: From the Toolbox, drag the Harmonic Response template to the Project Schematic. Define Engineering Data Basic general information about this topic ... for this analysis type: Both Young's modulus (or stiffness in some form) and density (or mass in some form) must be defined. Material properties must be linear but can be isotropic or orthotropic, and constant or temperature-dependent. Nonlinear properties, if any, are ignored. Attach Geometry Basic general information about this topic ... for this analysis type: There are no specific considerations for a harmonic analysis. Define Part Behavior Basic general information about this topic ... for this analysis type: You can define rigid bodies for this analysis type. Define Connections Basic general information about this topic ... for this analysis type: Any nonlinear contact such as Frictional contact retains the initial status throughout the harmonic analysis. The stiffness contribution from the contact is based on the initial status and never changes.

The stiffness as well as damping of springs is taken into account in a Full method of harmonic analysis. In a Mode-Superposition harmonic analysis, the damping from springs is ignored. Apply Mesh Controls/Preview Mesh Basic general information about this topic ... for this analysis type: There are no specific considerations for harmonic analysis. Establish Analysis Settings Basic general information about this topic ... for this analysis type: For a Harmonic Response analysis, the basic Analysis Settings include: Options The Options category enables you to specify the frequency range and the number of solution points at which the harmonic analysis will be carried out as well as the solution method to use and the relevant controls. Two solution methods are available to perform harmonic analysis: the ModeSuperposition method, the Direct Integration (Full) method, and the Variational Technology method. 

Mode-Superposition (MSUP) method: In this method a modal analysis is first performed to compute the natural frequencies and mode shapes. Then the mode-superposition solution is carried out where these mode shapes are combined to arrive at a solution. This is the default method, and generally provides results faster than the Full method or the Variational Technology method. The ModeSuperposition method cannot be used if you need to apply imposed (nonzero) displacements. This method also allows solutions to be clustered about the structure's natural frequencies. This results in a smoother, more accurate tracing of the response curve. The default method of equally spaced frequency points can result in missing the peak values. Without Cluster Option:

With Cluster Option:

The Store Results At All Frequencies option, when set to No, requests that only minimal data be retained to supply just the harmonic results requested at the time of solution. The availability of the results is therefore not determined by the settings in the Output Controls. Note: With this option set to No, the addition of new frequency or phase responses to a solved environment requires a new solution. Adding a new contour result of any type (stress or strain) or a new probe result of any type (reaction force or reaction moment) for the first time on a solved environment requires you to solve, but adding additional contour results or probe results of the same type does not share this requirement; data from the closest available frequency is displayed (the reported frequency is noted on each result). New and/or additional displacement contour results as well as bearing probe results do not share this requirement. These results types are basic data and are available by default. The values of frequency, type of contour results (stress or strain) and type of probe results (reaction force, reaction moment, or bearing) at the moment of the solution determine the contents of the result file and the subsequent availability of data. Planning these choices can significantly reduce the need to re-solve an analysis. Caution: Use caution when adding result objects to a solved analysis. Adding a new result invalidates the solution and requires the system to be re-solved, even if you were to add and then delete a result object.

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Full method: Calculates all displacements and stresses in a single pass. Its main disadvantages are: o It is more “expensive” in CPU time than the ModeSuperposition method. o It does not allow clustered results, but rather requires the results to be evenly spaced within the specified frequency range.

Damping Controls These properties enable you to specify damping for the structure in the Harmonic Response analysis. Controls include: Constant Damping Ratio, Stiffness Coefficient (beta damping), and a Mass Coefficient (alpha damping). They can also be applied as Material Damping using the Engineering Data tab. Element Damping: You can also apply damping through spring-damper elements. The damping from these elements is used only in a Full method harmonic analysis. Note: If multiple damping specifications are made the effect is cumulative. Analysis Data Management These properties enable you to save solution files from the harmonic analysis. The default behavior is to only keep the files required for postprocessing. You can use these controls to keep all files created during solution or to create and save the Mechanical APDL application database (db file). Define Initial Conditions Basic general information about this topic For a Pre-Stressed Full Harmonic analysis, the preloaded status of a structure is used as a starting point for the Harmonic analysis. That is, the static structural analysis serves as an Initial Condition for the Full Harmonic analysis. See the Applying Pre-Stress Effects section of the Help for more information. Note:  

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In the Pre-Stressed MSUP Harmonic Analysis, the pre-stress effects are applied using a Modal analysis. When you link your Harmonic (Full) analysis to a Structural analysis, all structural loading conditions, including Inertial loads, such as Acceleration and Rotational Velocity, are deleted from the Full Harmonic Analysis portion of the simulation once the loads are applied as initial conditions (via the Pre-Stress object). Refer to the MAPDL command PERTURB,HARM,,,DZEROKEEP for more details. If displacement loading is defined with Displacement, Remote Displacement, Nodal Displacement, or Bolt Pretension (specified as

Lock, Adjustment, or Increment) loads in the Static Structural analysis, these loads become fixed boundary conditions for the Harmonic solution. This prevents the displacement loads from becoming a sinusoidal load during the Harmonic solution. ... for this analysis type: Currently, the initial conditions Initial Displacement and Initial Velocity are not supported for Harmonic analyses. Apply Loads and Supports Basic general information about this topic ... for this analysis type: A Harmonic Response Analysis supports the following boundary conditions for a Solution Method setting of either Full or MSUP: Inertial Acceleration (Phase Angle not supported.) Loads        

Pressure Pipe Pressure (line bodies only) - Not supported for MSUP Solution Method. Force (applied to a face, edge, or vertex) Moment Remote Force Bearing Load (Phase Angle not supported.) Line Pressure Given a specified Displacement

Supports Any type of linear Support can be used in harmonic analyses. Note: The Compression Only support is nonlinear but should not be utilized even though it behaves linearly in harmonic analyses. Conditions Constraint Equation Direct FE (node-based Named Selection scoping and constant loading only) 

Nodal Orientation (Phase Angle not supported.)

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Nodal Force Nodal Displacement

Base Excitation (Not supported for Full Solution Method)  

Acceleration as a base excitation. Displacements as a base excitation.

Note: Support for boundary conditions varies for a Harmonic Response analysis that is linked to either a Static-Structural or Modal analysis. See the Harmonic Response Analysis Using Linked Modal Analysis System or the Harmonic Analysis Using Pre-Stressed Structural System sections of the Help for specific boundary condition support information. In a Harmonic Response Analysis, boundary condition application has the following requirements:     

You can apply multiple boundary conditions to the same face. All boundary conditions must be sinusoidally time-varying. Transient effects are not calculated. All boundary conditions must have the same frequency. Boundary conditions supported with the Phase Angle property allow you to specify a phase shift that defines how the loads can be out of phase with one another. As illustrated in the example Phase Response below, the pressure and force are 45o out of phase. You can specify the preferred unit for phase angle (in fact all angular inputs) to be degrees or radians using the Units toolbar.

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An example of a Bearing Load acting on a cylinder is illustrated below. The Bearing Load, acts on one side of the cylinder. In a harmonic analysis, the expected behavior is that the other side of the cylinder is loaded in reverse; however, that is not the case. The applied load simply reverses sign (becomes tension). As a result, you should avoid the use of Bearing Loads in this analysis type.

Solve Basic general information about this topic ... for this analysis type: Solution Information continuously updates any listing output from the solver and provides valuable information on the behavior of the structure during the analysis. Review Results Basic general information about this topic ... for this analysis type: Two types of results can be requested for harmonic analyses: 

Contour plots include stress, elastic strain, and deformation, and are basically the same as those for other analyses. If you wish to see the variation of contours over time for these results, you must specify an excitation frequency and a phase. The Sweeping Phase property in the details view for the result is the specified phase, in time domain, and it is equivalent to the product of the excitation frequency and time. Because Frequency is already specified in the Details view, the Sweeping Phase variation produces the contour results variation over time. The Sweeping Phase property defines the parameter used for animating the results over time. You can then see the total response of the structure at a given point in time, as shown below.

By setting the Amplitude property to Yes, you can see the amplitude contour plots at a specified frequency.

Since each node may have different phase angles from one another, the complex response can also be animated to see the time-dependent motion. 

Frequency Response and Phase Response charts which give data at a particular location over an excitation frequency range and a phase period (the duration of the Phase Response results, respectively). Graphs can be either Frequency Response graphs that display how the response varies with frequency or Phase Response plots that show how much a response lags behind the applied loads over a phase period.

Note: You can create a contour result from a Frequency Response result type in a Harmonic Analysis using the Create Contour Result feature. This feature creates a new result object in the tree with the same Type, Orientation, and Frequency as the Frequency Response result type. However, the Phase Angle of the contour result has the same magnitude as the frequency result type but an opposite sign (negative or positive). The sign of the phase angle in the contour result is reversed so that the response amplitude of the frequency response plot for that frequency and phase angle matches with the contour results. Release 17.0 - © SAS IP, Inc. All rights reserved.

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