Mode shape of a 3D beam

[Haifei Chen]

Hi all,

I'm trying to do a modal analysis for a beam restrained in y-direction for all nodes and in x-direction for the center node only. So the desired mode shape is vertical bending in Oxz plane, (un)symmetric about the center node, such as

What I get right now looks more like a cantilever (mp4 on google drive). Say the beam has 21 nodes. It seems that node #19 is somehow restrained, not the center node #10 or the end node #21. This can be clearly seen for higher-order modes, i.e. when the end node's displacement is larger.

https://drive.google.com/file/d/1Gmd-QI8xpDZLAMV-XnsyewASw6C88z44/view?usp=drive_link

I'm using Chrono v9.0.1. The main code block is attached here.

Thank you,

Haifei

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ChBuilderBeamEuler builder;

builder.BuildBeam(mesh, section, nelem,                        
    ChVector3d(xstart, 0, 0),      
    ChVector3d(xstart+beam_L, 0, 0),
    ChVector3d(0, 1, 0)
);

auto ground = chrono_types::make_shared<ChBody>();
sys.AddBody(ground);
ground->SetPos(ChVector3d(xstart+beam_L/2, 0, 0));
ground->SetFixed(true);

int ind = 0;
for (auto node: builder.GetLastBeamNodes())
{  
    // restrain horizontal bending
    {
        auto ylink = chrono_types::make_shared<ChLinkMateGeneric>();
        ylink->Initialize(node, ground, ChFrame<>(node->GetPos(), QUNIT));
        ylink->SetConstrainedCoords(false, true, false, true, false, false);
        sys.Add(ylink);
    }

    // constraint for the center node
    if (ind == int(nelem/2))
    {
        auto my_center = chrono_types::make_shared<ChLinkMateGeneric>();
        my_center->Initialize(node, ground, ChFrame<>(node->GetPos(), QUNIT));
        my_center->SetConstrainedCoords(true, false, false, false, false, false);
        sys.Add(my_center);
    }

    ind++;
}

auto factorization = chrono_types::make_shared<ChSolverSparseComplexQR>();
auto eig_solver = chrono_types::make_shared<ChUnsymGenEigenvalueSolverKrylovSchur>(factorization);
ChModalSolverDamped modal_solver(num_modes, 1e-5, true, false, eig_solver);
modal_solver.Solve(sys.GetAssembly(), eigvects, eigvals, freq, damping_ratios);

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